Evaluation of LS-DYNA

Wood Material Model 143

PUBLICATION NO. FHWA-HRT-04-096 AUGUST 2005

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
Foreword

This report documents the evaluation of a wood material model that has been implemented into 

the dynamic finite element code LS-DYNA, beginning with version 970. This material model was 

developed specifically to predict the dynamic performance of wood components used in 

roadside safety structures when undergoing a collision by a motor vehicle. This model is 

applicable for all varieties of wood when appropriate material coefficients are inserted. Default 

material coefficients for two wood varieties, southern yellow pine and Douglas fir, are stored in 

the model and can be accessed for use. 

This report is one of two that completely documents this material model. The first report, Manual 

for LS-DYNA Wood Material Model 143 (FHWA-HRT-04-097), completely documents this 

material model for the user. The second report, Evaluation of LS-DYNA Wood Material Model 

143 (FHWA-HRT-04-096), completely documents the model’s performance and the accuracy of 

the results. This performance evaluation was a collaboration between the model developer and 

the model evaluator. Regarding the model’s performance evaluation, the developer and the 

evaluator were unable to come to a final agreement regarding the model’s performance and 

accuracy. These disagreements are itemized and thoroughly discussed in chapter 17 of the 

second report. 

This report will be of interest to research engineers associated with the evaluation and 

crashworthy performance of roadside safety structures, particularly those engineers responsible 

for the prediction of the crash response of such structures when using the finite element code 

LS-DYNA. 

Michael F. Trentacoste 

Director, Office of Safety 

 Research and Development 

Notice 

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for its 

contents or use thereof. This report does not constitute a standard, specification, or regulation. 

The U.S. Government does not endorse products or manufacturers. Trade and manufacturers’ 

names appear in this report only because they are considered essential to the object of the 

document. 

Quality Assurance Statement 

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. 

Standards and policies are used to ensure and maximize the quality, objectivity, utility, and 

integrity of its information. FHWA periodically reviews quality issues and adjusts its programs 

and processes to ensure continuous quality improvement. 
 Technical Report Documentation Page 

1. Report No. 

FHWA-HRT-04-096 

2. Government Accession No. 3. Recipient’s Catalog No. 

5. Report Date 

August 2005 

4. Title and Subtitle 

Evaluation of LS-DYNA Wood Material Model 143 

6. Performing Organization Code 

7. Author(s) 

Y.D. Murray, J.D. Reid, R.K. Faller, B.W. Bielenberg, 

and T.J. Paulsen

8. Performing Organization Report No. 

9. Performing Organization Name and Address 

APTEK, Inc.

1257 Lake Plaza Drive, Suite 100 

Colorado Springs, CO 80906-3558

10. Work Unit No. (TRAIS) 

Midwest Roadside Safety Facility 

University of Nebraska at Lincoln 

1901 Y Street, Building C 

Lincoln, NE 68588-0601

11. Contract or Grant No. 

DTFH61-98-C-00071 

13. Type of Report and Period Covered 

Final Report 

Sept. 1998-Sept. 2002

12. Sponsoring Agency’s Name and Address 

Volpe National Transportation Systems Center 

55 Broadway, Kendall Square 

Cambridge, MA 02142-1093

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101-2296

14. Sponsoring Agency’s Code 

15. Supplementary Notes 

Contracting Officer’s Technical Representative (COTR): Martin Hargrave, Office of Safety Research 

and Development 

16. Abstract 

Calculations are performed with the finite element code LS-DYNA to evaluate the performance of 

wood material model 143 and to set default material properties for southern yellow pine and 

Douglas fir. Correlations with published test data include static bending and compression 

simulations of dry timbers, static bending of saturated posts, and dynamic simulation of saturated 

posts impacted by bogie vehicles. 

The companion manual to this report is: 

Manual for LS-DYNA Wood Material Model 143 (FHWA-HRT-04-097)

17. Key Words 

Wood, southern yellow pine, Douglas fir, 

LS-DYNA, modeling and simulation, damage, 

rate effects, plasticity. 

18. Distribution Statement 

No restrictions. This document is available to the 

public through the National Technical 

Information Service, Springfield, VA 22161. 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 

Unclassified 

21. No. of Pages 

152 

22. Price 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
ii 

Preface

The goal of the work performed under this program, Development of DYNA3D Analysis 

Tools for Roadside Safety Applications, is to develop wood and soil material models, 

implement the models into the LS-DYNA finite element code,(1) and evaluate the 

performance of each model through correlations with available test data. 

Two reports are available for each material model. One report is a user’s manual; the 

second report is a performance evaluation. The user’s manual, Manual for LS-DYNA 

Wood Material Model 143,

(2) thoroughly documents the wood model theory, reviews the 

model input, and provides example problems for use as a learning tool. It is written by 

the developer of the model. This report, Evaluation of LS-DYNA Wood Material Model 

143, comprises the performance evaluation for the wood model. It documents LS-DYNA 

parametric studies and correlations with test data performed by the model developer, 

and by a potential end user. The reader is urged to review the user’s manual before 

reading this evaluation report. A user’s manual(3) and evaluation report(4) are also 

available for the soil model. 

The development of the wood model was conducted by the prime contractor. The 

associated wood model evaluation effort to determine the model‘s performance and the 

accuracy of the results was a collaboration between the developer and the potential end 

user, with the user’s evaluation intended to be independent of the developer’s 

evaluation. The developer partially evaluated the wood model. The potential end user 

performed a second independent evaluation of the wood model, provided finite element 

meshes for the evaluation calculations, and provided static post and bogie impact test 

data for correlations with the model. 

Regarding the second independent evaluation of the wood model, the developer and 

evaluator were unable to come to a final agreement regarding several issues associated 

with the model‘s performance and accuracy. These issues are itemized and thoroughly 

discussed by the developer in chapter 17 of this evaluation report. 

Throughout this report, the developer of the wood material model is referred to as the 

developer. The potential end user of the wood material model is referred to as the user. 

The developer’s calculations and conclusions are given in chapters 1 through 8 of this 

report. The user’s calculations and conclusions are given in chapters 9 through 16 of 

this report. 
iii 

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha 

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx 

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2

 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac 

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E e 380. 

(Revised March 2003)
iv 

Table of Contents 

1 DEVELOPER’S INTRODUCTION........................................................................ 1 

1.1 MODEL THEORY ...................................................................................... 1

1.2 MODEL INPUT .......................................................................................... 1

1.3 LIMITATIONS OF LABORATORY MATERIAL PROPERTY DATA........... 3

1.4 EVALUATION PROCESS.......................................................................... 3

1.5 VERIFICATION AND VALIDATION........................................................... 4 

2 SINGLE-ELEMENT SIMULATIONS .................................................................... 5 

3 TIMBER COMPRESSION TEST CORRELATIONS ............................................ 7 

4 TIMBER-BENDING TEST CORRELATIONS ...................................................... 9 

5 QUASI-STATIC POST TEST CORRELATIONS................................................ 11 

5.1 SOUTHERN YELLOW PINE BENDING TEST DATA ............................. 11

5.2 LS-DYNA CORRELATIONS .................................................................... 16

5.3 LS-DYNA PARAMETRIC STUDIES ........................................................ 21 

6 DYNAMIC POST TEST CORRELATIONS ........................................................ 31 

6.1 BOGIE IMPACT TEST DATA .................................................................. 31

6.2 LS-DYNA CORRELATIONS .................................................................... 34

6.3 FILTERING AND SAMPLING ISSUES.................................................... 38

6.4 LS-DYNA PARAMETRIC STUDIES ........................................................ 43 

7 ADDITIONAL EVALUATION CALCULATIONS................................................ 47 

7.1 PLASTICITY ALGORITHM ITERATIONS................................................ 47

7.2 FULLY INTEGRATED ELEMENTS ......................................................... 48

7.3 EROSION CRITERIA............................................................................... 50

7.4 POST-PEAK HARDENING PARAMETER............................................... 53 

8 DEVELOPER’S SUMMARY AND RECOMMENDATIONS................................ 57 

9 USER’S INTRODUCTION.................................................................................. 63 

10 VALIDATION CRITERIA FOR THE WOOD MATERIAL MODEL ..................... 65 

10.1 NDOR TESTS: PERFORMANCE ENVELOPES ..................................... 65 

11 VERIFICATION OF RESULTS ON DIFFERENT COMPUTER PLATFORMS... 71 

11.1 SINGLE-ELEMENT MODELS ................................................................. 71

11.2 DYNAMIC POST TEST SIMULATION: BOGIE MODEL.......................... 73

11.3 DYNAMIC POST TEST SIMULATION: FAST BOGIE MODEL ............... 76

12 SINGLE ELEMENT: TENSION PARALLEL TO THE GRAIN ........................... 79 

12.1 STRESS-STRAIN BEHAVIOR: *MAT_WOOD_PINE.............................. 80
v 

12.2 VOLUME OF ELEMENT: *MAT_WOOD_PINE ....................................... 81

12.3 MATERIAL PROPERTIES: *MAT_WOOD_PINE .................................... 82 

13 STATIC WOOD POST TEST SIMULATIONS.................................................... 85 

13.1 STATIC POST MODEL............................................................................ 85 

13.2 BASELINE MODEL VERSUS TEST COMPARISON .............................. 87

13.3 BASELINE VERSUS REFINED-MESH COMPARISON.......................... 88

13.4 PARAMETER STUDY ............................................................................. 90 

14 DYNAMIC WOOD POST TEST SIMULATIONS................................................ 95 

14.1 DYNAMIC POST MODEL........................................................................ 95

14.2 VAPORIZATION AND TIME STEP.......................................................... 96

14.3 SHARP EDGE CONTACTS..................................................................... 97

14.4 BENDING ................................................................................................ 98

14.5 FURTHER ANALYSIS ............................................................................. 99 

15 ELEMENT FORMULATION: HOURGLASSING.............................................. 103 

16 USER’S CONCLUSIONS................................................................................. 107 

17 DEVELOPER’S COMMENTS ON USER’S EVALUATION ............................. 109 

17.1 TABLE OF WOOD MODEL TOPICS..................................................... 111

17.2 DISCUSSION OF WOOD MODEL TOPICS.......................................... 113

17.3 INSTABILITIES IN DYNAMIC ANALYSES............................................ 123 

18 REFERENCES................................................................................................. 141 
vi 

List of Figures 

Figure 1. LS-DYNA simulations of southern yellow pine showing brittle behavior in 

tension and shear, and ductile behavior in compression.......................................... 2

Figure 2. Good correlation between LS-DYNA simulations (dashed lines) and measured 

clear wood data (solid lines) for southern yellow pine in tension parallel to the grain.

................................................................................................................................. 5

Figure 3. Good correlation between LS-DYNA simulations (dashed lines) and measured 

clear wood data (solid lines) for southern yellow pine in compression perpendicular 

to the grain ............................................................................................................... 6

Figure 4. Schematic of FPL timber compression test setup. ........................................... 7

Figure 5. These comparisons of the model with test data were used to set the hardening 

behavior of the southern yellow pine model in parallel-to-the-grain compression. ... 8

Figure 6. These comparisons of the model with the parallel-to-the-grain timber-bending 

test data demonstrate the need for different quality factors in tension and 

compression........................................................................................................... 10

Figure 7. Quasi-static post test setup............................................................................ 11

Figure 8. Details for the rigid frame used in the quasi-static post test setup. ................ 12

Figure 9. Deformed configurations of posts in static tests............................................. 13

Figure 10. Closeup of damage observed in break region of posts in static tests........... 13

Figure 11. Measured load-deflection histories exhibit sudden drops in force as the post 

fails in the tensile region......................................................................................... 14

Figure 12. Quasi-static (blue solid line) and dynamic (pink dashed line) performance 

envelopes developed and plotted by the user........................................................ 15

Figure 13. Grades 1 and 1D static post test measurements exhibit substantial scatter.16

Figure 14. Good correlations between the LS-DYNA calculations and quasi-static 

performance envelopes determine the default quality factors for grade 1 southern 

yellow pine of QT = 0.47 with QC = 0.63. ................................................................ 18

Figure 15. Good correlations between the LS-DYNA calculations and quasi-static 

performance envelopes determine the default quality factors for DS-65 southern 

yellow pine of QT = 0.80 with QC = 0.93. ................................................................ 19

Figure 16. The parallel-to-the-grain post fracture calculated in the post just below the 

top of the rigid support is in agreement with the location of the damage observed in 

the tests. ................................................................................................................ 20

Figure 17. Three geometric models were set up for performing parametric calculations.

............................................................................................................................... 21

Figure 18. The force-deflection curve calculated with the fast-running, rigid-wall model is 

similar to that calculated with the full-support structure, making it useful for 

performing parametric calculations. ....................................................................... 22

Figure 19. Pinning a truss to the bolt to simulate the vertical force applied by the pulley 

system increases the peak force by about 4 percent. ............................................ 23

Figure 20. The peak force increases with the applied velocity until convergence is 

attained at 0.25 mm/ms.......................................................................................... 23

Figure 21. Quasi-static calculations are filtered for easier comparison with the unfiltered 

test data. ................................................................................................................ 24
vii 

Figure 22. The energy required to break the post increases as the value of the parallelto-the-grain fracture energy increases. .................................................................. 25

Figure 23. Calculations with QC > QT soften more rapidly than calculations with QC = QT.

............................................................................................................................... 25

Figure 24. The calculated peak force increases with increasing values of the softening 

parameter B. .......................................................................................................... 26

Figure 25. The softening parameter B determines the shape of the softening curve in 

these single-element simulations for tension parallel to the grain. ......................... 26

Figure 26. Type 4 stiffness control reduces hourglassing better than type 3 viscous 

control. ................................................................................................................... 28

Figure 27. The peak force calculated with type 4 stiffness control agrees with the fully 

integrated element calculation better than the type 3 viscous calculation.............. 29

Figure 28. Less final hourglass energy is calculated with type 4 stiffness control than 

with type 3 viscous control. .................................................................................... 29

Figure 29. Decreasing the moisture content by 6 percent increases the post-peak force 

by 80 percent. ........................................................................................................ 30

Figure 30. Post setup for dynamic bogie impact tests................................................... 32

Figure 31. Processed data from the user’s bogie impact tests...................................... 33

Figure 32. Damage in the breakaway region of the posts, just below ground level....... 34

Figure 33. These correlations between the LS-DYNA calculations and the performance 

envelopes were used to adjust the parallel fracture energy for grade 1 pine to 50 

times the perpendicular fracture energy................................................................. 35

Figure 34. These correlations between the LS-DYNA calculations and the performance 

envelopes were used to adjust the parallel fracture energy for DS-65 pine to 85 

times the perpendicular fracture energy................................................................. 35

Figure 35. These correlations between the LS-DYNA calculations and the energydeflection data were used to confirm that grade 1 Douglas fir can be simulated with 

the same parallel fracture energy and rate-effect parameters as grade 1 southern 

yellow pine, but with different quality factors. ......................................................... 36

Figure 36. These correlations between the LS-DYNA calculations and the energydeflection data were used to set the parallel fracture energy for frozen grade 1 pine 

to five times the perpendicular fracture energy. ..................................................... 36

Figure 37. The simulated post breaks just below ground level, in agreement with the 

failure location observed in the tests...................................................................... 38

Figure 38. User’s geometric bogie model used in the developer’s calculations............. 39

Figure 39. The filtered bogie acceleration history sampled at 3200 Hz is significantly 

different than the history sampled at 10,000 Hz..................................................... 40

Figure 40. Force-deflection histories calculated from bogie nodal accelerations depend 

significantly on the bogie type and output sampling frequency. ............................. 41

Figure 41. Force-deflection histories calculated from the wood post cross-sectional 

forces are not significantly affected by the details for the bogie model or sampling 

frequency. .............................................................................................................. 42

Figure 42. The internal energy calculated to break the wood post is less than the kinetic 

energy reduction of the bogie................................................................................. 43
viii 

Figure 43. These deformed configurations at 180 mm of deflection indicate that 

adjustments in the quality factors affect the deflection at which the grade 1 pine 

post breaks in two. ................................................................................................. 45

Figure 44. Although the grade 1 pine post breaks earlier in time with QT = 0.40 and 

QC = 0.70, the calculated energy and velocity histories are similar........................ 45

Figure 45. The default number of plasticity algorithm iterations is set to one because 

these static load-deflection curves are insensitive to the number of iterations....... 47

Figure 46. Erosion affects the fully integrated element curves, but not the underintegrated element curves, indicating that the fully integrated elements erode while 

still carrying load. ................................................................................................... 48

Figure 47. Deformed configurations and fringes of damage calculated with fully 

integrated elements (eight points) are similar to those calculated with underintegrated elements (one point).............................................................................. 49

Figure 48. Energy-deflection and bogie velocity-reduction histories are not strongly 

influenced by the type of element formulation (eight points or one point) modeled in 

the breakaway region............................................................................................. 49

Figure 49. The breakaway region calculated with perpendicular erosion in these static 

bending simulations looks more realistic than that calculated without perpendicular 

erosion; however, perpendicular erosion is not recommended for practical use.... 51

Figure 50. Load-deflection curves calculated with perpendicular erosion are slightly 

more brittle than those calculated without perpendicular erosion........................... 51

Figure 51. The breakaway region calculated with perpendicular erosion in this bogie 

impact simulation looks more realistic than that calculated without perpendicular 

erosion. .................................................................................................................. 52

Figure 52. Dynamic load-deflection and bogie velocity-reduction curves calculated with 

perpendicular erosion are nearly identical to those calculated without perpendicular 

erosion. .................................................................................................................. 52

Figure 53. Use of perpendicular erosion causes excessive erosion to be calculated in 

the impact region in this preliminary bogie impact calculation................................ 53

Figure 54. These single-element simulations demonstrate post-peak hardening in 

compression with positive values of Ghard. ............................................................. 54

Figure 55. Inclusion of post-peak hardening, both parallel and perpendicular to the 

grain, prevented this calculation from aborting at a large deflection....................... 55

Figure 56. Performance envelopes from 1995 NDOR testing. ...................................... 66

Figure 57. Static post setup........................................................................................... 67

Figure 58. Dynamic post setup...................................................................................... 67

Figure 59. Typical static post test results. ..................................................................... 68

Figure 60. Typical dynamic post test results. ................................................................ 69

Figure 61. Other dynamic post test results.................................................................... 70

Figure 62. Impact sequence of post simulation. ............................................................ 73

Figure 63. Damage (stored as effective plastic strain in d3plot files). ........................... 74

Figure 68. Contact penetrations caused locking of parts............................................... 75

Figure 69. Sequence of fast bogie simulations.............................................................. 76

Figure 70. Energy of post parts for fast bogie simulation. ............................................. 77

Figure 71. Section forces through post just below impact: Fast bogie simulation. ........ 77

Figure 72. Stress-strain behavior of single elements..................................................... 80
ix 

Figure 73. Volumetric behavior of single elements........................................................ 81

Figure 74. Static post models........................................................................................ 86

Figure 75. Rounded edge on brace............................................................................... 86

Figure 76. Force deflection: Baseline versus test.......................................................... 87

Figure 77. Energy deflection: Baseline versus test. ...................................................... 87

Figure 78. Force deflection: Baseline versus refined mesh........................................... 88

Figure 79. Energy deflection: Baseline versus refined mesh......................................... 88

Figure 80. Variations by mesh size: Deformed geometry.............................................. 89

Figure 81. Force-deflection behavior as a function of grade, moisture content, and 

temperature............................................................................................................ 90

Figure 82. Energy-deflection behavior as a function of grade, moisture content, and 

temperature............................................................................................................ 91

Figure 83. Variation by grade: Deformed geometry. ..................................................... 92

Figure 84. Variation by moisture content: Deformed geometry. .................................... 93

Figure 85. Variation by temperature: Deformed geometry. ........................................... 94

Figure 86. Dynamic wood post test model. ................................................................... 95

Figure 87. Post vaporization.......................................................................................... 96

Figure 88. Contact at sharp corner................................................................................ 97

Figure 89. Post bending. ............................................................................................... 98

Figure 90. Contact penetrations. ................................................................................... 99

Figure 91. Improved contact.......................................................................................... 99

Figure 92. Element vaporization at bottom of post. ..................................................... 100

Figure 93. Volume expansion of 75 percent in an element near the bottom of post.... 100

Figure 94. Vaporization with a time step of 0.0001 ms................................................ 101

Figure 95. Highly distorted elements sometimes do not erode.................................... 102

Figure 96. Damage of highly distorted element........................................................... 102

Figure 100. Southern yellow pine grade, DS-65: Hourglass control type 4, qm = 0.005.

............................................................................................................................. 105

Figure 101. Schematic demonstration of how a finite element treats fracture prior to 

erosion. ................................................................................................................ 114

Figure 102. Demonstration of void formation and crushing of wood specimens. ........ 114

Figure 103. User’s grades 1 and 1D simulation compared to the performance 

envelopes, using Gf|| = 50 Gf⊥............................................................................... 115

Figure 104. Most of the grades 1 and 1D static post test measurements exhibit brittle 

behavior. .............................................................................................................. 116

Figure 105. Good correlation is achieved between the simulation and the performance 

envelopes by increasing the fracture energy above the default value (to Gf|| = 250 

Gf⊥)....................................................................................................................... 117

Figure 106. DS-65 pine post modeled with simple pinned boundary conditions. ........ 119

Figure 107. Developer’s static post simulations using hourglass stiffness type 4 with a 

reduced (0.03) coefficient..................................................................................... 122

Figure 108. Finite element meshes used in demonstration problems. ........................ 124

Figure 109. Stable behavior in the developer’s single-flap calculation. ....................... 125

Figure 110. Unstable behavior in the developer’s double-flap calculation................... 125

Figure 111. Unstable behavior in the user’s single-flap calculation............................. 127
x 

Figure 112. LS-DYNA MESSAG file which shows that the stable time step is exceeded.

............................................................................................................................. 128

Figure 113. Stable behavior is achieved by reducing the time step to that needed for 

stable contact surface behavior (default grade 1 saturated pine properties without 

rate effects). ......................................................................................................... 129

Figure 114. LS-DYNA MESSAG file with diagnostics for the stable time step. ........... 130

Figure 115. Unstable behavior of an elastic element in the neoprene liner................. 132

Figure 116. The liner penetrates the post when the post is modeled with either elastic or 

wood material models. ......................................................................................... 133

Figure 117. The post breaks earlier when modeled with post-peak hardening (default 

saturated grade 1 pine properties with Ghard = 0.5). ............................................. 133

Figure 118. The post breaks by 15 ms in this Douglas fir simulation (default saturated 

grade 1 properties without rate effects)................................................................ 134

Figure 119. Bogie impact at 29.5 m/s for a grade 1 wood post modeled without rate 

effects (grade 1 default saturated pine properties)............................................... 135

Figure 120. Bogie impact at 29.5 m/s for a saturated grade 1 wood post modeled with 

rate effects (default pine properties)..................................................................... 135

Figure 121. Fringes of damage for bogie impact at 29.5 m/s (default properties for 

saturated grade 1 pine with rate effects).............................................................. 136

Figure 122. Unstable behavior in the developer’s rigid-sleeve calculation. ................. 137

Figure 123. Unstable behavior in the user’s rigid-sleeve calculation. .......................... 137

Figure 124. LS-DYNA diagnostics indicate that a contact surface is improperly 

positioned and requires movement of nodes prior to running the simulation. ...... 138

Figure 125. The liner does not penetrate the post in calculations conducted with LSDYNA, version 960............................................................................................... 138
xi 

List of Tables 

Table 1. Average of static post test data by grade. ....................................................... 12

Table 2. Summary of bogie impact tests on posts by grade.......................................... 32

Table 3. Approximate tensile strength ratios versus strain rate for saturated pine. ....... 44

Table 4. Model Cfa: Uniaxial Compression in Parallel Direction ................................... 71

Table 5. Model Cfe: Uniaxial Compression in Perpendicular Direction ......................... 72

Table 6. Model Tfa: Uniaxial Tension in Parallel Direction ............................................ 72

Table 7. Model Tfe: Uniaxial Tension in Perpendicular Direction .................................. 72

Table 8. Parameters based on wood grade. ................................................................. 82

Table 9. Parameters based on moisture content........................................................... 83

Table 10. Parameters based on temperature................................................................ 84

Table 11. Developer’s response to user’s review of wood model................................ 111

 1

1 DEVELOPER’S INTRODUCTION 

The calculations and conclusions in chapters 1 through 8 of this evaluation report were 

conducted and documented by the developer of the wood material model, herein 

referred to as the developer. The calculations and conclusions in chapters 9 through 16 

were conducted and documented by a potential end user of the wood material model, 

herein referred to as the user. Following these independent evaluation efforts is 

commentary, written by the developer in chapter 17, on the results of the user’s 

evaluation effort. 

1.1 MODEL THEORY 

The wood model was primarily developed to simulate the deformation and failure of 

wooden guardrail posts impacted by vehicles. The primary features of the model are: 

• Transverse isotropy for the elastic constitutive equations (different properties are 

modeled parallel and perpendicular to the grain). 

• Yielding with associated plastic flow formulated with separate yield (failure) 

surfaces for the parallel- and perpendicular-to-the-grain modes. 

• Hardening in compression formulated with translating yield surfaces. 

• Post-peak softening formulated with separate damage models for the paralleland perpendicular-to-the-grain modes. 

• Strength enhancement at high strain rates. 

The behavior of the model is shown figure 1 for single-element LS-DYNA simulations 

that are conducted parallel to the grain. The simulations are linear to the peak in tension 

and shear, followed by post-peak softening. For these simulations, the softening is more 

brittle in tension than in shear. The simulation in compression is nonlinear because of 

the application of pre-peak hardening. No softening (perfect plasticity) is modeled in 

compression. A thorough discussion of the model theory is documented in the wood 

model manual.(2)

1.2 MODEL INPUT 

There are two methods of setting up the model input: The traditional method is to supply 

all material parameters (e.g., moduli, strengths, hardening, softening, and rate-effect 

parameters). A more convenient method is to request default parameters. The default 

parameters are obtained from laboratory data that are documented in the literature for 

southern yellow pine(5) and Douglas fir. The default parameters vary as a function of 

moisture content, temperature, and grade. 
 2

(a) Tension 

(b) Shear 

(c) Compression 

Figure 1. LS-DYNA simulations of southern yellow pine showing brittle behavior 

in tension and shear, and ductile behavior in compression. 
 3

1.3 LIMITATIONS OF LABORATORY MATERIAL PROPERTY DATA 

One limitation of the data available for setting default parameters is that the data are for 

clear wood (small specimens without defects such as knots), whereas real-world posts 

are graded wood (e.g., grades 3, 2, and 1, or DS-65). Clear wood is stronger than 

graded wood. Clear wood strengths cannot be used directly as input for graded wood. 

Our approach for overcoming this limitation is to apply strength-reduction factors to the 

clear wood data, which we call quality factors, to account for reductions in strength as a 

function of grade. This is a practical approach compared to the alternative approach of 

modeling each defect explicitly. Our methodology is to estimate the quality factors from 

correlations with the user’s static post and Forest Products Laboratory (FPL) timber 

compression data. 

Other limitations of published laboratory test data for setting the default material 

properties include: 

• No direct measurement of the fracture energy parallel to the grain (the fracture 

energy is the area under the stress-displacement curve (from peak stress to zero 

stress)). 

• Limited information on rate effects. 

• Incomplete Douglas fir data. 

• Limited information on frozen pine properties. 

Our methodology is to estimate the missing material property values through LS-DYNA

correlations with static post and bogie impact data provided by the user. Thus, the 

LS-DYNA simulations discussed in this document not only serve to evaluate the 

material model, but also to set default material property values as well. 

1.4 EVALUATION PROCESS 

The evaluation of the wood model proceeded in two steps. The first step was the 

evaluation of the model as a user-defined material. This means that the model was 

hooked up to the LS-DYNA code as material model 42 via an interface. As the 

developer, we retained access to the wood model source code in order to enhance the 

formulation and adjust the default parameters during the evaluation process. 

Once the evaluation was near completion and all of the default parameters were 

selected, the wood model was forwarded to Livermore Software Technology 

Corporation (LSTC) for permanent implementation into the LS-DYNA code. LSTC and 

the developer implemented the model into LS-DYNA, beta version 970, as material 

model 143. 

The second step was the evaluation of the wood model as material model 143 in the 

LS-DYNA code. The objective was to check the permanent implementation to make 

sure that material model 143 produced the same results as the user-defined material. 

Adjustments in the LSTC implementation were made until agreement was achieved. 
 4

All evaluation calculations documented in this report were performed by the developer 

with the user-defined material model. Most were conducted using LS-DYNA,

version 960, on a DEC Alpha microprocessor using UNIX®. Subsequent calculations 

performed by the developer using material model 143 were conducted using LS-DYNA, 

version 970, on a personal computer (PC) using Microsoft® Windows®. Material 

model 143 calculations were in agreement with those performed by the developer via 

the interface. 

1.5 VERIFICATION AND VALIDATION 

Verification is a check on model implementation; it determines whether the material 

model has been implemented as the developer had intended (i.e., without coding 

errors). Stress-strain histories from single-element simulations were plotted to verify 

implementation of the wood material model. 

Validation is a check on model theory; it determines whether the material model 

simulates real-world behavior. Multi-element simulations were compared to four sets of 

test data to initiate validation of the wood material model: 

• Quasi-static compression tests of timbers (conduced by FPL). 

• Quasi-static bending tests of timbers (conducted by FPL). 

• Quasi-static bending tests of posts (conducted by the user). 

• Dynamic bogie impact tests into posts (conducted by the user). 

All of the test data discussed in this report were generated and documented by FPL and 

the user prior to performance of this contract. Comparisons of simulations with the 

user’s quasi-static and dynamic post tests are used to set the quality factors, fracture 

energies, rate effects, and frozen pine parameters used as default parameters in the 

wood model. 

One might suggest that only pre-test predictions can be used to validate a material 

model. By this, we mean that the analyst is unaware of the measured results prior to the 

simulation. Accurate predictions (rather than correlations) certainly build the most 

confidence in a model. However, all calculations performed to date, and discussed in 

this report, were performed with the knowledge of the test results. This is because 

correlations with test results were used to set various default parameters. Future 

calculations performed by roadside safety analysts (such as the Centers of Excellence 

(COE) and the National Highway Traffic Safety Administration (NHTSA) National Crash 

Analysis Center (NCAC)) will assess the predictive capability and provide a more 

thorough evaluation and validation of the wood material model. 
 5

2 SINGLE-ELEMENT SIMULATIONS 

Single-element simulations were performed to help verify implementation of the wood 

model. Two sets of simulations are shown in figures 2 and 3 that use default material 

properties for southern yellow pine at room temperature. The first set is for tension 

parallel to the grain. The second set is for compression perpendicular to the grain. Note 

that both stiffness and strength vary as a function of moisture content. These 

simulations indicate that saturated pine properties provide the lowest stiffness and 

strength in both tension and compression. The posts tested statically and dynamically 

by the user and analyzed by the developer are all saturated (23-percent moisture 

content). The test posts were pulled from the field throughout Nebraska, so saturation is 

a reasonable test and analysis condition. 

Figure 2. Good correlation between LS-DYNA simulations (dashed lines) and 

measured clear wood data (solid lines) for southern yellow pine in tension 

parallel to the grain. 
 6

Figure 3. Good correlation between LS-DYNA simulations (dashed lines) and 

measured clear wood data (solid lines) for southern yellow pine in compression 

perpendicular to the grain. 
 7

3 TIMBER COMPRESSION TEST CORRELATIONS 

FPL performed full-scale tests on dry southern yellow pine timbers in compression 

parallel to the grain.(6) A schematic of the test setup is reproduced in figure 4. The 

timber cross section is 15.24 centimeters (cm) by 15.24 cm, and the timber length is 

304.8 cm. Load-deflection histories were measured for select structural and grade 2 

timbers. Moisture content, failure location, and defect-initiated failures were 

documented. The average moisture content is 12 percent, although measurements as 

low as 7 percent and as high as 18 percent were recorded. The average strength 

measurements are: 

• 25.7 MPa for select structural. 

• 22.7 MPa for grade 2. 

The default strength of clear wood at 12-percent moisture content is 52.7 MPa. 

1 inch = 25.4 millimeters (mm), 1 pound force (lbf) = 0.004448 kilonewton (kN) 

Figure 4. Schematic of FPL timber compression test setup. 

The developer performed multi-element simulations of these tests to: 

• Evaluate the behavior of the model. 

• Select default quality factors. 

• Select default hardening parameters in parallel-to-the-grain compression. 

Comparisons of the simulations with the test data are shown in figure 5 as a function of 

grade. The black lines are the simulations. The red and colored lines are the test data. 

The colored lines highlight specific data curves whose strength is approximately 

average. 
 8

Load-deflection curves from two calculations are shown in each plot. One curve is a 

clear wood simulation that models a higher yield strength than measured. The second 

curve applies a strength-reduction quality factor (QC) to the compressive strength to 

correlate the calculated yield strength with the measured yield strength. 

A good correlation of the select structural simulation is obtained with a factor of 

QC = 0.49 applied to the compressive strength. This factor is the ratio of the average 

select structural timber compression strength (25.7 MPa) divided by the average clear 

wood compression strength (52.7 MPa) at 12-percent moisture content. A good 

correlation of the grade 2 simulation is obtained with a factor of QC = 0.43 applied to the 

compressive strength. This factor is the ratio of the average grade 2 timber compression 

strength (22.7 MPa) divided by the average clear wood compression strength 

(52.7 MPa) at 12-percent moisture content. No quality factors are applied to the 

stiffness, although a factor of 0.8 is probably reasonable for grade 2. 

 

(a) Select structural (b) Grade 2 

Figure 5. These comparisons of the model with test data were used to set the 

hardening behavior of the southern yellow pine model in parallel-to-the-grain 

compression. 

These comparisons were made with different hardening parameter values for each 

grade. Good correlations could not be achieved using the same hardening parameter 

values for each grade. Therefore, the default material property methodology was set up 

to specify hardening parameters as a function of grade. This is more thoroughly 

discussed in the wood model user’s manual.(2)
 9

4 TIMBER-BENDING TEST CORRELATIONS 

FPL performed full-scale tests of southern yellow pine timbers in parallel-to-the-grain 

four-point bending.(6) The timber cross section is 15.24 cm by 25.24 cm, and the timber 

length is 304.8 cm. Load-deflection histories were measured for select structural and 

grade 2 timbers. Moisture content and failure mode were recorded. The average 

moisture content is 14 percent, although measurements as low as 9 percent and as 

high as 23 percent were recorded. 

The developer performed multi-element simulations of one or more tests to evaluate the 

bending response of the wood material model and to select quality factors in tension. 

Comparisons of the simulations with measured load-deflection curves are shown in 

figure 6 as a function of grade. The black lines are the simulations. The red and colored 

lines are the test data. The colored lines highlight specific data curves for better viewing. 

Load-deflection curves from three calculations are shown in each plot. One curve is a 

clear wood simulation that models a higher bending strength than that measured. The 

second curve applies a quality factor to the tensile strength (QT) that is equal to the 

quality factor applied to the compressive strength (QC). The QC value is that selected 

from the timber compressive simulations discussed in the previous section. These 

simulations also model higher bending strengths than those measured. The third curve 

applies a tensile quality factor that is less than the compressive factor. In addition, a 

quality factor is also applied to the stiffness (Qstiff). These simulations correlate well with 

the measured data. 

A good correlation of the select structural simulation is obtained with a quality factor of 

QT = 0.25. This value is much lower than that previously selected in compression 

(QC = 0.49). A good correlation of the grade 2 simulation is obtained with a quality factor 

of QT ≤ 0.25. This value is also lower than that previously selected in compression 

(QC = 0.43). These correlations prompted the developer to model different quality 

factors in tension than in compression. The tensile quality factors are also applied to the 

shear strength. 

Also note that a quality factor of 0.8 is applied to the stiffness for correlation with the test 

data (for both grades), although a quality factor of 1.0 is still reasonable. No 

methodology is currently implemented in the initialization routines of material model 143 

to specify quality factors for stiffness. This is because clear wood stiffnesses are 

adequate for simulating graded wood stiffnesses based on calculations performed to 

date. However, quality factors for stiffness could readily be added if the need arises. 
 10

 (a) Select structural 

 (b) Grade 2 

Figure 6. These comparisons of the model with the parallel-to-the-grain timberbending test data demonstrate the need for different quality factors in tension 

and compression. 
 11

5 QUASI-STATIC POST TEST CORRELATIONS 

The main reason for developing the wood material model is to analyze wood posts in 

roadside safety applications. Such posts are often saturated. Although the FPL data 

discussed in the preceding sections are useful for model evaluation and input parameter 

selection, the data focus on dry timbers rather than saturated wood posts. Therefore, 

additional bending test correlations are reported here for saturated wood posts. 

The main objective for simulating the user’s quasi-static tests is to select specific default 

parameters, namely, quality factors and parallel-to-the-grain fracture energies, as a 

function of grade. The user’s test data are reviewed first, followed by correlation of the 

LS-DYNA simulations with the test data. Finally, the results from a number of parametric 

studies are reported. 

5.1 SOUTHERN YELLOW PINE BENDING TEST DATA 

The user conducted 25 bending tests on southern yellow pine posts of three grades 

(DS-65, 1D, and 1).(7) The grading was performed without considering waning on the 

ends of the posts. The posts were removed from the field from guardrail installations 

throughout Nebraska. They were cantilevered in a rigid frame and were loaded at a 

constant rate (as shown in figure 7). In some tests, neoprene and steel were wedged 

between the wood post and the steel support (as shown in figure 8). Load and 

deformation were continuously recorded. All post failure was dominated by tensile 

failure of the growth rings. 

Figure 7. Quasi-static post test setup. 
 12

(a) Steel at bottom of support (b) Neoprene at top of support on compression side 

Figure 8. Details for the rigid frame used in the quasi-static post test setup. 

Peak force, deflection, and energy are listed in table 1. Moderate scatter is observed in 

the data. For the grade 1 and DS-65 posts, all peak-force measurements are within 

20 percent of the average measurements. For the grade 1D posts, all peak-force 

measurements are within 33 percent of the average measurement. For example, for 

grades 1 and 1D posts, peak forces range from 24.0 to 72.5 kilonewtons (kN) and 

deflections at peak force range from 30.5 to 94.0 mm. For DS-65 posts, peak forces 

range from 53.8 to 77.8 kN and deflections at peak force range from 43.2 to 91.4 mm. 

Table 1. Average of static post test data by grade. 

Peak Force 

Grade 

Number of 

Posts 

Force 

(kN) 

Deflection 

(mm) 

Energy 

(kN-mm) 

DS-65 

1D 

1 

10 

7 

8 

67 

55 

42 

68 

49 

53 

3040 

1970 

1440 

Deformed configurations from one grade DS-65 and one grade 1 southern yellow pine 

specimen are given in figure 9. Closeup views of damage in the break region are given 

in figure 10. Example load-deflection histories are given in figure 11. The curves exhibit 

slight pre-peak nonlinearity, followed by sudden drops in load as the specimens fail in 

the tensile region. 
 13

 

(a) DS-65 test 1420 (b) Grade 1 test 418 

Figure 9. Deformed configurations of posts in static tests. 

 (a) DS-65 post (b) Grade 1D post 

Figure 10. Closeup of damage observed in break region of posts in static tests. 
 14

Figure 11. Measured load-deflection histories exhibit sudden drops in force as the 

post fails in the tensile region. 

The user developed performance envelopes from quasi-static load-deflection and 

energy-deflection curves. These envelopes are shown in figure 12, along with the 

performance envelopes developed from the dynamic bogie impact tests (to be 

discussed later). The user constructed the envelopes using curves from posts that 

exhibited the most typical behavior. For example, the DS-65 performance envelopes 

were developed from 6 of the 10 tests reported in table 1. The grade 1 performance 

envelopes were also developed from some, but not all, of the 15 tests reported in 

table 1. The grade 1 performance envelopes represent the combined curves from the 

grades 1 and 1D tests because the behavior of the grades 1 and 1D posts was similar. 

Note that the minimum and maximum curves that define the performance envelopes do 

not represent any one particular curve from the tests. 

Measured curves plotted by the user are reproduced in figure 13 for grades 1 and 1D. 

Showing all of the curves allows us to better see the character of the data (such as 

scatter and sudden drops in force). This is important because the static post test 

analyses performed by the developer, which are discussed in the next section, exhibit 

large variations in post-peak behavior and sudden drops in force. A comparison of the 

performance envelopes in figure 12 with the measured data curves in figure 13 

suggests that the static performance envelopes are developed from data that exhibit the 

largest fracture energies. 

The relatively small scatter of the performance envelopes is surprising, especially 

considering that the failure (softening) curves are being measured. For example, see 

the scatter in the data measured by FPL for their timber compression and bending tests 

in figures 5 and 6. The reader is also referred to appendixes A and B of the wood model 

user’s manual(2) for plots of clear wood stiffness and strength measurements. Clear 

wood stiffnesses (and strengths) vary by a factor of three from high measurement to low 

measurement. 
 15

 

Figure 12. Quasi-static (blue solid line) and dynamic (pink dashed line) 

performance envelopes developed and plotted by the user. 

(a) Force versus deflection 

(b) Energy versus deflection 
 16

(a) Force versus deflection 

(b) Energy versus deflection 

Figure 13. Grades 1 and 1D static post test measurements exhibit substantial 

scatter. 

5.2 LS-DYNA CORRELATIONS 

Multi-element simulations of guardrail posts in bending were performed at two grade 

levels for comparison with the performance envelopes (as shown in figures 14 and 15). 

Good correlations in the loading region primarily determine the tensile and compressive 

quality factors. The compressive quality factor also has a significant effect on the latetime softening response. The quality factors selected were QT = 0.47 with QC = 0.63 for 

grade 1 posts, and QT = 0.80 with QC = 0.93 for DS-65 posts. 

90 

45 

0

Force (kN) 

90 

45 

0

Force (kN) 

(mm) 

 0 51 102 152 203 254 

(mm) 

0 51 102 152 203 254 

(mm) 

 0 51 102 152 203 254 (mm) 

 0 51 102 152 203 254 

11.3 

5.6 

0 

Energy (kN-mm) (E+03) 

11.3 

5.6 

0 

Energy (kN-mm) (E+03) 
 17

Good correlations in the post-peak softening region determine the parallel-to-the-grain 

fracture energies. Parallel fracture energies (Gf ||) are reported here as multiples of the 

perpendicular fracture energies (Gf ⊥). Fracture energies used in these simulations are 

Gf || = 250 Gf ⊥ kN-mm for grade 1 and Gf || = 380 Gf ⊥ kN-mm for DS-65, with B = 30 for 

both grades. 

Deformed configurations at 200 milliseconds (ms) (approximately 190 mm) are shown in 

figure 16, along with fringes of damage. The damage plotted is the maximum of the 

parallel and perpendicular damage. High damage (greater than 80 percent) is indicated 

by the red elements. 
 18

(a) Force versus deflection 

(b) Energy versus deflection 

Figure 14. Good correlations between the LS-DYNA calculations and quasi-static 

performance envelopes determine the default quality factors for grade 1 southern 

yellow pine of QT = 0.47 with QC = 0.63. 
 19

(a) Force versus deflection 

(b) Energy versus deflection 

Figure 15. Good correlations between the LS-DYNA calculations and quasi-static 

performance envelopes determine the default quality factors for DS-65 southern 

yellow pine of QT = 0.80 with QC = 0.93. 
 20

 

(a) Grade 1 deformed configuration (b) Fringes of damage 

(c) DS-65 deformed configuration (d) Fringes of damage 

 

Figure 16. The parallel-to-the-grain post fracture calculated in the post just below 

the top of the rigid support is in agreement with the location of the damage 

observed in the tests. 
 21

Details for the geometric models and parametric calculations used to establish these 

default parameters are given in the following section. 

5.3 LS-DYNA PARAMETRIC STUDIES 

Various parametric calculations were conducted to further evaluate the material model 

and default material property selection. 

Meshing: The parametric calculations were performed with three geometric models as 

shown in figure 17. The first geometric model uses fixed nodal constraints, without the 

use of slide surfaces. Neither the steel support nor the loading bolt is modeled. 

Therefore, it is the fastest running model. The second geometric model uses planar rigid 

walls of a finite size to model the steel support. The slide surface between the wood 

post and the rigid wall is modeled with a coefficient of friction of 0.30. In addition, the 

steel loading bolt is explicitly modeled. The third geometric model explicitly meshes the 

steel support as brick elements of rigid material. This mesh was developed by the user. 

 

(a) Fixed nodes (b) Rigid walls (c) Full-support structure 

Figure 17. Three geometric models were set up for performing parametric 

calculations. 

Load-deflection curve comparisons are given in figure 18 for the full-support and rigidwall models. Behaviors are similar, as though the load-deflection curve of the fullsupport model is shifted relative to the rigid-wall model. All default quality factors were 

selected from final calculations performed with the full-support structure. However, most 

parametric calculations were performed with either the rigid-wall model or the fixedApplied 

Velocity 

X 

No X or Z

displacement

No X or Z

displacement

Z 
 22

node model. This is because the rigid-wall model runs 15 times faster than the fullsupport model, while the fixed-node model runs 45 times faster than the full-support 

structure. Unless otherwise stated, all parametric calculations reported in this section 

are conducted with the rigid-wall model. 

 (a) Force deflection (b) Energy deflection 

Figure 18. The force-deflection curve calculated with the fast-running, rigid-wall 

model is similar to that calculated with the full-support structure, making it useful 

for performing parametric calculations. 

Loading Method and Rate: The method of loading the bolt has a minor effect on the 

calculated response. This is demonstrated in figure 19(a) for two loading methods. In 

the first method, horizontal velocity is applied to the rigid bolt (or post). This means that 

no vertical forces are applied to the bolt, so the post is free to rotate. In the second 

method, horizontal velocity is applied to the end of a truss that is pinned to the bolt (as 

shown in figure 19(b)). This means that small vertical forces are applied to the bolt to 

simulate the effect of the pulley system on post rotation. The pulley system of the test 

configuration was previously shown in figure 7. It was used to load the bolt attached to 

the wood post. Application of the pinned truss increases the peak force by about 

4 percent. All default parameters were selected from calculations performed with the 

truss. The calculations previously shown in figure 18 were performed with a truss. 
 23

(a) Load-deflection comparisons (b) Rigid-wall mesh with truss 

Figure 19. Pinning a truss to the bolt to simulate the vertical force applied by the 

pulley system increases the peak force by about 4 percent. 

The calculations are intended to simulate static tests, so the rate of loading must be 

slow enough to eliminate dynamic oscillations that can initiate premature damage and 

plastic hardening. This is achieved by ramping the applied velocity (to the post or truss) 

from zero to a constant sustained value over a 15-ms interval. Clear wood calculations 

performed with the simplest (fixed nodes) mesh are compared in figure 20 for sustained 

velocities of 1.0 and 0.25 meters per second (m/s). The calculated load-deflection 

curves are quite similar, particularly the peak force. All default parameters were 

selected from calculations performed at 1.0 m/s. 

Figure 20. The peak force increases with the applied velocity until convergence is 

attained at 0.25 mm/ms. 
 24

Filtering: All static computational force histories are also post-processed using the

Society of Automotive Engineers (SAE International) 60 filter in LS-TAURUS (an LSDYNA post-processor) to remove the high-frequency post-peak oscillations that occur 

as the elements soften in the tensile region. A different filtering method is used for the 

bogie impact calculations discussed later. Filtering is used because it is not practical to 

run the calculations slow enough to eliminate all post-peak oscillations; the calculations 

are quasi-static rather than static. The filtering primarily clarifies the post-peak softening 

response for comparison with the unfiltered test data. One comparison between clear 

wood calculations, with and without filtering, is shown in figure 21. These calculations 

were performed with the simplest (fixed nodes) mesh. 

Figure 21. Quasi-static calculations are filtered for easier comparison with the 

unfiltered test data. 

Fracture Energy: The calculated response depends on the value of the parallel-to-thegrain fracture energy. Comparisons at two different fracture energy levels are shown in 

figure 22. The greater the parallel fracture energy, the more gradual the post-peak 

softening response, and the more energy it takes to break the post. These comparisons 

were performed with B = 30, and QT = 0.47 with QC = 0.63. 

The two values used in the simulations are Gf || = 250 Gf ⊥ kN-mm and Gf || = 50 Gf ⊥

kN-mm for grade 1. Here, Gf || is the parallel-to-the-grain fracture energy and Gf ⊥ is the 

perpendicular-to-the-grain fracture energy. The 250 value is obtained from correlations 

with the static performance envelopes. The 50 value is obtained from correlations with 

the dynamic performance envelopes (discussed in subsequent sections). Although the 

peak forces are similar, the post-peak response is substantially different. The 

calculation conducted with Gf || = 50 Gf ⊥ kN-mm does not fit within the performance 

envelopes; however, it does correlate well with the suite of measured data previously 

plotted in figure 13. In this figure, 9 out of 15 of the data curves peak between 25 and 50 

mm of deflection and then exhibit a sudden drop in force. The calculation is consistent 

with the measured behavior. 
 25

Figure 22. The energy required to break the post increases as the value of the 

parallel-to-the-grain fracture energy increases. 

Compressive Quality Factor: For a given fracture energy, the softening response also 

depends on the compressive quality factor. Two computational comparisons are shown 

in figure 23. The calculation with QT = QC = 0.60 gives approximately the same peak 

force as the calculation with QT = 0.47 with QC = 0.63, but does not soften as rapidly. 

Numerous parametric calculations have demonstrated that increasing the value of QC

above QT increases the force at the peak, but decreases the force at a large deflection 

(reduces the tail). This is because yielding in the compressive region is delayed by 

increasing QC. Allowing QC to be greater than QT is consistent with our fits to the FPL

static bending test data previously shown in figure 6. All default quality factors were 

selected with QC greater than QT. 

 (a) Force deflection (b) Energy deflection 

Figure 23. Calculations with QC > QT soften more rapidly than calculations with QC 

= QT. 
 26

Softening Shape Parameter: The calculated response also depends on the value of 

the softening parameter B (as shown in figure 24). The greater the value of B, the 

greater the peak force. Recall that the parameter B determines the shape of the 

softening curve in single-element simulations. This is shown in figure 25 for tension 

parallel to the grain. A moderate value of B = 30 was selected for use as a default 

parameter. This value is somewhat arbitrary because no softening-curve measurements 

are available from the FPL direct-pull simulations for fitting the softening model. 

Softening curves are often difficult to measure. These clear wood calculations were 

performed with the simplest mesh at 1 m/s using Gf || = 300 Gf ⊥. 

Figure 24. The calculated peak force increases with increasing values of the 

softening parameter B. 

Figure 25. The softening parameter B determines the shape of the softening curve 

in these single-element simulations for tension parallel to the grain. 
 27

Hourglass Control: The calculated response also depends on the hourglass control. 

To demonstrate this, calculations performed with viscous and stiffness hourglass 

controls are compared to a calculation performed with selectively reduced (S/R) 

integrated elements (ELFORM 2 is called a fully integrated S/R solid). Deformed 

configurations in the break region are shown in figure 26. Load-deflection curves are 

shown in figure 27. Hourglass energy histories are shown in figure 28. 

 

The simulation with viscous hourglass control exhibits hourglassing at an early time, 

resulting in an unrealistic pinching behavior on the backside of the post in the 

compressive region near ground level. Hourglassing is concentrated in the breakaway 

region of the post, where the damage accumulates. Type 3 viscous control, with a 

default coefficient of QM = 0.1, was used throughout the post breakaway region. The 

simulation with stiffness hourglass control exhibits less visual hourglassing and 

pinching. Type 4 stiffness control, with a reduced coefficient of QM = 0.005, was used 

throughout the post breakaway region. The third simulation was performed with fully 

integrated elements (eight integration points) in the breakaway region. Fully integrated 

elements do not require hourglass control. Note that the deformed configuration and the 

peak force calculated with stiffness hourglass control are in best agreement with those 

calculated with the fully integrated elements. 

One common concern is that stiffness hourglass control overstiffens the calculated 

response. These comparisons indicated that stiffness hourglass control does not stiffen 

the calculated response unrealistically. In fact, the calculation with stiffness control 

matches the peak force calculated with fully integrated elements. In addition, the final 

hourglass/internal energy ratio in the breakaway region is slightly less with stiffness 

control than with viscous control. Therefore, stiffness hourglass control with QM = 0.005 

was used in the breakaway region of all calculations involving default parameter 

selection. As a bonus, the calculation with stiffness control runs the fastest. The viscous 

control and fully integrated element calculations run 7 percent and 51 percent longer, 

respectively, than the stiffness control calculation. 
 28

 (a) Viscous control (b) Stiffness control (c) Fully integrated S/R 

120-mm deflection 

 (d) Viscous control (e) Stiffness control (f) Fully integrated S/R 

190-mm deflection 

Figure 26. Type 4 stiffness control reduces hourglassing better than type 3 

viscous control. 
 29

Figure 27. The peak force calculated with type 4 stiffness control agrees with the 

fully integrated element calculation better than the type 3 viscous calculation. 

Figure 28. Less final hourglass energy is calculated with type 4 stiffness control 

than with type 3 viscous control. 

Moisture Content: Moisture content has a strong effect on the calculated loaddeflection curves (as shown in figure 29). The peak force calculated in the post at 17- 

percent moisture content is 80 percent greater than the peak force calculated in the post 

at 23-percent (saturated) moisture content. 

Calculations with variations in moisture content along the length of the post were also 

performed. One calculation was performed with three regions of differing moisture 

content, while a second calculation was performed with five regions of differing moisture 

content. The moisture content at ground level, where parallel-to-the-grain fracture 
 30

occurs, has the greatest effect on the force in the post. These calculations were 

performed with the simplest (fixed nodes) mesh. 

Figure 29. Decreasing the moisture content by 6 percent increases the post-peak 

force by 80 percent. 

(a) 3 MC levels 

18.5% 18.5%

20.0%

23.0% 23.0%

21.0%

20.0%

22.0%

(b) 5 MC levels (c) Force versus deflection 
 31

6 DYNAMIC POST TEST CORRELATIONS 

The main objectives of the dynamic post test correlations are to evaluate the wood 

material model and to select specific default parameters. Although we mainly expected 

to select rate-effect parameters as a function of grade, we instead adjusted the parallel 

fracture energies previously selected from the static post tests. 

The user’s bogie impact test data are reviewed first, followed by correlation of the 

LS-DYNA simulations with the test data. Then, filtering and sampling issues are 

discussed. Finally, the results from a number of parametric studies are reported. 

Wood posts installed in the field are typically situated in a deformable medium (such as 

soil or concrete). The post/medium interaction complicates validation of the wood 

model. Here, wood posts installed in a fixed-type base are analyzed to eliminate 

post/medium interaction and to facilitate evaluation of the wood model. 

6.1 BOGIE IMPACT TEST DATA 

The user conducted 80 bogie tests on southern yellow pine posts of five grades (DS-65, 

1D, 1, 2D, and 2) and 7 tests on Douglas fir posts of one grade (1).(6) Significant knots 

and defects were cataloged. The posts were placed in a steel tube embedded in 

reinforced concrete (as shown in figure 30). The post/steel interface was padded with 

neoprene on the front and back. The posts were impacted at approximately 9.6 m/s by a 

944-kilogram (kg) bogie. A summary of the test results at peak force and rupture is 

given in table 2. Example force, velocity, and deflection histories are given in figure 31. 

An accelerometer was located near the center of the bogie frame. Force, velocity, and 

deflection were derived from the measured deceleration. Post damage in the breakaway 

region of the post, just below ground level, is shown in figure 32. 
 32

Figure 30. Post setup for dynamic bogie impact tests. 

Table 2. Summary of bogie impact tests on posts by grade. 

Number Peak Force Rupture 

of 

Posts 

Grade Force 

(kN) 

Time

(ms) 

Defl. 

(mm) 

Energy 

(kN-mm)

Time 

(ms) 

Defl. 

(mm) 

Energy 

(kN-mm) 

16 

16 

 9 

 7 

16 

16 

 7 

 5 

 7 

DS-65 

1D 

1 (Worst) 

1 (Random) 

2D 

2 

Douglas Fir 

Frozen DS-65 

Frozen 1 

95 

49 

38 

47 

52 

44 

46 

62 

43 

9.0 

8.2 

9.3 

8.3 

8.6 

9.1 

8.4 

7.9 

7.9 

86.3 

78.7 

86.3 

81.2 

83.8 

88.9 

81.2 

76.2 

76.2 

4462.6 

2265.4 

1867.0 

2151.6 

2424.8 

2151.6 

2151.6 

2686.6 

1878.4 

18.8 

15.4 

18.0 

15.5 

17.5 

16.7 

15.9 

14.5 

14.9 

170.1 

144.7 

162.5 

149.8 

165.1 

160.0 

149.8 

139.7 

142.2 

8811.4 

4212.1 

3608.8 

4132.4 

4758.6 

4041.4 

4075.5 

5122.9 

3563.2 

Impact 
 33

(a) Force deflection 

(b) Velocity time 

(c) Displacement time 

 Figure 31. Processed data from the user’s bogie impact tests. 
 34

(a) DS-65 pine (b) Grade 1 pine 

(c) Grade 1 frozen pine (d) Grade 1 fir 

Figure 32. Damage in the breakaway region of the posts, just below ground level. 

These test results provide information on post performance versus grade. The user’s 

results indicate that the DS-65 posts are significantly stronger than all other posts. In 

addition, the user reports that there is no statistically significant difference in the energy 

absorbed by the dense and low-density posts. Thus, the posts can be effectively divided 

into two grades―high (DS-65) and low (all others). 

These test results also provide information on rate effects. The peak force measured in 

the dynamic bogie tests is 1.42 times that measured in the static bending tests for the 

DS-65 posts. Dynamic and static peak forces are similar for the grade 1 posts. This is 

seen by examining the static and dynamic performance envelopes previously shown in 

figure 12.

6.2 LS-DYNA CORRELATIONS 

The developer performed LS-DYNA simulations of the bogie impact tests for four 

combinations of post material and grade. These combinations are grade 1 southern 

yellow pine, DS-65 southern yellow pine, grade 1 frozen pine, and grade 1 Douglas fir. 

Calculated energy-deflection curves are compared to the user’s performance envelopes 

and measured curves in figures 33 through 36. Calculated bogie velocity-reduction 

histories are also compared to the user’s measured histories. 
 35

 

 (a) Energy (b) Velocity reduction 

Figure 33. These correlations between the LS-DYNA calculations and the 

performance envelopes were used to adjust the parallel fracture energy for 

grade 1 pine to 50 times the perpendicular fracture energy. 

 

 (a) Energy (b) Velocity reduction 

Figure 34. These correlations between the LS-DYNA calculations and the 

performance envelopes were used to adjust the parallel fracture energy for DS-65 

pine to 85 times the perpendicular fracture energy. 
 36

 (a) Energy versus deflection (b) Velocity versus time 

Figure 35. These correlations between the LS-DYNA calculations and the energydeflection data were used to confirm that grade 1 Douglas fir can be simulated 

with the same parallel fracture energy and rate-effect parameters as grade 1 

southern yellow pine, but with different quality factors.

 (a) Force versus deflection (b) Velocity versus time 

Figure 36. These correlations between the LS-DYNA calculations and the energydeflection data were used to set the parallel fracture energy for frozen grade 1 

pine to five times the perpendicular fracture energy. 

The first comparison in figure 33 is for grade 1 pine. Although a parallel fracture energy 

of 250 Gf ⊥ was selected from static post correlations, a parallel fracture energy of 

50 Gf ⊥ provides a better correlation with the dynamic performance envelopes. The 

reason for the discrepancy in the fracture energy is not known; however, there are two 

possibilities: 
 37

• The static performance envelopes are biased toward high fracture energy, as 

previously discussed. 

• The boundary conditions in both the static and dynamic tests are not well defined 

and are difficult to model computationally. The selection of fracture energy, 

particularly for the static simulations, is dependent on how the boundary conditions 

are modeled. 

The expected application of the wood model is dynamic, so all default parallel fracture 

energies are those that are identified through dynamic correlations. On the other hand, 

all quality factors used in the dynamic calculations are identical to those used in the 

static calculations; thus, there is no ambiguity about the default quality factors. 

Similarly, for the DS-65 pine simulations in figure 34, the statically selected fracture 

energy of Gf || = 380 Gf ⊥ is adjusted downward to Gf || = 85 Gf ⊥ in order to obtain good 

correlation with the measured data. For grade 1 Douglas fir simulations in figure 35, the 

correlations are obtained using the same fracture energy as for grade 1 pine, but with 

slight adjustments in the pine quality factors. For frozen grade 1 pine simulations in 

figure 36, the correlations are obtained with the same quality factors as for unfrozen 

grade 1 pine, but with a drastic reduction in the fracture energy from Gf || = 50 Gf ⊥ to 

Gf || = 5 Gf ⊥ to make the frozen pine more brittle than the unfrozen pine. 

Deformed configurations for the grade 1 pine simulations are shown in figure 37. 

Figure 37(a) shows the post surrounded by the rigid support structure. The wood post 

mesh with the rigid support structure was created by the user. This support structure is 

removed in figure 37(b) to better view the post failure location. The post breaks just 

below ground level, in agreement with the location of the breakage observed in the 

tests. Neoprene, modeled as an elastic material with external damping, is visible along 

the front and back faces of the post. 
 38

 (a) With rigid support (b) Without rigid support (c) Fringes of damage 

Figure 37. The simulated post breaks just below ground level, in agreement with 

the failure location observed in the tests. 

Figure 37(c) shows fringes of damage in the post, as indicated by the colored elements. 

The highest levels of damage (above 80 percent) are indicated by the red elements. 

These fringes indicate a large split in the post running downward below ground level, 

consistent with the type of damage observed in the tests. Slight damage is also visible 

in the impact region, although impact damage was not reported in the tests. 

6.3 FILTERING AND SAMPLING ISSUES 

It is important to note that good correlation between the calculated and measured data 

not only depends on the wood post model, but on the bogie model (geometric and 

material models) as well. This is because the performance envelopes were derived from 

deceleration measurements recorded by an accelerometer placed near the center of the 

bogie frame. No measurements were made on the wood post or the bogie cylinder. The 

deceleration measurements were sampled at 3200 hertz (Hz) and filtered according to 

SAE J-211 specifications using a channel frequency class (CFC) filter of 60 Hz 

(CFC 60). The filtered deceleration histories were multiplied by the bogie mass 

(approximately 944 kg) to convert to force histories. The filtered deceleration histories 

were also integrated to form bogie velocity-reduction and post deflection histories. A 

more thorough discussion of the user’s data-processing technique is given in reference 

9. 
 39

Bogie Models: The user developed and forwarded three bogie models to the 

developer. The first model is the simplest and is primarily an elastic model. The second 

model is an enhanced version of the first model. One main enhancement is the 

placement of neoprene around the bogie cylinder to more realistically model the test 

vehicle. The bogie materials are modeled primarily as elastic, except that the elastic 

neoprene includes external damping. The third bogie model is geometrically identical to 

the second model; however, the bogie materials (except the neoprene) are modeled as 

rigid materials. All default parameters were selected from calculations performed with 

the rigid bogie model (third model) (as shown in figure 38). 

C

Figure 38. User’s geometric bogie model used in the developer’s calculations. 

The developer performed numerous bogie impact calculations with the three different 

bogie models and derived force-deflection curves from two sources: the bogie 

deceleration history and the cross-sectional forces in the wood post. Output from some 

calculations was also requested at two different sampling frequencies: 3200 Hz (every 

0.3125 ms) and 10,000 Hz (every 0.1 ms). 

Sampling Frequency: The effect of the sampling frequency on the rigid bogie response 

is shown in figure 39. Unfiltered and filtered histories are plotted. The filtered histories 

are processed with a Butterworth four-pole phaseless digital filter according to the 

SAE J-211 specification.(8) The filtered bogie acceleration history significantly depends 

on the output sampling frequency. In fact, the filtered history is inaccurate if sampled at 

3200 Hz (the measured sampling frequency) because much of the high-frequency 

content is missed. One possible explanation for this discrepancy is that the virtual bogie 

model contains higher frequency content than encountered in the real-world bogie 

measurements. Another possible explanation is that the measured accelerations were 

sampled at too low of a frequency and some higher frequency content was 

unintentionally missed. 

1.1.1.1 Accelerometer
 40

 (a) Calculated acceleration histories (b) Calculated force-deflection histories 

Figure 39. The filtered bogie acceleration history sampled at 3200 Hz is 

significantly different than the history sampled at 10,000 Hz. 

Filtered force-deflection curves derived from the calculated deceleration history are 

compared to the processed test data in figure 39(b). The comparisons demonstrate that 

the peak force of the calculation sampled at 3200 Hz is overpredicted. The peak force of 

the calculation sampled at 10,000 Hz is roughly the same as that of the measured data. 

These calculations are preliminary (prior to selection of the final default parameters 

previously shown in figure 33) and were performed with QT = QC = 0.6 and Gf || = 50 Gf ⊥

with no rate effects. 

Model Type: The bogie model type (rigid or elastic) also affects the calculated 

acceleration histories. Calculated force-deflection curves from the elastic (first model) 

and rigid bogies are compared to each other in figure 40 and to a grade 1 pine 

measurement. Two curves are plotted for the elastic bogie. One curve is derived from a 

nodal acceleration calculated on the bogie frame at the approximate gauge location of 

the real-world bogie. It exhibits substantial oscillations despite being filtered and does 

not correlate well with the measured data. The other curve is derived from a nodal 

acceleration calculated on the bogie cylinder. It is less oscillatory, with a peak force 

similar to that of the measured data, although the curve shape is qualitatively different 

from that of the measured data. 
 41

Figure 40. Force-deflection histories calculated from bogie nodal accelerations 

depend significantly on the bogie type and output sampling frequency. 

Two curves are also plotted for the rigid bogie―one curve at an output sampling 

frequency of 3200 Hz and the other at 10,000 Hz (as previously shown in figure 39(b)). 

Since the bogie is rigid, output from the bogie cylinder is identical to output from the 

bogie frame. As previously discussed, the curve derived from the 3200-Hz output is in 

very poor agreement with the data. The curve derived from the 10,000-Hz output is 

similar to that calculated on the cylinder of the elastic bogie, with a peak force similar to 

that of the measured data. 

These comparisons indicate that the computed force-deflection histories depend on the 

bogie model type (elastic or rigid) and sampling frequency. None of the calculations 

match the entire measured history, although most peak-force correlations are 

reasonable. The calculated curves that are post-processed most similarly to the data 

are derived from the rigid bogie at 3200 Hz (because the data were sampled at 

3200 Hz) and from the elastic bogie using the bogie frame node. These calculations are 

in poorest agreement with the measured data. Therefore, other computed output 

quantities for validating the model, such as the post cross-sectional forces, the bogie 

energy output, and the bogie velocity reduction were examined. 

Wood Post Forces: Although bogie type (elastic or rigid) and output sampling 

frequency have a significant effect on the filtered bogie acceleration histories, they do 

not significantly affect the wood post cross-sectional force histories. Force-deflection 

histories derived from the cross-sectional forces in the post are compared to each other 

in figure 41. Note that all curves have similar peak forces and shapes, indicating that the 

details for the bogie model and sampling frequency are not significant in wood post 

response. This suggests that placing instrumentation on the wood post, rather than on 

the bogie frame, is desirable for future bogie impact tests. The user is examining 
 42

methods of placing instrumentation on the posts; however, post breakage and splitting 

complicate the task. 

Figure 41. Force-deflection histories calculated from the wood post crosssectional forces are not significantly affected by the details for the bogie model or 

sampling frequency. 

The wood post force-deflection curves are also compared to the one measured bogie 

curve in figure 41. Note that the calculated and measured peak forces are similar; 

however, the calculated response softens faster than the measured response. This 

indicates that less energy is being calculated in the wood post than is measured from 

the bogie (as shown in figure 42). The energy-deflection curves are derived by 

integrating the force-deflection curves. The reduction in bogie kinetic energy (as 

measured by the accelerometer) is primarily balanced by the energy needed to break 

the post (as calculated via the cross-sectional forces), plus the kinetic energy of the 

broken post, and the energy lost to post sliding and neoprene damping. Therefore, it is 

expected that the post energy calculated from the cross-sectional forces would be less 

than the bogie kinetic energy reduction. This means that direct correlations between the 

calculated post energy and the measured bogie energy cannot be made. These 

calculations were preliminary and were performed with QT = QC = 0.6 and Gf || = 50 Gf ⊥

with no rate effects. 
 43

Figure 42. The internal energy calculated to break the wood post is less than the 

kinetic energy reduction of the bogie. 

Bogie Energy Histories: Bogie kinetic energy reduction histories can be gathered 

directly from the post-processor. Unlike the acceleration histories, the energy histories 

are not significantly affected by the bogie model type (rigid or elastic) or sampling 

frequency. Therefore, all default parameters (parallel fracture energies) were selected 

from calculated kinetic energy reduction histories correlated with the measured energy 

performance envelopes. These correlations were previously shown in figures 33 

through 36. 

6.4 LS-DYNA PARAMETRIC STUDIES 

Rate Effects: The developer originally planned to select rate-effect parameters from 

good correlations with the performance envelopes. Instead, as just discussed, fracture 

energies were selected from the correlations because lower values were needed in the 

bogie impact calculations than in the static calculations. Therefore, the default rateeffect parameters used in the bogie impact simulations were obtained from fits to the 

data available in the literature.(9,10) Only one set of parameters is implemented as the 

default parameters for pine and fir, frozen or unfrozen, independent of the grade. For 

saturated pine, the default parameters give the approximate dynamic-to-static tensile 

strength ratios shown in table 3. Compressive strength ratios and the ratios at other 

moisture contents would be different. Here, 0 degrees indicates the parallel-to-the-grain 

direction and 90 degrees indicates the perpendicular-to-the-grain direction. Strain rates 

experienced by the wood posts in the bogie impact calculations are below 10/s-1, so 

dynamic-to-static ratios are not large at this strain rate. Bogie impact calculations 

performed with and without rate effects at 9.6 m/s indicate that the inclusion of the rate 

effects increases the peak force by less than 10 percent. However, rate effects may be 

more pronounced at higher bogie impact velocities. A more thorough discussion of the 

rate-effect parameters is given in the wood model user’s manual.(2)
 44

Table 3. Approximate tensile strength ratios versus strain rate for saturated pine. 

Rate (s-1

) R(0°) R(90°) 

0 

10 

500 

1000 

 1.0 

 1.01 

 1.3 

 1.6 

 1.0 

 1.2 

 7.2 

12.6 

Post Breakage: The bogie impact test report does not indicate the time or deflection at 

which the post broke completely in two. The simulated deformed configurations 

previously shown in figure 37 indicate that the breakage is incomplete at 180 mm, which 

is the final deflection of the performance envelope plots. Although this may or may not 

be correct, parametric studies were performed and it was determined that adjustments 

in the quality factors affect the deflection at which the post breaks in two. This is 

demonstrated in figure 43. Here, the default quality factors were adjusted for grade 1 

pine from QT = 0.47 and QC = 0.63 to QT = 0.4 and QC = 0.7. The trend noted is that the 

post will break earlier in time as QT is adjusted downward and QC is adjusted upward. 

The load-deflection and bogie velocity-reduction curves calculated with either set of 

quality factors look similar (as shown in figure 44). 
 45

C

(a) QT = 0.47 and QC = 0.63 (b) QT = 0.40 and QC = 0.70 

Figure 43. These deformed configurations at 180 mm of deflection indicate that 

adjustments in the quality factors affect the deflection at which the grade 1 pine 

post breaks in two. 

 

 (a) Energy versus deflection (b) Velocity versus time 

Figure 44. Although the grade 1 pine post breaks earlier in time with QT = 0.40 and 

QC = 0.70, the calculated energy and velocity histories are similar. 
 
 47

7 ADDITIONAL EVALUATION CALCULATIONS 

A number of LS-DYNA parameter calculations were performed in order to understand 

wood model issues related to: (1) plasticity algorithm iterations, (2) use of fully 

integrated elements, (3) the erosion criteria, and (4) the assumption of perfect plasticity. 

These issues are discussed here for both the static post and dynamic bogie impact 

simulations. 

7.1 PLASTICITY ALGORITHM ITERATIONS 

Static post bending simulations indicate that the calculated load-deflection curves are 

insensitive to the number of plasticity algorithm iterations. Figure 45 demonstrates that 

there is little difference in the load-deflection curves calculated with one or five 

iterations. However, bogie impact calculations performed with five iterations produced 

erroneous behavior in which damage, followed by erosion, was overcalculated. 

All default parameters were selected from static and dynamic calculations performed 

with one iteration. Therefore, one iteration is selected as the default number of 

iterations. The user may override this number. Caution is suggested when using more 

than one iteration because the iterations parameter has not been thoroughly evaluated. 

Additional evaluations of the iterations parameter are recommended for future efforts. 

Figure 45. The default number of plasticity algorithm iterations is set to one 

because these static load-deflection curves are insensitive to the number of 

iterations. 
 48

7.2 FULLY INTEGRATED ELEMENTS 

The static post peak-load deflection comparisons previously shown in figure 27 indicate 

that the fully integrated S/R (type 2 eight-point integration) elements produce a more 

brittle behavior than the standard under-integrated elements. This is probably because 

the fully integrated elements erode when just one of the eight integration points fails. By 

failure, we mean that the wood material model calculates a 99.9-percent reduction in 

stiffness and strength (in all six stress components both parallel and perpendicular to 

the grain) at that integration point. Therefore, seven of the eight integration points could 

still be loaded in tension when the element erodes. 

As a check, static bending calculations were performed with and without erosion using 

both the standard and fully integrated elements (as shown in figure 46). There is 

essentially no difference between the responses calculated with and without erosion 

when standard elements are used (not shown). However, some difference is calculated 

when fully integrated elements are used. This indicates that the fully integrated 

elements are eroding prematurely (while still carrying load). One possible consequence 

of premature erosion is a fracture energy that is mesh-size sensitive and problemdependent. 

Figure 46. Erosion affects the fully integrated element curves, but not the underintegrated element curves, indicating that the fully integrated elements erode 

while still carrying load. 

Roadside safety applications are primarily dynamic, so bogie impact simulations were 

also performed with fully integrated elements in the breakaway region for comparison 

with under-integrated elements. Deformed configurations with damage fringes are 

shown in figure 47. Energy-deflection and velocity-reduction histories are shown in 

figure 48. The damage fringes and histories calculated with eight-point integration are 

similar to those calculated with single-point integration. These bogie impact simulations 

suggest that eight-point integration can currently be used in the breakaway region of 

bogie impact simulations; however, analysts are urged to use it with caution. Preliminary 
 49

calculations performed with eight-point integration in the impact region simulate 

excessive erosion. Therefore, use of eight-point integration in the impact region is not 

currently recommended. 

C

(a) With eight-point integration (b) With one-point integration 

Figure 47. Deformed configurations and fringes of damage calculated with fully 

integrated elements (eight points) are similar to those calculated with underintegrated elements (one point). 

 (a) Energy versus deflection (b) Velocity versus time 

Figure 48. Energy-deflection and bogie velocity-reduction histories are not 

strongly influenced by the type of element formulation (eight points or one point) 

modeled in the breakaway region. 
 50

7.3 EROSION CRITERIA 

Checks were also performed on the erosion criteria. As the default setup, elements 

erode when failure occurs parallel to the grain because all six components of stress are 

degraded to near zero. Elements do not erode when failure occurs perpendicular to the 

grain because only three components of stress (perpendicular to the grain) are 

degraded to near zero. The parallel-to-the-grain stress components are not degraded 

with perpendicular damage. Thus, the element is still able to carry load parallel to the 

grain after perpendicular failure occurs. All default parameters were selected from static 

and dynamic calculations performed with the default erosion criteria. 

As an option, a flag is included to request erosion once perpendicular-to-the-grain 

failure occurs. For simplicity, this flag is called the perpendicular erosion flag and this 

erosion option is referred to as perpendicular erosion. Both static and dynamic 

simulations were performed with and without perpendicular erosion. The static 

calculations are discussed first, followed by the dynamic calculations. 

Static deformed configurations and load-deflection curves are shown in figures 49 and 

50, respectively, for calculations performed with and without perpendicular erosion. The 

deformed configuration calculated with perpendicular erosion is more realistic than the 

deformed configuration calculated without perpendicular erosion. To see the 

perpendicular damage in the calculation without perpendicular erosion, one can look at 

damage fringes (as shown in figure 49(c)). Red denotes elements with damage levels of 

d > 0.80, blue denotes elements with a damage range of 0.60 < d < 0.80, and cyan 

denotes elements with a damage range of 0.40 < d < 0.60. 

Perpendicular erosion also has a minor effect on the static load-deflection curves. The 

post-peak softening behavior calculated with perpendicular erosion is slightly more 

brittle than that calculated without perpendicular erosion (figure 50). 

Dynamic deformed configurations and load-deflection curves are shown in figures 51 

and 52, respectively, for calculations performed with and without perpendicular erosion. 

As similarly noted for the static simulations, the breakaway region calculated 

dynamically with perpendicular erosion looks more realistic than that calculated without 

perpendicular erosion. However, slight erosion is also calculated in the impact region 

even though no visible damage was reported in the tests. Perpendicular erosion has 

little demonstrated effect on the load-deflection curves. 
 51

(a) Without perpendicular (b) With perpendicular (c) Fringes of damage 

 erosion erosion 

Figure 49. The breakaway region calculated with perpendicular erosion in these 

static bending simulations looks more realistic than that calculated without 

perpendicular erosion; however, perpendicular erosion is not recommended for 

practical use. 

Figure 50. Load-deflection curves calculated with perpendicular erosion are 

slightly more brittle than those calculated without perpendicular erosion. 
 52

C

 (a) With perpendicular erosion (b) Damage fringes without 

perpendicular erosion 

Figure 51. The breakaway region calculated with perpendicular erosion in this 

bogie impact simulation looks more realistic than that calculated without 

perpendicular erosion. 

 (a) Energy versus deflection (b) Velocity versus time 

Figure 52. Dynamic load-deflection and bogie velocity-reduction curves 

calculated with perpendicular erosion are nearly identical to those calculated 

without perpendicular erosion. 

In fact, in some cases, perpendicular erosion can have an unrealistic effect on the 

calculated response. Some preliminary calculations performed with the simplest elastic 

bogie (without neoprene on the cylinder) simulated excessive erosion in the impact 
 53

region. One such calculation is demonstrated in figure 53. One possible approach is to 

request perpendicular erosion in the breakaway region, but not request it in the impact 

region. Therefore, perpendicular erosion is not the default option (it must be specifically 

requested), nor is it recommended for general use. 

C

Figure 53. Use of perpendicular erosion causes excessive erosion to be 

calculated in the impact region in this preliminary bogie impact calculation. 

7.4 POST-PEAK HARDENING PARAMETER 

The default behavior of the wood model is perfectly plastic in both parallel- and 

perpendicular-to-the-grain compression. This means that there is no increase or 

decrease in strength with increasing strain. Perfectly plastic behavior was previously 

demonstrated in figure 1(c). 

The FPL clear wood and timber compression data previously analyzed in figures 3 and 

5 exhibit perfect plasticity, at least for perpendicular strains as great as 4 percent. 

However, parallel strains of 20 to 30 percent are typically calculated at ground level in 

the compressive region of the post in the bogie impact calculations. Recent 

uninstrumented, unconfined compression tests of pine samples conducted by the user 

indicate softening at large strain parallel to the grain and hardening perpendicular to the 

grain. 

Post-peak softening in compression (parallel or perpendicular) is not currently available 

in the wood material model. Although the damage model (which is responsible for 

softening) is applied to the stresses in compression, the stresses do not soften, 

because a compressive fracture energy of infinity is assumed. Fracture energy in 

compression is not currently an input value (as it is for tension and shear). Infinite 
 54

fracture energy is hardwired into the model. To elicit softening, finite fracture energy 

needs to be included as input. 

 

Post-peak hardening in compression is currently available as an option in the wood 

model. Single-element simulations with and without post-peak hardening are 

demonstrated in figure 54 parallel to the grain. Post-peak hardening requires the input 

of a single hardening parameter. A value of zero models perfect plasticity. Values 

greater than zero model hardening. At this time, the same parameter is used for both 

parallel and perpendicular modes (because of the limited input parameter slots available 

during development as a user-supplied material model). Separate parameters are 

recommended as a future modification to the model. 

Figure 54. These single-element simulations demonstrate post-peak hardening in 

compression with positive values of Ghard. 

All default parameters were selected from calculations run with perfect plasticity in 

compression. Small amounts of post-peak hardening have little effect on the static or 

bogie impact simulations. However, calculations involving high levels of compaction 

may benefit from post-peak hardening. This is demonstrated in figure 55 for a 

calculation performed with post-peak hardening (parallel and perpendicular). The post 

exhibits substantial compression in the elements in the vicinity of the rigid support. 

However, this same calculation aborted, prior to achieving the deformed configuration 

shown, when perfect plasticity was modeled. 
 55

C

Figure 55. Inclusion of post-peak hardening, both parallel and perpendicular to 

the grain, prevented this calculation from aborting at a large deflection. 

Recommendations for future efforts include laboratory compression measurements and 

wood model enhancements. The laboratory compression measurements should include 

stress displacement and fracture energy for clear wood and graded wood samples, both 

parallel and perpendicular to the grain. These measurements should be made as a 

function of moisture content. If these measurements show softening, as recently 

measured parallel to the grain, then model enhancements should proceed. The wood 

model enhancements should include an input slot for compressive fracture energy; 

smooth variation of the fracture energy between compression, shear, and tension; and 

identification of default compressive fracture energy values as a function of moisture 

content. If these measurements show hardening, as recently measured perpendicular to 

the grain, then the existing post-peak hardening model should be evaluated for 

accuracy and for selection of default post-peak hardening parameters. Some porous 

materials exhibit substantial stiffening at high strain levels (70 to 80 percent) after all 

pores are compacted, which is called lockup. The current post-peak hardening 

formulation does not model lockup. The need for a lockup model should be assessed 

with regards to roadside safety applications. 
 
 57

8 DEVELOPER’S SUMMARY AND RECOMMENDATIONS 

A wood material model was developed, implemented into the LS-DYNA finite element 

code, and evaluated for use in roadside safety applications. Eight evaluation 

calculations (four quasi-static and four dynamic) were performed by the developer with 

the results documented in chapters 1 through 7 of this report. The main evaluation 

calculations were dynamic bogie impact at 9.6 m/s into southern yellow pine (grade 1 

unfrozen, grade 1 frozen, and DS-65 unfrozen) and Douglas fir (grade 1) posts. The 

wood model calculates post breakage just below ground level (in agreement with the 

measured breakage locations). The wood model also calculates bogie kinetic energy 

and velocity reductions that are in reasonable agreement with final measured quantities. 

However, the evaluation calculations indicate some limitations in both the test data and 

model formulation. Recommendations for future efforts, based on these limitations, are 

itemized here. These enhancements are not required for achieving good correlation 

between the wood model and post data. 

1. Parallel Fracture Energy: Perform quasi-static tensile tests of clear wood 

specimens to directly measure the parallel-to-the-grain fracture energy as a 

function of moisture content. 

Fracture energy is the area under the stress-displacement curve from peak 

stress to zero stress, measured during unconfined tension tests conducted 

parallel to the grain. Parallel fracture energy is an important input parameter 

whose value has a strong effect on post response in bogie impact and static 

bending simulations. Although the suite of FPL clear wood pine data 

implemented into the wood model as default properties is quite extensive, it does 

not include fracture energy measurements. Therefore, correlations with bogie 

impact and static bending test data were used to set the default fracture 

energies. However, the parallel fracture energy selected from the static bending 

correlations is five times greater than that selected from the bogie impact 

correlations. This should be clarified. 

A minimum of 15 quasi-static tensile tests of clear wood pine are recommended 

in order to develop quadratic equations for parallel fracture energy as a function 

of moisture content. These tests should be conducted at five moisture content 

levels, with each test repeated three times. Additional tests conducted on grade 2 

and DS-65 pine would provide information on the variation of fracture energy as 

a function of grade. Dynamic tensile tests (e.g., at 0.1 or 1.0 s-1 (a typical strain 

rate in the post)) would also provide useful information on the variation of fracture 

energy with strain rate. 

2. Perfect Plasticity: Perform quasi-static compression tests of clear and graded 

wood pine specimens to moderate compression levels to evaluate the 

assumption of perfect plasticity in compression. 

 
 58

The wood material model simulates perfectly plastic behavior in compression 

both parallel and perpendicular to the grain (as the default behavior). An option is 

also included to model post-peak hardening in compression; however, no option 

is included to model softening in compression. 

FPL conducted a suite of laboratory compression tests on clear wood samples 

for strain levels up to about 4 percent that were used to set the model behavior. 

The measured stress-strain data indicate that perfect plasticity is a reasonable 

assumption (at least for strains up to 4 percent). However, parallel strain levels 

up to 30 percent are noted in the bogie impact simulations. Therefore, the user 

conducted a few quick-look compression tests of graded pine specimens for 

strains up to 90 percent. Their measured stress-strain data indicate softening 

parallel to the grain and hardening perpendicular to the grain.1

Future efforts could generate hardening and/or softening data for wood in 

compression to moderate strain levels (about 30 percent). A suite of tests are 

recommended for clear wood and two grades of saturated pine (grade 1 and 

DS-65) to obtain plots of load versus axial and lateral deflection for strains up to 

30 percent. Tests should be conducted both parallel and perpendicular to the 

grain as a function of moisture content. If a review of the test data indicates that 

softening is evident, then a compressive softening formulation is recommended 

for implementation, which may or may not affect post fracture. It is not clear to 

the developer that a compressive softening formulation is needed or that it would 

enhance post fracture behavior. 

3. Quality Factors: Perform static tensile and compression tests of dry, partially 

saturated, and saturated pine to determine how quality factors vary as a function 

of moisture content. 

The suite of pine data implemented into the wood model as default properties is 

for clear wood, whereas real posts are graded wood such as grades 2, 1, or 

DS-65. Clear wood is stronger than graded wood. The approach for setting 

default properties for graded wood is to apply quality factors (strength-reduction 

factors) to the clear wood to account for reductions in strength as a function of 

grade. Two quality factors are set. One quality factor is applied to the tensile and 

shear strengths, the other is applied to the compressive strengths. 

Default quality factors are estimated from correlations of calculations with static 

bending test data. However, the quality factors estimated from simulations of the 

user’s saturated-post bending tests are about twice as high as those estimated 

from the simulation of FPL’s partially saturated timber-bending tests. This 

suggests that quality factors vary as a function of moisture content. Quality 

 

1

The measured hardening behavior perpendicular to the grain was unexpected. It looked similar to the 

behavior of the isotropic porous materials in uniaxial strain, not uniaxial stress. This unexpected behavior 

may be because wood is orthotropic. 
 59

factors currently implemented in the model as default properties are those from 

the saturated-post correlations. 

Static tests (compression and tension) of graded wood are recommended at a 

minimum of three moisture content levels in order to develop quadratic equations 

for quality factors as a function of moisture content. Conducting compression and 

tension tests, rather than bending tests, would isolate the tensile quality factors 

from the compressive factors. A related issue is whether the same quality factors 

should be applied perpendicular to the grain as those applied parallel to the 

grain, as is the current default implementation (although an option is available to 

neglect quality factors perpendicular to the grain). If possible, tests should be 

conducted both parallel and perpendicular to the grain. 

4. Coupling Between Parallel and Perpendicular Modes: Evaluate and enhance 

the parallel and perpendicular yield surface and plasticity formulations to include 

coupling between the parallel and perpendicular modes. Evaluation of such 

coupling would require measurement of the volume expansion/contraction 

(effective Poisson’s ratio in the plastic region) behavior of wood. 

One theoretical limitation of the wood model is that there is no coupling between 

the parallel and perpendicular modes in the plastic region. Such coupling affects 

volumetric behavior. The suite of clear wood data provided by FPL included 

measurement of the major Poisson’s ratio in the elastic region. Typical values are 

around νLT = 0.16 for pine at the fiber saturation point. No measurements were 

reported for the effective Poisson’s ratio in the plastic/damage regions (once the 

material yields or softens). The effective Poisson’s ratio is the ratio of the lateral 

strain to the axial strain in uniaxial stress tests (without lateral confinement). 

Porous materials tend to flow during yielding and softening, which can result in 

an effective Poisson’s ratio that is larger or smaller than the elastically measured 

value. For example, for porous geological materials such as concrete, the 

effective Poisson’s ratio is typically modeled as being greater than the elastic 

ratio in unconfined compression (with values greater than 1) and less than the 

elastic ratio in unconfined tension. 

The user has examined the behavior of the wood model for single elements of 

pine in unconfined tension. An increase in the volume of the element was noted. 

The user believes that there should be no change in the volume of wood in 

tension (i.e., wood is incompressible). To achieve no change in volume, the 

elastic and effective Poisson’s ratios would have to be 0.5. The FPL data indicate 

that the elastic Poisson’s ratio parallel to the grain is not 0.5. However, no lateral 

strain or change in volume measurements is available to confirm or refute an 

effective Poisson’s ratio of 0.5 in the plastic region. Therefore, we recommend 

that all additional test data generated should include lateral strain measurements. 

The unconfined compression and tension tests recommended in items 2 and 3 

above should include measurement of both axial and lateral strain. 
 60

Setting the compressibility or effective Poisson’s ratio behavior of the wood 

model is not simply a matter of specifying an input value, rather, it requires that 

changes be made to the formulation of the model to include coupling between 

the parallel (axial) plasticity and perpendicular (lateral) plasticity. The current 

wood model includes separate yield surfaces and plasticity computations for 

yielding parallel and perpendicular to the grain. As a result, yielding parallel to the 

grain does not induce plastic flow perpendicular to the grain. Similarly, yielding 

perpendicular to the grain does not include plastic flow parallel to the grain. We 

recommend exploring and implementing methods of coupling the plastic flow 

once sufficient test data are generated to set the coupling via measurement of 

the effective Poisson’s ratio or volume change. This could be done regardless of 

whether or not the tests indicate incompressibility. 

5. Erosion Method: All erosion criteria could be enhanced to be user-specified, 

including the damage-based criteria. Future efforts could also include 

modifications, additions, and/or elimination of the distorted element checks and 

possible inclusion of an input flag to turn these checks on and off. 

The primary erosion mechanism is based on damage. Element erosion, by 

default, is based on parallel damage in excess of 99 percent. Erosion, by option, 

may also be based on perpendicular damage in excess of 98.9 percent. As 

element damage approaches 99 percent, strength and stiffness approach 

1 percent of their original values. Elements with nearly zero strength and stiffness 

could possibly experience shooting nodes and drastically deform, invert, expand, 

or contract in response to very small loads. Such behavior can cause a 

calculation to abort. Element erosion is a technique that prevents the calculation 

from aborting by removing these elements from the calculation before large 

distortions occur. Erosion also provides a good visual image of breakage in the 

damage region. 

Because elements do not automatically erode with perpendicular damage, the 

model includes a check on the maximum strains perpendicular to the grain to 

determine whether they are greater than 90 percent. If so, the element erodes if 

perpendicular damage has already exceeded 98 percent. 

 

In addition to the damage-based erosion criteria, a number of checks are 

implemented in the model to prevent highly distorted elements from causing 

computational problems. These distorted element checks were implemented for 

the explicit purpose of debugging the model during use of the user-defined 

material model interface and do not necessarily need to be retained in the final 

model. They include: 

• A check on the element volume to determine whether it is less than zero. 

• A check on the current relative volume to determine whether it is less than 

10 percent. 
 61

• A check on the maximum strain increment to determine whether it is greater 

than 1 percent. 

Element erosion will occur if any of these conditions are met. 

6. Mesh-Size Dependency: Future efforts could include direct-pull and unconfined 

compression simulations of wood specimens at different mesh refinements to 

demonstrate mesh-size response. The issue here is to isolate the material 

response without the complicating effects of other materials and contact issues. 

A related issue that is recommended for evaluation is whether to use the initial 

element length or the updated element length in the calculation of the damage 

parameter. The updated element length is currently implemented. Damage is 

based on element length in an effort to regulate mesh-size sensitivity. 

7. Iterations Parameter: Evaluate and enhance the plasticity algorithm iterations 

method. 

The plasticity algorithm returns the stress state to the yield surface if the elastic 

stress state is predicted to lie outside the yield surface. The purpose of the 

iterations parameter is to increase the accuracy of the return through iteration 

and subsequent tolerance checks to ensure that the stress state lies on the yield 

surface. Static calculations indicate that one iteration is just as accurate as five 

iterations. In contrast, bogie impact simulations calculate excessive damage and 

erosion with five iterations. Therefore, the default number of iterations has been 

set to one. Future model enhancements should include debugging of the 

iterations parameter for dynamic applications. 

8. Accelerometer Measurements: Perform future bogie impact tests with 

measurements made on the post rather than on the bogie. 

The force-deflection and energy-deflection performance envelopes from the 

user’s bogie impact tests are measurements processed from an accelerometer 

located at the center of the bogie frame. The high-frequency measurements are 

filtered to produce a smooth signal. Because all measurements are made on the 

bogie rather than on the post, good correlations between the calculations and the 

processed data require an accurate bogie model (geometric and material) as well 

as an accurate wood post model. 

Calculations completed to date indicate that the computed bogie accelerations 

strongly depend on the bogie model type (rigid or elastic) and output sampling 

rate. For example, the calculated bogie acceleration (force) histories contain a 

higher frequency content than that measured. The calculated histories are also 

more oscillatory than those measured. On the other hand, computed force 

histories derived from cross-sectional forces in the post are much less sensitive 

to the sampling rate and bogie model type than those derived from the bogie 
 62

accelerometer location. This suggests that measurements recorded directly on 

the post would isolate wood performance and facilitate evaluation of the wood 

model. Instrumenting the wood posts could prove to be a challenging endeavor. 

9. Boundary Conditions: Perform future static and bogie impact tests on posts 

with well-defined boundary conditions. 

Posts are typically situated in highly deformable media, such as soil. Therefore, 

static and bogie impact tests were intended to be conducted under fixed-base 

conditions. The posts in the static tests were placed in a rigid base with steel and 

neoprene shims to wedge the post into the support. The posts in the dynamic 

tests were loosely placed in a steel tube in the ground and wedged in with 

neoprene and plywood shims. 

LS-DYNA results calculated with simple (post nodal constraints) to sophisticated 

(support and neoprene modeled explicitly) meshes produce different 

computational results. Performing future tests with simple, easy-to-model 

boundary conditions would help with future evaluation of the wood model.
 63

9 USER'S INTRODUCTION 

The calculations and conclusions of chapters 9 through 16 were conducted and 

documented by the user. 

Several finite element models were developed throughout the validation effort, including 

single-element models for tension and compression, a cube crushing model, several 

static wood post testing models, and a dynamic wood post testing model. 

As a first step in the simulation validation effort, the user successfully reproduced 

results obtained by the developer on the user’s computers. Next, the user applied the 

new wood material model to several different methods not attempted by the developer. 

Several areas of concern were revealed at this stage. These concerns are documented 

throughout chapters 9 through 16. 

The majority of the simulations reported in this document were performed using 

LS-DYNA, version 970, revision 1812, compiled on June 7, 2002, on both PC Windows 

and SGI® UNIX-based machines. All areas of concern listed in this report were tested 

on this latest version of the wood model. 
 
 65

10 VALIDATION CRITERIA FOR THE WOOD MATERIAL 

MODEL 

To validate the wood material model, several criteria must first be developed in order to 

determine whether the model is working as desired. To this end, the validation process 

at the user’s facility consisted of verifying that the results were similar on different 

computer platforms (chapter 11) by simulating single-element models in order to check 

basic fundamental behavior (chapter 12), simulating static wood post tests (chapter 13), 

simulating dynamic wood post tests (chapter 14), checking the sensitivity of the 

simulation models by varying numerous parameters (throughout chapters 12, 13, and 

14), and by simulating wood-cube crushing tests performed in parallel with this project. 

Because of time constraints, the cube crushing test and simulation were not revisited in 

this final report. Interested readers are urged to contact the user for details. 

10.1 NDOR TESTS: PERFORMANCE ENVELOPES 

In 1995, the user ran a series of static and dynamic post testing for the Nebraska 

Department of Roads (NDOR). The series consisted primarily of 152.4-mm by 

203.2-mm by 1828.8-mm (6-inch by 8-inch by 72-inch) southern yellow pine of various 

grades and ages. The wood posts were obtained from previously installed guardrail 

systems throughout Nebraska. A smaller series of dynamic tests using frozen southern 

yellow pine and Douglas fir wood posts were also conducted. 

Data collected from the 1995 NDOR project were to be used for validating the wood 

material model. Based on several meetings and discussions, the simulation user 

community requested that the wood material model have specific options for selecting 

southern yellow pine of grades DS-65 and 1/1D (among other options). In order to 

validate the material model for those specific cases, the 1995 NDOR data were 

completely analyzed to determine the appropriate tests with which to compare the 

simulation results. The details for the results of this analysis are not presented herein; 

however, interested readers are urged to contact the user for details. Grades 1 and 1D 

wood post test results showed very little difference in behavior; thus, this report will use 

the terminology of grade 1 to represent the combined grades 1 and 1D. 

Performance envelopes were constructed using the most typical behavior of the desired 

wood and grades for both static and dynamic test conditions (see figure 56). Forcedeflection and energy-deflection results from the simulations would need to fall within 

the performance envelopes in order to be considered validated. Photographs from the 

testing are presented in figures 57 through 61. 
 66

 (c) Grade DS-65 energy (d) Grade 1 energy 

Figure 56. Performance envelopes from 1995 NDOR testing. 

(a) Grade DS-65 force (b) Grade 1 force 
 67

Figure 57. Static post setup. 

 (a) Post and bogie vehicle (b) Post 

Figure 58. Dynamic post setup. 
 68

DS-65 

 Grade 1D 

 Grade 1 

Figure 59. Typical static post test results. 

(a) DS-65 post (b) DS-65 closeup 

(c) Grade 1D post (d) Grade 1D closeup 

(e) Grade 1 post (f) Grade 1 closeup 
 69

DS-65 

Grade 1D 

Grade 1 

Figure 60. Typical dynamic post test results. 

(a) DS-65 breakage 

(c) Grade 1D breakage 

(e) Grade 1 breakage 

(b) DS-65 post 

(d) Grade 1B post 

(f) Grade 1 post 
 70

 

(a) Clean break 

 

(b) Atypical behavior 

Figure 61. Other dynamic post test results. 
 71

11 VERIFICATION OF RESULTS ON DIFFERENT COMPUTER 

PLATFORMS 

In this section, a comparison of three different types of models using the developer’s 

wood model in LS-DYNA is made using different computer platforms. The results from 

an Intel®-based PC (using Windows) are provided by the developer, while the results 

from an SGI Octane® (using UNIX) are provided by the user. Although the results are 

shown to be somewhat different on the different computer platforms, they are 

considered to be within an acceptable range based on previous experiences using 

different computers. This phenomenon is well known and is documented in the 

LS-DYNA user’s manual. It is a computer platform issue and not a software issue. 

The models discussed in this section are good for verifying the accuracy of the codes 

between computer platforms, but are shown to be unacceptable for validating the wood 

model itself as an accurate material for modeling wood in roadside hardware 

applications. However, investigating the wood material model itself is left for the 

remaining sections of this report. 

11.1 SINGLE-ELEMENT MODELS 

Four single-element models were run to check the consistency between PC (Intel)-

based computers and SGI-based computers. The specific results for each model are 

described in tables 4, 5, 6, and 7 below. In general, for single-element models, PC and 

SGI computers give equivalent results. Material summaries (matsum) and global 

statistics (glstat) were consistent throughout. Also, displacements were consistent 

throughout. 

Table 4. Model Cfa: Uniaxial Compression in Parallel Direction 

Output File 

Examined Variables Checked Differences Between Computers 

d3plot (history) Effective stress No visible differences 

glstat Internal energy, kinetic 

energy, and time-step size No visible differences 

Matsum Internal energy and kinetic 

energy 

No visible differences 
 72

Table 5. Model Cfe: Uniaxial Compression in Perpendicular Direction 

Output File 

Examined Variables Checked Differences Between Computers 

d3plot (history) x-stress, z-stress, and 

pressure 

No visible differences 

Glstat Internal energy, kinetic 

energy, and total energy No visible differences 

Table 6. Model Tfa: Uniaxial Tension in Parallel Direction 

Output File 

Examined Variables Checked Differences Between 

Computers 

d3hsp Inertial tensor and principal 

directions 

Slight differences for values 

that are near zero 

d3plot (history) 

Nodal: x, y, and z 

displacements 

Element: plastic strain and 

stress 

No visible differences 

Glstat Time-step size No visible differences 

Matsum 

Internal energy 

Kinetic energy 

No visible differences 

Slight difference; however, 

magnitudes are very small 

(E-6) 

Table 7. Model Tfe: Uniaxial Tension in Perpendicular Direction 

Output File 

Examined Variables Checked Differences Between Computers 

d3plot (history) Plastic strain, stress, and 

pressure 

No visible differences 

Glstat Internal energy and timestep size No visible differences 

Matsum Internal energy No visible differences 
 73

11.2 DYNAMIC POST TEST SIMULATION: BOGIE MODEL 

This model is a rather detailed model of the dynamic post tests performed at the user’s 

facility. As evidenced in figures 62 through 67, the results from the developer’s 

computers match the results from the user’s computers very well for the first 15 ms of 

simulation. After that time, the results begin to diverge a little with regards to the contact 

forces and internal energy absorbed by the post (as shown in figures 64 and 66, 

respectively). Overall, agreement between the results is acceptable. 

Model Validity: Although the developer and the user are getting nearly the same 

results for this model, the model itself is unacceptable for evaluating the validity of the 

wood model. This is because the contact between the wood and the neoprene-lined 

concrete sleeve is not behaving appropriately (as shown in figure 68). The 

interpenetration of the neoprene into the wood causes a local lockup that prevents the 

post from sliding along that edge. 

Developer’s 

Results 

User’s Results 

Figure 62. Impact sequence of post simulation. 

(a) 0 ms (developer) (b) 10 ms (developer) (c) 30 ms (developer) 

(d) 0 ms (user) (e) 10 ms (user) (f) 30 ms (user) 
 74

 

(a) Developer’s results 

(b) User’s results 

Figure 63. Damage (stored as effective plastic strain in d3plot files). 
 75

 

Figure 64. Contact forces. Figure 65. Cross section at ground level. 

 Figure 66. Energy of post parts. Figure 67. Bogie velocity.

Figure 68. Contact penetrations caused locking of parts. 

[ms] 

X-force [kN] 
 76

11.3 DYNAMIC POST TEST SIMULATION: FAST BOGIE MODEL 

The fast bogie model is a simplification of 

the bogie model described above. This 

model was generated by the developer to 

speed up the calculation time. As 

evidenced in figures 69 through 71, the 

results from the developer’s computers 

match the results from the user’s 

computers very well for the first 10 ms of 

simulation. After that time, the results 

begin to diverge. Overall, agreement 

between the results is acceptable, 

considering the crudeness of the model. 

Model Validity: Because of the 

excessive bending of the post without 

total fracture at ground level, this model 

is considered to be unacceptable for 

evaluating the validity of the wood model. 

Figure 69. Sequence of fast bogie simulations. 

(e) 40 ms (developer) (f) 40 ms (user) 

(a) 0 ms (developer) 

(c) 10 ms (developer) 

(b) 0 ms (user) 

(d) 10 ms (user) 
 77

Figure 70. Energy of post parts for fast bogie simulation. 

Figure 71. Section forces through post just below impact: Fast bogie simulation. 

Time [ms] 
 
 79

12 SINGLE ELEMENT: TENSION PARALLEL TO THE GRAIN 

A single solid element is used to study the developer’s wood material model in uniaxial 

tension parallel to the grain. Specifically, a parameter study investigating the southern 

yellow pine option is performed. The parameters investigated are wood grade, moisture 

content, and temperature. Stress-strain curves, volume-time curves, and changes in the 

29 wood parameters (as reported in the d3hsp file) are presented. 

The stress-strain behavior of the single element in tension is as desired. In all cases, 

stress increases linearly with respect to strain until a peak strength is reached, followed 

by a gradual decrease in stress as the material undergoes damage and eventually fails. 

With respect to wood grade, increasing strength is observed as the grade is improved. 

With respect to moisture content, fully saturated wood is relatively weak, but ductile. As 

the moisture content decreases, the material becomes stronger and more brittle. When 

the wood becomes very dry, the strength decreases, yet maintains a brittle behavior. 

With respect to temperature, low-temperature pine is relatively strong, yet brittle, while 

wood at a high temperature is relatively weak and ductile. 

The volume of the single elements in tension parallel to the grain uniformly increases 

during all simulations by as much as 6 percent. This is an unexpected and undesirable 

result because it is believed by the user that, at a minimum, volume should be 

conserved for wood. A significant example of this volume expansion is shown in 

chapter 14 of this report. 

Because of time limitations, various other single-element simulations were not 

performed, but are recommended (including compression, shear, and torsion loading 

both parallel and perpendicular to the grain).
 80

12.1 STRESS-STRAIN BEHAVIOR: *MAT_WOOD_PINE 

In all cases, stress increases 

linearly with respect to strain until a 

peak strength is reached, followed 

by a gradual decrease in stress as 

the material undergoes damage and 

eventually fails. 

With respect to wood grade, 

increasing strength is observed as 

the grade is improved. 

With respect to moisture content, fully 

saturated wood is relatively weak, but 

ductile. As the moisture content 

decreases, the material becomes 

stronger and more brittle. When the 

wood becomes very dry, the strength 

decreases, yet maintains a brittle 

behavior. 

With respect to temperature, lowtemperature pine is relatively strong, 

yet brittle, while wood at a high 

temperature is relatively weak and 

ductile. 

Figure 72. Stress-strain behavior of single elements. 

(a) Variation by grade 

(b) Variation by moisture 

(c) Variation by temperature 

°C 
 81

12.2 VOLUME OF ELEMENT: *MAT_WOOD_PINE

The volume of the single 

element in tension parallel to 

the grain uniformly increases 

during all simulations by as 

much as 6 percent. This is an 

unexpected and undesirable 

result because it is believed by 

the user that, at a minimum, 

volume should be conserved 

for wood. A significant example 

of this volume expansion is 

shown in chapter 14 of this 

report.

Note: The drop-off of volume on 

curves is where failure of the 

element occurs.

Figure 73. Volumetric behavior of single elements.

(a) Variation by grade 

(b) Variation by moisture 

Volume [mm3] (E+3) Volume [mm3] (E+3) Volume [mm3] (E+3) 

°C 

(c) Variation by temperature 

Time [ms] 
 82

12.3 MATERIAL PROPERTIES: *MAT_WOOD_PINE 

When using the *MAT_WOOD_PINE option, the user specifies parameters such as 

wood grade, moisture content, and temperature. However, the underlying wood material 

model is based on a large set of theoretical parameters. By setting the wood grade, for 

example, the underlying parameters are modified appropriately. This section provides a 

set of tables (tables 8, 9, and 10) that record the variations in the underlying parameters 

based on changing a single parameter. 

Table 8. Parameters based on wood grade. 

Single Solid Element – Uniaxial Tension Parallel to the Grain 

Units kg, mm, ms, kN, GPa 

Density 6.731E-07 kg/mm3 

*MAT_WOOD_PINE 

Default Parameters Except for Grade 

Stiffmess: Grade 1 

(default) 

Grade DS-65 Grade Clear 

EL Parallel Normal Modulus 11.350000 

ET Perpendicular Normal Modulus 0.246800 

GLT Parallel Shear Modulus 0.715200 

GLR Perpendicular Shear Modulus 0.087510 

PR Parallel Major Poisson’s Ratio 0.156800 

 

Strength: 

Xt Parallel Tensile Strength 0.040030 0.068130 0.085160 

Xc Parallel Compressive Strength 0.013320 0.019670 0.021150 

Yt Perpendicular Tensile Strength 0.000963 0.001640 0.002050 

Yc Perpendicular Compressive Strength 0.002571 0.003796 0.004082 

Sxy Parallel Shear Strength 0.004275 0.007277 0.009096 

Syz Perpendicular Shear Strength 0.005985 0.010190 0.012730 

 

Damage: 

Gf1 Parallel Fracture Energy in Tension 0.020050 0.034130 0.042660 

Gf2 Parallel Fracture Energy in Shear 0.041480 0.070610 0.088260 

Bfit Parallel Softening Parameter 30.000000 

Dmax Parallel Maximum Damage 0.999900 

Gf1 Perpendicular Fracture Energy in Tension 0.000401 

Gf2 Perpendicular Fracture Energy in Shear 0.000830 

Dfit Perpendicular Softening Parameter 30.000000 

Dmax Perpendicular Maximum Damage 0.990000 

 

Rate Effects: 

Flpar Parallel Fluidity Parameter: Tension/Shear 0.000 

Flparc Parallel Fluidity Parameter: Compression 0.000 

Pow_par Parallel Power 0.000 

Flper Perpendicular Fluidity Parameter: Tension/Shear 0.000 

Flperc Perpendicular Fluidity Parameter: Compression 0.000 

Pow_per Perpendicular Power 0.000 

 

Hardening: 

Npar Parallel Hardening Initiation 0.500 

Cpar Parallel Hardening Rate 1008.000 462.500 400.000 

Nper Perpendicular Hardening Initiation 0.400 

Cper Perpendicular Hardening Rate 252.000 115.600 100.000 

 

Note: Only those values that changed because of the change in grade are provided in the table. 
 83

Table 9. Parameters based on moisture content. 

Single Solid Element – Uniaxial Tension Parallel to the Grain 

Units kg, mm, ms, kN, GPa 

Density 6.731E-07 kg/mm3

*MAT_WOOD_PINE 

Default Parameters Except for Moisture Content (MS) 

Stiffness: 

MC = 30% 

(default) 

MC = 20% MC = 10% MC = 1% 

EL Parallel Normal Modulus 11.350000 12.560000 15.490000 16.720000 

ET Perpendicular Normal Modulus 0.246800 0.461900 0.910100 0.959700 

GLT Parallel Shear Modulus 0.715200 0.736900 0.789800 0.811900 

GLR Perpendicular Shear Modulus 0.087510 0.165500 0.332300 0.349300 

PR Parallel Major Poisson’s Ratio 0.156800 0.184200 0.258600 0.303300 

 

Strength: 

Xt Parallel Tensile Strength 0.040030 0.052380 0.066190 0.042590 

Xc Parallel Compressive Strength 0.013320 0.018580 0.037000 0.054760 

Yt Perpendicular Tensile Strength 0.000963 0.001458 0.002139 0.001477 

Yc Perpendicular Compressive Strength 0.002571 0.003627 0.007145 0.010310 

Sxy Parallel Shear Strength 0.004275 0.005577 0.008526 0.009351 

Syz Perpendicular Shear Strength 0.005985 0.007808 0.011940 0.013090 

 

Damage: 

Gf1 Parallel Fracture Energy in Tension 0.020050 0.015660 0.013840 0.011670 

Gf2 Parallel Fracture Energy in Shear 0.041480 0.046150 0.050160 0.028480 

Bfit Parallel Softening Parameter 30.000000 

Dmax Parallel Maximum Damage 0.999900 

Gf1 Perpendicular Fracture Energy in Tension 0.000401 0.00313 0.000277 0.000233 

Gf2 Perpendicular Fracture Energy in Shear 0.00830 0.000923 0.001003 0.000570 

Dfit Perpendicular Softening Parameter 30.000000 

Dmax Perpendicular Maximum Damage 0.990000 

 

Rate Effects: 

Flpar Parallel Fluidity Parameter: Tension/Shear 0.000 

Flparc Parallel Fluidity Parameter: Compression 0.000 

Pow_par Parallel Power 0.000 

Flper Perpendicular Fluidity Parameter: Tension/Shear 0.000 

Flperc Perpendicular Fluidity Parameter: Compression 0.000 

Pow_per Perpendicular Power 0.000 

 

Hardening: 

Npar Parallel Hardening Initiation 0.500 

Cpar Parallel Hardening Rate 1008.000 

Nper Perpendicular Hardening Initiation 0.400 

Cper Perpendicular Hardening Rate 252.000 

 

Note: Only those values that changed because of the change in moisture content are provided in the table. 
 84

Table 10. Parameters based on temperature. 

Single Solid Element – Uniaxial Tension Parallel to the Grain 

Units kg, mm, ms, kN, GPa 

Density 6.731E-07 kg/mm3

*MAT_WOOD_PINE 

Default Parameters Except for Temperature 

Stiffness: 

Temperature 

= 30°C 

Temperature 

= 20°C 

(default) 

Temperature 

= 10°C 

Temperature 

= 1°C 

EL Parallel Normal Modulus 10.620000 11.350000 11.970000 12.420000 

ET Perpendicular Normal Modulus 0.230800 0.246800 0.260200 0.270000 

GLT Parallel Shear Modulus 0.668900 0.715200 0.754000 0.782400 

GLR Perpendicular Shear Modulus 0.081840 0.087510 0.092250 0.095730 

PR Parallel Major Poisson’s Ratio 0.156800 

 

Strength: 

Xt Parallel Tensile Strength 0.034840 0.040030 0.044370 0.047550 

Xc Parallel Compressive Strength 0.011600 0.013320 0.014770 0.015830 

Yt Perpendicular Tensile Strength 0.000839 0.000963 0.001068 0.001144 

Yc Perpendicular Compressive Strength 0.002238 0.002571 0.002850 0.003055 

Sxy Parallel Shear Strength 0.003721 0.004275 0.004739 0.005079 

Syz Perpendicular Shear Strength 0.005210 0.005985 0.006634 0.007110 

 

Damage: 

Gf1 Parallel Fracture Energy in Tension 0.021440 0.020050 0.010460 0.002657 

Gf2 Parallel Fracture Energy in Shear 0.044360 0.041480 0.021640 0.005498 

Bfit Parallel Softening Parameter 30.000000 

Dmax Parallel Maximum Damage 0.999900 

Gf1 Perpendicular Fracture Energy in Tension 0.000429 0.000401 0.000380 0.000367 

Gf2 Perpendicular Fracture Energy in Shear 0.000887 0.000830 0.000787 0.000758 

Dfit Perpendicular Softening Parameter 30.000000 

Dmax Perpendicular Maximum Damage 0.990000 

 

Rate Effects: 

Flpar Parallel Fluidity Parameter: Tension/Shear 0.000 

Flparc Parallel Fluidity Parameter: Compression 0.000 

Pow_par Parallel Power 0.000 

Flper Perpendicular Fluidity Parameter: 

Tension/Shear 

 0.000 

Flperc Perpendicular Fluidity Parameter: Compression 0.000 

Pow_per Perpendicular Power 0.000 

 

Hardening: 

Npar Parallel Hardening Initiation 0.500 

Cpar Parallel Hardening Rate 1008.000 

Nper Perpendicular Hardening Initiation 0.400 

Cper Perpendicular Hardening Rate 252.000 

 

Note: Only those values that changed because of the change in moisture content are provided in the table. 
 85

13 STATIC WOOD POST TEST SIMULATIONS 

13.1 STATIC POST MODEL 

Static post testing consisted of both using neoprene and not using neoprene wedged 

between the wood post and the braces holding the post. Similar results were obtained 

with or without the neoprene, so eventually the static tests switched entirely to no 

neoprene being used for convenience. 

Because of anticipated contact difficulties with the simulations, two models were made 

to simulate the physical testing: one model with neoprene and one model without (see 

figure 74). The area of concern was at the contact interface between the wood post and 

the edge of the brace. It was thought, and later proven to be true, that the neoprene 

acted like a softening mechanism between the relatively soft wood post and the rigid 

clamping frame. However, this effect also proved to be insignificant with regards to the 

overall post behavior. 

In the model, the wood post is divided into three parts: (1) part 8001, the loading area 

on the post; (2) part 8002, the area where the post breaks; and (3) part 8000, the 

remainder of the post. All three post parts have the same wood material properties. The 

post is clamped between rigid, fixed braces (part 8004). Loading is supplied to the post 

through the loading bolt (part 8003) using a prescribed velocity motion of 1 mm/ms. 

After many different model variations, it was determined that the model without the 

neoprene could be used for simulating the physical static tests. Some difficulties were 

encountered while developing the baseline static model. A final model variation was 

developed that incorporated a rounded edge on the brace (as shown in figure 75). This 

rounded edge eliminated several contact issues that made the previous models very 

sensitive to the new wood material model. 

Baseline Model 

A baseline model is established to compare the various static post test simulations. This 

baseline model uses the default wood material properties for southern yellow pine, 

which has a grade of 1, a moisture content of 30 percent, and a temperature of 

20 degrees Celsius (°C) (*MAT_WOOD_PINE). 
 86

 

― Part 8000 (post) 

― Part 8001 (post loading area) Part 8003 (loading bolt) ―

 

 ― Part 8002 (post breaking area) Part 8008 (neoprene) ―

 ― Part 8004 (braces)

 Part 8006 (steel shim: between brace and post) ―

(a) Without neoprene (b) With neoprene 

Figure 74. Static post models. 

Figure 75. Rounded edge on brace. 
 87

13.2 BASELINE MODEL VERSUS TEST COMPARISON 

This section compares baseline simulation results to physical testing for the static post 

test. The initial behavior of the model is good; however, during fracture, the material 

model is too weak (as shown in figures 76 and 77 below). 

The initial fracture strength of 

the baseline simulation occurs 

between the minimum and 

maximum test values. Once the 

post begins to fracture, 

simulation forces fall below the 

minimum force levels seen in 

testing. 

Figure 76. Force deflection: Baseline versus test. 

The total fracture energy of the 

baseline simulation falls below 

the minimum test value. 

Figure 77. Energy deflection: Baseline versus test. 
 88

13.3 BASELINE VERSUS REFINED-MESH COMPARISON

This section shows that the wood material model is mesh-size dependent. After the 

initial fracture, the reduced-size mesh is shown to be much weaker than the baseline 

mesh (as shown in figures 78 and 79). The baseline mesh uses an element size of 25.4 

mm by 25.4 mm by 25.4 mm, while the refined mesh uses an element size of 12.7 mm 

by 12.7 mm by 12.7 mm. 

Similar initial fracture strengths 

occur in both the baseline 

model and the refined-mesh 

model. The baseline model 

retains strength over a longer 

distance than the model with 

the refined mesh. 

Figure 78. Force deflection: Baseline versus refined mesh. 

The baseline model has higher 

fracture energy than the 

refined-mesh model. 

Figure 79. Energy deflection: Baseline versus refined mesh. 
 89

Baseline 

 (a) 29 mm (b) 58 mm (c) 116 mm (d) 189 mm 

Refined 

 (e) 29 mm (f) 59 mm (g) 116 mm (h) 189 mm 

Figure 80. Variations by mesh size: Deformed geometry. 
 90

13.4 PARAMETER STUDY

Force-Deflection Behavior: *MAT_WOOD_PINE, Static Post Test Simulation 

With respect to wood grade, 

increasing strength is 

observed as the grade is 

improved. 

With respect to moisture 

content, fully saturated wood 

is weak, but ductile. As 

moisture content decreases, 

the material becomes 

stronger and more brittle. 

When the wood becomes 

very dry, the strength 

decreases, yet maintains 

brittle behavior. 

With respect to temperature, 

the wood becomes stronger 

as the temperature 

decreases. 

Figure 81. Force-deflection behavior as a function of 

grade, moisture content, and temperature. 

(a) Variation by grade 

(c) Variation by Temperature 

(b) Variation by moisture 

Force [kN] 

°C

(c) Variation by temperature 
 91

Energy-Deflection Behavior: *MAT_WOOD_PINE, Static Post Test Simulation

With respect to wood grade, 

fracture energy increases with 

improved grade. 

With respect to moisture content, 

fracture energy varies slightly 

with changes in moisture content. 

When wood becomes very dry, 

fracture energy is reduced 

significantly. 

Fracture energy varies slightly 

with changes in temperature. 

 

 

Figure 82. Energy-deflection behavior as a 

function of grade, moisture content, and 

temperature. 

(a) Variation by grade 

(c) Variation by temperature 

(b) Variation by moisture 

°C
 92

1 Default 

 (a) 29 mm (b) 58 mm (c) 116 mm (d) 189 mm 

DS-65 

 (e) 29 mm (f) 58 mm (g) 116 mm (h) 188 mm 

Clear

(i) 29 mm (j) 58 mm (k) 115 mm (l) 188 mm 

Figure 83. Variation by grade: Deformed geometry. 
 93

30% Default 

20% Default 

10% Default

1% Default 

Figure 84. Variation by moisture content: Deformed geometry. 

(a) 29 mm (b) 58 mm (c) 116 mm (d) 189 mm 

(e) 29 mm (f) 58 mm (g) 116 mm (h) 189 mm 

(i) 29 mm (j) 59 mm (k) 116 mm (l) 190 mm 

(m) 29 mm (n) 59 mm (o) 117 mm (p) 190 mm 
 94

30°C Default

20°C Default

10°C Default

 

1°C Default 

Figure 85. Variation by temperature: Deformed geometry. 

(m) 29 mm (o) 115 mm (p) 189 mm (n) 58 mm 

(i) 29 mm (k) 115 mm (l) 189 mm (j) 58 mm 

(e) 29 mm (g) 116 mm (h) 189 mm (f) 58 mm 

(a) 29 mm (c) 115 mm (d) 188 mm (b) 58 mm 
95

14 DYNAMIC WOOD POST TEST SIMULATIONS 

14.1 DYNAMIC POST MODEL 

The model used for dynamic post test simulations is shown in figure 86. The bogie 

impact height is 610 mm (24 inches) above ground level. The impactor on the bogie is 

modeled with a rigid cylinder wrapped with a deformable neoprene model. The ground 

is modeled with rigid, fixed solid elements. Deformable neoprene is placed between the 

ground and the post on both the back and front sides of the post. On the impact side of 

the post, the neoprene sticks out of the ground approximately 200 mm, while on the 

other side, the neoprene was slightly below ground level. 

The dynamic model went through a few modifications. The two primary changes were: 

(1) the neoprene cover on the cylinder was remeshed to a much finer mesh, and (2) the 

neoprene used between the ground and the post was also remeshed and sized to 

match the majority of the testing conditions. Finally, unusual energy problems exhibited 

on certain hardware platforms with the bogie wheels were fixed by making the wheels 

rigid (this had no effect on the simulation results). 

A baseline model was established to compare the various dynamic post test 

simulations. This baseline model used the default wood material properties for southern 

yellow pine that had a grade of 1, a moisture content of 30 percent, and a temperature 

of 20°C (*MAT_WOOD_PINE). Note that the different colors on the post shown in 

figure 86 represent the different parts being used to store those post elements. This was 

done to monitor the behavior and the energy distribution more precisely. The material 

properties for all of the post parts were identical. 

Figure 86. Dynamic wood post test model. 
96

14.2 VAPORIZATION AND TIME STEP 

The initial simulation of the dynamic post test resulted in the post vaporizing at around 

10.5 ms into the event (as shown in figure 87). 

(a) 0 ms (b) 10.501 ms (c) 10.796 ms (d) 10.848 ms 

Figure 87. Post vaporization. 

After many iterations and model changes, the problem was isolated and proven to be a 

time-step problem. The LS-DYNA calculated time step for the 25.4-mm hexagonal

element using the wood material is 0.005 ms. This time step is too large and can cause 

model instabilities as shown in figure 87. It was found that by limiting the time step to 

0.001 ms for the 25.4-mm hexagonal, the material remained stable for this specific 

simulation case. The maximum time step allowable can be set in LS-DYNA using the 

*CONTROL_TIMESTEP command. 
97

14.3 SHARP EDGE CONTACTS 

With a reduced time step, the dynamic simulation proceeded farther into the impact, but 

resulted in contact difficulties at the sharp edge between the wood post and the 

neoprene-lined concrete base (as shown in figure 88). 

 (a) 0 ms (b) 30 ms (c) 50 ms 

(d) Closeup 

Figure 88. Contact at sharp corner. 

This type of contact penetration is typical when sharp edges are involved. The sharp 

edge contact was originally analyzed for static post testing simulations. The correction 

was to round off the sharp edge. For the dynamic wood post model, the contact 

correction will be to add a neoprene flap to that side of the foundation, identical to the 

flap on the other side. Note that, in testing, both cases (with and without double flaps) 

were tested with the results showing no identifiable differences. 
98

14.4 BENDING 

With the double flap in place, simulation of the dynamic post test continued until 

completion. However, the post did not snap off as it did in physical testing. Instead, the 

post bent about the last remaining elements (as shown in figure 89). Several runs were 

made with various contact friction properties to see if this bending (instead of snapping 

off) was the result of something other than the material itself. However, the results were 

similar between all runs, indicating that something was not quite right in the material 

model or its parameters for pine. 

 (a) 40 ms (b) 80 ms 

Figure 89. Post bending. 
99

14.5 FURTHER ANALYSIS 

The developer recommended an investigation into the cause of the bending elements, 

possibly related to the neoprene. To start, the neoprene was removed from the model 

and a rigid sleeve was used to constrain the post. To avoid potential contact troubles, 

the rigid sleeve was rounded at the edge. However, penetrations were observed as 

shown in figure 90. Even though the soft option for contact was being used in this 

model, the contact needed additional study to eliminate significant penetrations. To fix 

the trouble, an additional node-to-surface contact was added between the rigid sleeve 

and the wood post. This addition seemed to work appropriately (as shown in figure 91). 

Note, however, that this was not the only contact difficulty experienced during this 

investigation. For some reason, it appears that the new wood material model was overly 

sensitive to contact behavior. Further study is recommended. 

 (a) Undeformed (b) Deformed 

Figure 90. Contact penetrations. 

Figure 91. Improved contact. 
100

With this latest model (i.e., rigid sleeve with no observable contact penetrations), the 

results were undesirable. Specifically, even with the previously discussed smaller time 

step of 0.001 ms being used, the lower post began to vaporize (as shown in figure 92). 

Also, the volume of the elements at the bottom of the post began to significantly expand 

(as shown in figure 93). This was discussed previously for a single-element model and it 

was noted that the user did not believe that this volume expansion was realistic. 

 (a) State 1 (b) State 2 (c) State 3 (d) State 4 

Figure 92. Element vaporization at bottom of post. 

Figure 93. Volume expansion of 75 percent in an element near the bottom of post. 

Time [ms] [ms] 

Volume (E+3) [mm3] 
101

Next, because vaporization had returned to the model, it was thought that the cause 

might be a result of the time step (as discussed in section 6.2). However, when the time 

step was reduced again to 0.0005 ms and then even further down to 0.0001 ms, the 

results did not improve. In fact, using the very impractical time step of 0.0001 ms, 

vaporization occurred much more quickly in the model and caused the model to become 

unstable much earlier than with the larger time step. The deformed geometry of the post 

just before becoming unstable is shown in figure 94. 

Figure 94. Vaporization with a time step of 0.0001 ms. 
102

In a final attempt to determine more about the difficulties occurring with the dynamic 

post model (i.e., contacts, vaporization, bending instead of snapping off, etc.), the rigidsleeve model with some contact penetrations (which alleviated the vaporization) was 

investigated near the damage area. It was believed that the failure of the wood 

elements away from the contact area would be unaffected by the contact penetrations. 

Unfortunately, the damaged area appeared to be incorrect (as shown in figure 95) (i.e., 

the elements in the center of the damage area became highly distorted, but did not 

erode). Plotting the damage of one of those elements showed that the element should 

have eroded since it had reached the critical value of 0.99 (the preset damage level for 

erosion) (see figure 96). 

 (a) State 1 (b) State 2 (c) State 3 

Figure 95. Highly distorted elements sometimes do not erode. 

Figure 96. Damage of highly distorted element. 
103

15 ELEMENT FORMULATION: HOURGLASSING 

There are three applicable solid-element formulations available within LS-DYNA: 

1. Constant stress. 

2. Fully integrated S/R solid. 

3. Fully integrated quadratic eight-node element with nodal rotations. 

These are listed in the order of increasing accuracy and in the order of increasing 

computational costs. Element formulation 1 can exhibit hourglassing, while formulations 

2 and 3 have no hourglassing. The details for hourglassing and the various hourglass 

control algorithms will not be provided here. Readers are referred to the LS-DYNA 

user’s and theoretical manuals for details. 

Current simulation practices often use all three element formulations in a typical 

application where the post is considered to be critical for detailed modeling. A post is 

divided into three parts: (1) the area of loading, (2) the area around the ground line 

(breakage area), and (3) the remaining sections. Reasonable results have been 

obtained using element formulation 2 for the area of loading, formulation 3 for the 

ground line area, and formulation 1 for the rest of the post. An important goal of the new 

wood material model is too eliminate this cumbersome task of dividing a wood post into 

multiple parts. 

When using element formulation 1, an hourglass control algorithm is mandatory. The 

default hourglass control is referred to as control type 1. An important parameter 

associated with hourglass control is called the hourglass coefficient and is given the 

label qm. The default value is qm = 0.1. 

The new wood material model has exhibited hourglassing when element formulation 1 

was used for the entire wood post. To quantify this phenomenon, the static wood post 

model was divided into three parts as described above. Hourglass energy and internal 

energy were compared for part 8002, which is the section of the post that breaks at 

ground level. 

Using default wood parameters for grade 1 southern yellow pine, hourglass control was 

investigated. The default hourglass control (type 1, qm = 0.1) results are shown in 

figure 97, while the results for hourglass control type 3 with qm = 0.1 are shown in 

figure 98. Clearly, both of these simulations resulted in excessive hourglassing (this is 

shown both graphically and numerically in the figures). When using hourglass control 

type 4 with qm = 0.005, the hourglass is brought under control for this model (as shown 

in figure 99). Note that hourglassing is considered to be under control when there are no 

obvious element distortions caused by hourglassing, and the hourglass energy 

measurement is less than 10 percent of the internal energy of the elements within a 

reasonable neighborhood of where the hourglassing is occurring. 
104

Unfortunately, when using the same hourglass control that worked well for grade 1 

southern yellow pine wood material properties for the grade DS-65 southern yellow pine 

wood material properties, significant hourglassing reappeared in the model (as shown in 

figure 100). 

Note that for chapters 13 and 14 of this report, hourglass control type 4 with qm = 0.005 

was used throughout. 

 (a) Deformed configuration (b) Hourglass energy 

Figure 97. Southern yellow pine, grade 1: Hourglass control type 1, qm = 0.1. 

 (a) Deformed configuration (b) Hourglass energy 

Figure 98. Southern yellow pine, grade 1: Hourglass control type 3, qm = 0.1. 

[ms] Time [ms] 

Time [ms] [ms] 
105

 (a) Deformed configuration (b) Hourglass energy 

Figure 99. Southern yellow pine, grade 1: Hourglass control type 4, qm = 0.005. 

 (a) Deformed configuration (b) Hourglass energy 

Figure 100. Southern yellow pine grade, DS-65: Hourglass control type 4, qm = 

0.005. 

To eliminate hourglassing completely and to increase the accuracy of the simulation, 

element formulations 2 and 3 were tried. Unfortunately, the results were undesirable 

because of the way failure (i.e., eroding) was handled for elements with multiple 

integration points. Thus, the developer has recommended that fully integrated element 

formulations not be used for the wood material. However, the user believes that fully 

integrated element formulations for the wood material model are critical for the success 

of the current implementation of the new wood material model. This would reduce the 

trial-and-error approach for finding the appropriate hourglass control parameters.

Time [ms] [ms] 

Time [ms] [ms] 

107

16 USER’S CONCLUSIONS 

Conclusions that were documented by the user and based on the validation effort 

detailed in chapters 8 through 15 of this report are as follows: 

Single-element models pulled in tension parallel to the grain behaved well and a 

parametric study involving grade, moisture content, and temperature yielded good 

results. Because of time limitations, various other single-element simulations were not 

performed, but are recommended (including compression, shear, and torsion loading 

both parallel and perpendicular to the grain). 

Static post test simulation results did not match the physical test results. The initial 

fracture strength of the simulation was good; however, the strength of the fracturing post 

was significantly below the minimum strength seen in physical testing. 

Wood material behavior is very sensitive to mesh size. When a refined mesh was used 

in the static post test simulation, the initial fracture strength was similar to the baseline 

model. However, the strength of the fracturing post dropped by almost an order of 

magnitude relative to the baseline model. 

The dynamic post test simulations had significant problems with time-step calculations, 

contacts, and bending behavior as opposed to a snap-off behavior. Further analysis 

resulted in post vaporization even when using an extremely small time step 

(0.0001 ms). Also, a significant volume expansion of the wood elements was noted (up 

to 75 percent volume expansion in individual elements). Additionally, highly distorted 

elements with damage values of 0.99 did not erode as expected. Because of these 

difficulties with the dynamic post simulations, a comparison to physical testing of 

dynamic posts was not made. 

Finally, hourglassing in the wood material model appears to be a very significant issue. 

A parameter study was needed to determine a good hourglass control type and 

hourglass control parameter for the dynamic post model. When the grade of the wood 

was changed from grade 1 to grade DS-65, hourglassing reappeared in the model using 

that same hourglass control. Fully integrated elements are not an option at this time 

because the eroding characteristics of the wood model do not behave well for fully 

integrated elements. 

109

17 DEVELOPER’S COMMENTS ON USER’S EVALUATION 

This section was written by the developer and begins with topics selected by the 

developer and previously discussed by the user in chapters 9 through 16. These are 

topics that the developer concluded were worthy of additional discussion and 

explanation. These topics and the corresponding developer’s comments are briefly 

tabulated in table 7. Following this table is a more indepth discussion of these topics. 

For ease of discussion, each topic can be grouped roughly into one of three categories: 

1. LS-DYNA code behavior. 

2. User’s (analyst’s) responsibility. 

3. Wood model theory or wood model input parameter selection. 

Material models, like the wood and soil models, are not stand-alone codes. They are 

subroutines that work only in conjunction with the LS-DYNA code. Therefore, the results 

of any analyses performed depend on the formulation of the LS-DYNA code, the user’s 

specification of the geometric mesh and boundary conditions, the user’s specification of 

the input parameter values for various LS-DYNA features and material models, and the 

formulation and input parameter values for the wood material model. 

The user’s evaluation chapters demonstrate the behavior of the finite element systems 

under various operating conditions. By system, we mean the wood material model used 

in conjunction with other material models/structures and LS-DYNA controls. An example 

is a vehicle impacting a wood post embedded in a neoprene and concrete support 

structure. Code issues are related to the functioning of the LS-DYNA features via the 

LS-DYNA controls, which affect the behavior of the system. These controls are 

independent of the wood model and are typically proprietary in formulation. The user’s 

issues are related to the proper user’s setup of the finite element mesh, the user’s 

regard for LS-DYNA diagnostics, and the user’s selection of LS-DYNA input 

parameters. It is the user’s responsibility to learn the LS-DYNA code, set up the mesh 

properly, and input the correct control parameters. 

Most calculations documented by the user show good system behavior, with the wood 

material model behaving realistically. However, some calculations show poor system 

behavior, which the user did not adequately explain. The user is a potential end user of 

the code (not a material model or code developer) and, therefore, did not distinguish 

between LS-DYNA code issues, user’s setup and input parameter selection issues, and 

wood model issues. 

Of the 10 topics chosen for discussion, we can categorize 5 as code- and user-related 

issues, and 5 as wood model issues. No changes to the wood model theory or wood 

model input parameter values affect the results regarding the five code- and userrelated issues. The five wood model issues are: 

• Volume expansion and contraction. 

• Static post simulation behavior. 
110

• Mesh-size dependency. 

• Post breakage and fracture. 

• Erosion criteria. 

The developer performed many additional calculations that were related to some of 

these wood model issues, as discussed in section 17.3. The additional calculations 

indicate that none of the wood model issues are wood model deficiencies that warrant 

changes to the theoretical formulation of the model. However, changes to the wood 

model input parameter values may positively affect the results. 

The developer wishes to thank the user for providing a detailed report on the initial use 

of the wood material model. The questions and comments provided by a novice user of 

the wood model are a good learning tool for other novice users. However, the tone and 

conclusions (or lack thereof) in some portions of the user’s evaluation report in chapters 

9 through 16 may leave the reader wondering whether the wood model is ready for use. 

Both the developer’s and the user’s wood model evaluation sections were reviewed by 

individuals at FHWA, NHTSA NCAC, and each COE before publication. One 

experienced analyst and reviewer stated that he understood that many of the issues 

brought up by the user were LS-DYNA code and user input parameter selection issues, 

and not wood model issues. However, a beginning analyst might not make this 

distinction and think that the model was deficient. This is because the user’s evaluation 

report brings up various issues without thoroughly defining them or resolving them and, 

more importantly, without identifying how the issue relates to the wood material model. 

Therefore, all analytical results provided by the user have been included in this report, 

whether or not the simulation was performed correctly, and whether or not the problem 

and solution are directly related to the wood model. As the developer, we believe that 

this consolidated, comprehensive report provides a very valuable learning tool for 

analysts who want to learn how to use the wood (or soil) model as part of the LS-DYNA 

code. We think that identifying and providing commentary on issues is a much better 

approach than removing issues that are not directly related to the wood model. Some of 

the issues in the user’s evaluation report are potential hurdles that other users may run 

into and, therefore, warrant publication. We hope that the following discussion provides 

inexperienced users with guidelines on how to correctly run the wood model. 

It is the developer’s opinion that the user’s wood model evaluation revealed no 

substantial problems with the model. In fact, the developer performed various analyses 

to positively determine that none of the issues were model deficiencies. The developer 

has demonstrated that all of the user’s evaluation calculations gave reasonable results 

when reasonable LS-DYNA control parameters and reasonable wood input parameters 

were used. In particular, see section 17.3 for a thorough discussion of the excessive 

erosion problem and solution, and a discussion of post breakage. 
17.1 TABLE OF WOOD MODEL TOPICS 

Table 11. Developer’s response to user’s review of wood model.

Developer’s Response 

Issue User’s Comment 

Volume Expansion and Contraction 

Wood is incompressible, while wood material model admits compressible behavior. 

- FPL data show compressibility of wood. - User does not furnish incompressible data. 

Static Post Simulations 

Calculated forces fall below minimum seen during tests. 

- Developer’s calculations show excellent correlation with data. 

Mesh-Size Dependency 

Wood model behavior is very sensitive to mesh size. 

- Wood softening model is formulated to be mesh-size independent; verified on single elements. - User has not demonstrated that mesh-size 

dependency is related to the wood model. - Geometric or contact portion of the model is suspect. 

Time-Step Control Time-step reduction is needed to 

prevent excessive erosion of wood model. 

- LS-DYNA diagnostics indicate that stable time step was exceeded because of user’s input specification. - Calculations remain stable with stable time step. 

Post Breakage and Fracture 

Post bends rather than snapping off. - Developer’s calculations demonstrate snap-o

behavior. - Adjustment of input parameters/boundary conditions affects snap-off behavior. - Default parameters could be adjusted if snapoff time is furnished by testers. 

Element Erosion Excessive erosion of elements occurs 

where post contacts support. 

- LS-DYNA diagnostics indicate substantial initpenetration, which is a result of the user’s inpu- User should redefine mesh and contact. 

Erosion Criteria Elements should erode when damage 

reaches 99 percent. 

- Not true - Elements erode when all six stress components reach 99 percent damage. 

111
Table 11. Developer’s response to user’s review of wood model (continued). 

Developer’s Response 

Issue User’s Comment 

Hourglassing Hourglassing of the wood model 

appears to be a very significant issue. 

- Hourglassing occurs for ALL material models with under-integrated elements. - Developer demonstrates significant 

hourglassing for elastic material model 1. - Hourglass controls are separate from wood model. 

Fully Integrated Elements 

Fully integrated elements are not an option at this time. 

- Disagree - Developer demonstrates excellent results with fully integrated elements while exercising caution on erosion. 

Contact Surfaces Wood model is overly sensitive to 

contact surfaces. 

- Disagree - Surface penetration controlled by contact algorithms, not the material model. - Developer demonstrated similar penetration 

with elastic material model 1. 

112
113

17.2 DISCUSSION OF WOOD MODEL TOPICS 

These items are listed in the order that they were brought up by the user in chapters 9 

through 16. 

Volume Expansion and Contraction: The user demonstrates that the volume of the 

single elements pulled in tension expands by as much as 6 percent (previously shown 

in figure 73). The user believes that there should be no change in volume for wood (i.e., 

wood is incompressible, but shows no credible data or peer-reviewed documentation to 

support this position). It is the developer’s position that Poisson’s ratios measured by 

FPL and reported in the literature(11) do not support the assumption of incompressibility. 

Therefore, modeling wood as an incompressible material is not recommended by the 

developer. 

The suite of clear wood data provided by FPL (documented in the user’s manual)(2)

included measurement of the major Poisson’s ratio in the elastic region. A transversely 

isotropic material such as wood has three ratios. Typical values are around νLT = 0.16, 

νTL = 0.004, and νTR = 0.4 for pine at the fiber saturation point. No measurements were 

reported for the effective Poisson’s ratios in the plastic/damage regions (once the 

material yields or softens). By effective Poisson’s ratio, we mean the ratio of the lateral 

strain to the axial strain in uniaxial stress tests (without lateral confinement). Porous 

materials tend to flow during yielding and softening, which can result in an effective 

Poisson’s ratio that is larger or smaller than the elastically measured value. For 

example, for porous geological materials such as concrete, the effective Poisson’s ratio 

is typically modeled as greater than the elastic ratio in unconfined compression (with 

values greater than 1) and less than the elastic ratio in unconfined tension. The effective 

ratio depends on the shape of the yield surfaces, coupling of the yield surfaces, and 

how the plasticity algorithm is formulated. 

 

To achieve no change in volume, the elastic and effective Poisson’s ratios would have 

to be 0.5. The FPL data indicate that the elastic Poisson’s ratios are not 0.5. However, 

no lateral strain or change in the volume measurements is available to confirm or refute 

an effective Poisson’s ratio of 0.5 in the plastic region. Therefore, we recommend that 

any future test data generated (such as uniaxial tension and compression tests) include 

lateral strain measurements. 

For a material to be modeled as incompressible in the elastic region, it must also be 

modeled as isotropic. By examining the elastic constitutive equations in the wood model 

user’s manual,(2) one can readily determine that all Poisson’s ratios can only be equal to 

0.5 when all stiffnesses (parallel and perpendicular) are equal. Wood, on the other 

hand, is modeled as transversely isotropic (a simplification of orthotropic) because the 

stiffness parallel to the grain is about 50 times greater than that perpendicular to the 

grain. 

Another point to note is that the volume change being modeled implicitly includes 

expansion and compaction of pores and the opening up of fracture surfaces. This is 
114

demonstrated schematically in figure 101. The formation of voids and the compaction of 

pores are shown in figure 102. The fracture of wood creates voids, which are modeled 

as volume expansion with continuum models like the wood model. Wood is also porous. 

The crushing of pores is modeled as volume compaction. 

 

 

(a) Fracture of wood (specimen breaks in two) (b) Finite element simulation (element 

 stretches)

Figure 101. Schematic demonstration of how a finite element treats fracture prior 

to erosion. 

(a) Void formation(11) (b) Pore compaction(11)

Figure 102. Demonstration of void formation and crushing of wood specimens. 
115

Setting the compressibility or effective Poisson’s ratio behavior of the wood model is not 

simply a matter of specifying an input value. Rather, it requires changes to the 

formulation of the model to include coupling between the parallel (axial) plasticity and 

perpendicular (lateral) plasticity. The current wood model includes separate yield 

surfaces and plasticity computations for yielding parallel and perpendicular to the grain. 

As a result, yielding parallel to the grain does not induce plastic flow perpendicular to 

the grain. Similarly, yielding perpendicular to the grain does not include plastic flow 

parallel to the grain. We recommend exploring and implementing methods of coupling 

the plastic flow once sufficient test data are generated to set the coupling via 

measurement of the effective Poisson’s ratio or volume change. 

Static Post Simulations: The user states that, during fracture, the wood model is too 

weak: Once the post begins to fail, the simulation forces fall below the minimum force 

levels seen in testing. As the developer, we disagree. Comparison of the simulation 

force histories with data (as opposed to performance envelopes) demonstrates that the 

simulation forces are not too low. In addition, excellent correlations between the 

simulations and the performance envelopes are achieved through careful selection of 

the input fracture energy. No changes to the material model formulation are required to 

achieve good agreement between the simulations and the static post test data. We 

suggest that the user plot all data curves in comparison to the performance envelopes 

and more thoroughly discuss their performance envelope selection process. The static 

data are highly scattered and display both brittle and ductile behaviors. 

Figure 103. User’s grades 1 and 1D simulation compared to the performance 

envelopes, using Gf|| = 50 Gf⊥. 
116

 (a) Set 1 (b) Set 2 

Figure 104. Most of the grades 1 and 1D static post test measurements exhibit 

brittle behavior. 

The user’s simulation and performance envelopes are shown in figure 103. The suite of 

test data used to generate these performance envelopes is shown in figure 104 for 

grades 1 and 1D. The simulation conducted by the user peaks at about 47 MPa, then 

softens in a brittle mode between 25 and 50 mm of deflection. The behavior of the 

simulation is similar to 9 out of 15 of the data curves shown in figure 104, which fail in a 

brittle mode between 25 and 50 mm of deflection. This is good agreement. 

However, it is evident that the user’s simulation fails in a more brittle manner than that 

represented by the performance envelopes. The user supposedly constructed the 

envelopes using curves from posts that exhibited the most typical behavior. The 

minimum and maximum curves, which define the performance envelopes, do not 

represent any one particular curve from the tests. The simulation was conducted using 

the default fracture energies recommended by the developer. 

Good agreement between the simulation and the performance envelopes can be 

achieved by increasing the parallel-to-the-grain fracture energy above the default value 

(as shown in figure 105). Refer to chapter 5 for a thorough review of the developer’s 

static post simulations. Simulations conducted at two different fracture energies were 

previously shown in figure 22. The calculation with Gf || = 50 Gf ⊥ (green dotted line) 

agrees with the brittle data. The calculation with Gf || = 250 Gf ⊥ (red solid line) agrees 

with the ductile data. It is important to note that the default fracture energy for saturated 

room-temperature pine is based on correlations with the dynamic (bogie impact) 

performance envelopes. A higher value than the default is needed to achieve good 

correlations with the static performance envelopes. 

 (mm) 

0 51 102 152 203 254 (mm) 

 0 51 102 152 203 254 

Brittle

Ductile

90 

45 

 0 

 90 

 45 

 0 

Force (kN) 

Force (kN) 

Ductile

Brittle
117

Figure 105. Good correlation is achieved between the simulation and the 

performance envelopes by increasing the fracture energy above the default value 

(to Gf|| = 250 Gf⊥). 

Mesh-Size Dependency: The user suggests that the wood model is mesh-size 

dependent because static post calculations conducted at two different mesh 

refinements (25.4-mm and 12.7-mm elements) exhibit different late-time force-deflection 

behaviors. These behaviors were previously shown in figure 78. 

It is not clear to the developer that the origin of the different late-time responses is the 

wood model, rather than the overall (geometric/material/contact) model. The user 

demonstrated mesh-size sensitivity of a finite element system. However, the user did 

not demonstrate that the sensitivity was a result of the wood model formulation. The 

origin of the different responses is an issue because the developer could possibly adjust 

the model formulation if the material model is the source of the different responses, 

otherwise, the geometric model must be adjusted. 

Often, material models exhibit mesh-size sensitivity because of their softening 

formulations. However, the developer included coding to regulate mesh-size sensitivity 

by making the softening formulation of the wood model a function of element size and 

checking this behavior for single elements. The softening formulation of the wood model 

for single elements does not depend on element size. In addition, the user’s early-time 

force-deflection behaviors are in good agreement for peak strength and initial softening, 

which suggests that the softening formulation has been adequately regulated. 

On the other hand, the developer’s static post calculations discussed in chapter 5 (for 

example, see figure 27) indicate that the late-time behavior is the most sensitive portion 

of the simulations. For example, the late-time behavior is sensitive to input parameter 

selection, hourglass control, element formulation, and geometric modeling details. In 

fact, two other reviewers suggested that the perceived mesh-size sensitivity is not an 
118

issue because the discrepancy in the response occurs at a late time, where data are not 

adequately measured. 

We note that the deformed configurations in the user’s plots look different in the region 

where the post is rolling over the rounded edge on the brace. It appears that more wood 

compaction is taking place at this location in the crude mesh than in the refined mesh. 

Therefore, the source of the sensitivity could also be a result of modeling details in this 

region. 

 

We recommend reexamining this calculation in the future to determine the source of the 

mesh-size sensitivity. If the wood model is the source of the sensitivity, then 

modifications should be made to make the material model independent of the mesh 

size. Perhaps simpler geometries and loads, such as direct pull (with softening) and 

unconfined compression (with hardening) of coupons or timbers, could be used to 

evaluate the model’s mesh-size response. Unconfined compression is suggested so 

that the mesh-size sensitivity of the hardening formulation can be evaluated. In 

particular, single material simulations that isolate the wood model without the use of 

other materials, contact surfaces, and complex boundary conditions are recommended. 

Time-Step Control: The user reports that a reduction in the time step is needed to 

control excessive erosion of the wood model (instability), as previously shown in 

figure 87. The user corrected this behavior by reducing the time step via the 

*CONTROL_TIMESTEP command. The developer disagrees with this assessment 

because the user requested that the LS-DYNA code exceed the stable time for contact 

surface stability. Thus, the calculation became unstable. The instability is the result of a 

deliberate override of the stable time step for the contact surfaces, not the wood model, 

and is caused by the user's input. 

A review of the user’s input files and output diagnostics indicates that the time step for 

stable contact surface behavior was exceeded in the user’s calculations. This is 

because the user requested, via the *CONTROL_CONTACT card, that the stable time 

step for contact surface stability be ignored. In other words, the user first increased the 

time-step size above the stable value via *CONTROL_CONTACT (and caused an 

instability), then reduced the time-step size below the stable value via 

*CONTROL_TIMESTEP (to relieve the instability). This dual process is both 

unnecessary and inefficient. The developer recommends letting LS-DYNA automatically 

select the time-step size based on the element size, wave transit time, and contact 

surface stability. All calculations performed by the developer in chapters 1 through 9 

remained stable because the developer did not override the stable LS-DYNA time step. 

A very thorough discussion of instabilities in the post-impact analyses is discussed in 

section 17.3. 

Post Breakage/Fracture: The user reports that the post is bending, rather than 

snapping off, and suggests that “something is not quite right in the material model or its 

parameters for pine.” The developer has demonstrated both snapping (complete 
119

breakage) and bending (partial breakage) behaviors with the wood model. Five 

calculations that demonstrate complete breakage are: 

1. Grade 1 pine with small adjustments in default quality factors (as previously 

shown in figure 43). 

2. DS-65 post modeled with simple pinned boundary conditions (as shown in figure 

106 below). 

3. Grade 1 pine with post-peak hardening (as shown in figure 117 of section 17.3). 

4. Grade 1 Douglas fir (as shown in figure 118 of section 17.3). 

5. Grade 1 pine impacted at 29.5 m/s (66 miles per hour (mi/h)) (as shown in figure 

119 of section 17.3). 

 (a) Without modeling rate effects (b) With modeling rate effects 

Figure 106. DS-65 pine post modeled with simple pinned boundary conditions. 

No data was documented that indicated the snap-off time (average and scatter) that 

occurred in the bogie impact tests, so snap-off time was not used to set the default 

parameters. It is our understanding that the data for the breakage of wood posts are 

highly scattered. Post breakage does not occur at one particular time after impact or at 

a particular deflection. No theoretical model changes are required to simulate snap-off. 

This is an input parameter selection issue, not a wood model formulation issue. The 

default parameters could readily be adjusted to modify the snap-off time given the 

appropriate data. However, input parameter values are ultimately the responsibility of 

the user. 

To elaborate, calculations conducted using the final default properties for saturated 

room-temperature pine, reported by either the developer or the user, indicate that post 

breakage is incomplete at 180 mm, which is the final deflection of the performance 

envelope plots. However, a number of calculations performed by the developer 

C
120

simulated complete breakage. For example, the developer determined that adjustments 

in the quality factors affect the deflection at which the post breaks in two. This was 

previously demonstrated in figure 43. Here, the default quality factors for grade 1 pine 

were adjusted from QT = 0.47 and QC = 0.63 to QT = 0.4 and QC = 0.7. This adjustment 

of the quality factors reduces the tensile strengths and increases the compressive 

strengths. Recall that the quality factors are applied to the clear wood strengths (QT to 

the tensile and shear strengths, and QC to the compressive strengths) to reduce the 

strength as a function of the grade. The trend noted is that the post will break earlier in 

time as QT is adjusted downward and QC is adjusted upward. The load-deflection and 

bogie velocity-reduction curves calculated with either set of quality factors are similar 

(refer back to figures 43 and 44). 

The snap-off time may also be dependent on other material properties besides strength. 

The developer suggests that each user examine: 

• Rate effects: Rate effects tend to make the simulation more elastic, which should 

enhance standoff. 

• Late-time hardening in compression via the Ghard parameter: This parameter was 

implemented to override perfect plasticity in compression. 

• The parameter IQUAL: By default, the quality factors are simultaneously applied 

to both the parallel and perpendicular strengths. As an option, setting IQUAL to 1 

removes the application of the quality factors from the perpendicular strengths. 

This would strengthen the behavior perpendicular to the grain. 

The snap-off behavior not only depends on the behavior of the wood material model, 

but on the overall behavior of the geometric and material models in the snap-off region 

(neoprene, contact, and mesh refinement), and on how the wood post is being loaded 

and pulled (or not pulled). For example, the wood post is more likely to snap off with 

more pull (from higher tensile stresses). The amount of pull depends on how the post is 

gripped in the support and the contact between the bogie cylinder and the post. The 

post slides up the support in the simulations (perhaps a couple of inches or more). Also, 

the impact cylinder bounces off the post with little late-time contact in the simulations. 

The developer never received feedback from the user (testers) on how this simulated 

behavior compared to the measured behavior. 

Future efforts could further explore the material parameters and geometric issues that 

affect snap-off. However, the developer strongly recommends that each user evaluate 

the default material properties prior to their use. The developer has made its best effort 

to set the default parameters with the test data, time, and funding available for this 

project. However, users are not limited to using default properties and are encouraged 

to do their own evaluation and share their results with others in the roadside safety 

community.
121

Excessive Erosion at Bottom of Post: The user reports excessive erosion where the 

post is in contact with the rigid support (as previously shown in figure 85). The 

developer determined that this excessive erosion is not a problem in the wood model 

formulation. Rather, it is caused by user input. The user meshed the rigid support such 

that it penetrated the wood post, and this interpenetration caused the instability. The 

LS-DYNA code provided warning diagnostics to assist in determining the cause of the 

instability; however, these warnings were ignored by the user. This issue is thoroughly 

discussed in section 17.3 below. 

Damage: The user incorrectly states that elements should erode when damage reaches 

99 percent. This is not true. Elements automatically erode when all six stress 

components reach 99 percent damage via the parallel damage parameter. The 

elements do not automatically erode when the three perpendicular stress components 

reach 99 percent damage via the perpendicular damage parameter. The wording in the 

wood model user’s manual(2) has been updated in an attempt to make this point clear.

To elaborate, the user plotted the default damage and noted that some elements do not 

erode when the plotted damage reaches 99 percent. By default, the maximum of either 

the parallel or the perpendicular damage parameters is plotted. Therefore, the damage 

being plotted by default could be the parallel damage parameter or it could be the 

perpendicular damage parameter, whichever is larger. The elements automatically 

erode when the parallel damage parameter exceeds 99 percent, but not when the 

perpendicular damage parameter reaches 99 percent (unless IFAIL = 1, as set by the 

user). Therefore, damage that is 99 percent, but not accompanied by erosion, is 

perpendicular damage. Alternatively, the user may request that only perpendicular 

damage be plotted by setting NPLOT = 2. 

Hourglassing: The user states that hourglassing appears to be a very significant issue 

for the wood model. The developer states that hourglassing occurs when underintegrated elements are used with any material model, not just the wood model. For 

example, even a simple elastic material model generates as much hourglass energy as 

the wood model in the static post simulation shown in figure 107. The developer 

discusses hourglass control in section 5.3. Hourglass controls are separate from the 

material models. 

Fully Integrated Elements: The user erroneously states that fully integrated elements 

are not an option for the wood model at this time. This is not true. The developer

obtained excellent results with fully integrated elements (as previously shown in figure 

27). Our only caution is that users must recognize that fully integrated elements erode 

when any one of the eight integration points fails, regardless of which material model is 

used. 
122

Wood Material Model

 (a) Deformed configuration for wood model (b) Energy ratio 

Elastic Material Model

 

(c) Deformed configuration (d) Energy ratio for elastic material model 

Figure 107. Developer’s static post simulations using hourglass stiffness 

type 4 with a reduced (0.03) coefficient. 

C

 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 75.00 80.00 85.00 90.00 95.00 100.00

 0.00E+00

 2.00E-02

 4.00E-02

 6.00E-02

 8.00E-02

 1.00E-01

 1.20E-01

 1.40E-01

 1.60E-01

 1.80E-01

 2.00E-01

 2.20E-01

 2.40E-01

 2.60E-01

 2.80E-01

 3.00E-01

 MWRSF BENDING TEST SIMULATION CLEAR WOOD PINE SATURATED Material Hourglass /Internal Energy Ratio

Time minimum = 0.0000E+00

 maximum = 3.0030E-01

Material A=1, B=2, C=3, D=4, E=5,

A

A

A

A A

A

A

B B B

B B C

C

C

C

C

C

D

D

D

D

D

D

E

E

E E

E

Loaded Region – 30% 

Break Region – 14% 

Hourglass-to-Internal Energy Ratio 

(%) 

28 

24 

20 

16 

12 

8 

4 

0 

Time [ms] 

Loaded Region

Break Region

Hourglass-to-Internal Energy Ratio (%) 
123

Contact Surfaces: The user misleadingly states that “for some reason, the wood model 

is overly sensitive to contact surfaces,” after noting penetration between the wood post 

and the liner previously shown in figures 68 and 91. Contact surface penetration is 

controlled by the user’s selection of the contact type and the input, not by the material 

model formulation or input. This is not a wood model issue that requires changes to the 

wood model formulation or wood model input parameters. See section 17.3 for a 

discussion of the penetration problem. It has been demonstrated that similar penetration 

behavior is simulated with an elastic post (Mat 1) as with a wood post (Mat 143). It has 

also been demonstrated that penetration was relieved using a different version of the 

code. 

A user should realize that contact algorithms use material stiffness to relieve 

penetration. The stiffness extracted from orthotropic materials such as wood is the 

greatest stiffness. For saturated wood, the greatest stiffness is parallel to the grain and 

is 50 times greater than the stiffness perpendicular to the grain. The user should note 

whether the contact is parallel or perpendicular to the grain and should adjust contact 

surface parameters accordingly. 

17.3 INSTABILITIES IN DYNAMIC ANALYSES 

The user’s LS-DYNA simulations of wood posts impacted by bogie vehicles sporadically 

behave in an unstable manner (for example, see chapter 14). The objective of this 

section is to help the reader understand the conditions that lead to this unstable 

behavior. This is accomplished by running the user’s exact LS-DYNA input file on the 

developer’s computer system, then determining which input parameters cause the 

instability. Unless otherwise specified, the developer’s calculations are conducted with 

beta version 970, revision 1877 (Intel-based PC). The user’s calculations are conducted 

with beta version 970, revision 1812 (SGI Octane). 

Demonstration of Unstable Behavior

Two calculations were conducted by the developer to demonstrate unstable behavior. 

The mesh used in each calculation is nearly identical (both created by the user). The 

main difference between the two calculations is the inclusion of a second flap of 

neoprene between the post and the concrete support (as shown in figure 108). The 

other differences are in the input: 

• Rate effects (turned on in the single-flap analysis, turned off in the double-flap 

analysis). 

• Initial velocity specification (not applied to the cylinder neoprene in the single-flap 

calculation, but applied to the cylinder neoprene in the double-flap calculation). 

• Output force plane location (76 mm (3 inches) below the impact location in the 

single-flap calculation, 51 mm (2 inches) below the impact location in the doubleflap calculation). 
124

(a) Single flap (b) Double flap 

Figure 108. Finite element meshes used in demonstration problems. 

Mesh With Single Flap: This calculation did not exhibit unstable behavior on the 

developer’s computer system. The deformed configurations at the various time steps 

are shown in figure 109. 

Mesh With Double Flap: This calculation exhibited unstable behavior. The unstable 

behavior was sudden excessive erosion of the wood post, primarily between the impact 

and breakaway regions. Excessive erosion is shown in figure 110. LS-DYNA 

diagnostics indicate that numerous elements are being deleted with negative volume. 

No Flap 

Flap

Flap Flap 
125

(a) 0.0 ms (b) 30 ms (c) 50 ms (d) 100 ms 

Figure 109. Stable behavior in the developer’s single-flap calculation. 

 (a) 0.0 ms (b) 10.752 ms (c) 10.785 ms (d) 11.0 ms 

Figure 110. Unstable behavior in the developer’s double-flap calculation. 

These calculations indicated that small changes in the mesh and input can trigger 

instabilities. 

Variation of Instabilities by Computer Platform 

The developer’s calculations with the single and double flaps were conducted on an 

Intel-based PC (using Windows) computer platform. These same calculations were 
126

conducted by the user on their SGI Octane (using UNIX) computer platform. The user’s 

results also demonstrated excessive erosion; however, they were not identical to the 

developer’s results. The main difference was that the user noted unstable behavior in 

both calculations (single and double flap), whereas the developer only noted unstable 

behavior in one calculation (double flap). The unstable behavior in the user’s single-flap 

calculation is shown in figure 111. 
127

 (a) 0.0 ms (b) 10.501 ms (c) 10.750 ms (d) 10.801 ms 

Figure 111. Unstable behavior in the user’s single-flap calculation. 

These comparisons indicated that the unstable behavior was not identical and 

reproducible from computer platform to computer platform.

Time-Step Control 

The diagnostics provided by the LS-DYNA code indicated that a possible source of the 

instability was the time step (because of the contact surface algorithms). The output 

diagnostics from both the single- and double-flap analyses are shown in figure 112. This 

output indicates that the stable time step for the contact surface algorithms is less than 

that calculated for the critical element (which is based on the element size and the wave 

transit time across the element). 

 
128

(a) Single flap 

(b) Double flap 

Figure 112. LS-DYNA MESSAG file which shows that the stable time step is 

exceeded. 

A review of the LS-DYNA input file provided by the user indicates that the user specified 

that contact stability be ignored for the time-step determination (via the eroding contact 

time step parameter (ECDT) on the *CONTROL_CONTACT). Therefore, two 

calculations were conducted by the developer to determine whether the instabilities 

were relieved when contact stability was considered for the time-step determination: 

The LS-DYNA time step size should not exceed 0.235E-02 

 to avoid contact instabilities. If the step size is 

 bigger then scale the penalty of the offending surface. 

 0 t 0.0000E+00 dt 0.00E+00 flush i/o buffers 

 1 t 0.0000E+00 dt 5.01E-03 flush i/o buffers 

 1 t 0.0000E+00 dt 5.01E-03 write d3plot file 

 1118 t 5.0000E+00 dt 4.36E-03 write d3plot file 

 2279 t 9.9985E+00 dt 4.25E-03 write d3plot file 

 3498 t 1.4998E+01 dt 3.99E-03 write d3plot file 

 4769 t 1.9997E+01 dt 3.83E-03 write d3plot file 

 5000 t 2.0874E+01 dt 3.76E-03 flush i/o buffers 

 6143 t 2.4999E+01 dt 3.62E-03 write d3plot file 

 7603 t 3.0000E+01 dt 3.33E-03 write d3plot file 

 7603 t 3.0003E+01 dt 3.33E-03 write d3dump01 file 

The LS-DYNA time step size should not exceed 0.235E-02 

 to avoid contact instabilities. If the step size is 

 bigger then scale the penalty of the offending surface. 

 0 t 0.0000E+00 dt 0.00E+00 flush i/o buffers 

 1 t 0.0000E+00 dt 5.01E-03 flush i/o buffers 

 1 t 0.0000E+00 dt 5.01E-03 write d3plot file 

 205 t 9.9578E-01 dt 4.53E-03 write d3plot file 

 448 t 1.9972E+00 dt 3.88E-03 write d3plot file 

 693 t 2.9998E+00 dt 4.31E-03 write d3plot file 

 922 t 3.9962E+00 dt 4.26E-03 write d3plot file 

 1156 t 4.9982E+00 dt 4.20E-03 write d3plot file 

 1392 t 5.9970E+00 dt 4.20E-03 write d3plot file 

 1635 t 7.0000E+00 dt 4.07E-03 write d3plot file 

 1874 t 7.9981E+00 dt 4.39E-03 write d3plot file 

 2112 t 8.9964E+00 dt 4.18E-03 write d3plot file 

 2350 t 9.9974E+00 dt 4.19E-03 write d3plot file 
129

1. Time Step Set Considering Contact Stability: The *CONTROL_CONTACT 

card allows the user to specify whether or not contact stability is considered by 

LS-DYNA when determining the time step of each calculation. By default, contact 

stability is considered with LS-DYNA, version 970 (at least for the 

*CONTACT_ERODING_SINGLE_SURFACE algorithm used in these 

calculations). The double-flap calculation conducted by the developer is stable if 

the time step is based on the minimum needed for contact stability via the default 

value of ECDT on the *CONTROL_CONTACT card. The deformed configuration 

at 30 ms is shown in figure 113. LS-DYNA diagnostics are shown in figure 

114(a). 

2. Time Step Set Globally: Another option is to scale back the element-based time 

step via the *CONTROL_TIMESTEP card. The double-flap calculation conducted 

by the developer is stable if the time step is scaled back to 40 percent of the 

element-based step. This reduces the initial time step to that needed for stable 

contact behavior. The results are identical to those shown in figure 113. 

LS-DYNA diagnostics are shown in figure 114(b). Keep in mind that for this 

calculation, the time step was scaled up by overriding the time step for stable 

contact via *CONTROL_CONTACT, then scaled down via *CONTROL_ 

TIMESTEP. This is the way that the user ran their calculations to control stability. 

 (a) 0.0 ms (b) 15 ms (c) 50 ms (d) 100 ms 

Figure 113. Stable behavior is achieved by reducing the time step to that needed 

for stable contact surface behavior (default grade 1 saturated pine properties 

without rate effects). 
130

(a) *CONTROL_CONTACT 

(b) *CONTROL_TIMESTEP 

Figure 114. LS-DYNA MESSAG file with diagnostics for the stable time step. 

The LS-DYNA time step size should not exceed 0.235E-02 

 to avoid contact instabilities. If the step size is 

 bigger then scale the penalty of the offending surface. 

 0 t 0.0000E+00 dt 0.00E+00 flush i/o buffers 

 1 t 0.0000E+00 dt 2.23E-03 flush i/o buffers 

 1 t 0.0000E+00 dt 2.23E-03 write d3plot file 

 2606 t 4.9993E+00 dt 1.85E-03 write d3plot file 

 5000 t 9.3315E+00 dt 1.81E-03 flush i/o buffers 

 5367 t 9.9986E+00 dt 1.81E-03 write d3plot file 

 8161 t 1.4998E+01 dt 1.81E-03 write d3plot file 

 10000 t 1.8351E+01 dt 1.80E-03 flush i/o buffers 

 10936 t 1.9999E+01 dt 1.74E-03 write d3plot file 

 13868 t 2.4999E+01 dt 1.63E-03 write d3plot file 

 15000 t 2.6814E+01 dt 1.58E-03 flush i/o buffers 

 17062 t 2.9999E+01 dt 1.51E-03 write d3plot file 

 20000 t 3.4343E+01 dt 1.45E-03 flush i/o buffers 

 20455 t 3.5000E+01 dt 1.44E-03 write d3plot file 

 23978 t 4.0000E+01 dt 1.41E-03 write d3plot file 

 25000 t 4.1440E+01 dt 1.47E-03 flush i/o buffers 

 27565 t 4.4999E+01 dt 1.38E-03 write d3plot file 

 30000 t 4.8342E+01 dt 1.37E-03 flush i/o buffers 

 31210 t 5.0000E+01 dt 1.37E-03 write d3plot file 

 31210 t 5.0001E+01 dt 1.37E-03 write d3dump01 file 

The LS-DYNA time step size should not exceed 0.235E-02 

 to avoid contact instabilities. If the step size is 

 bigger then scale the penalty of the offending surface. 

 0 t 0.0000E+00 dt 0.00E+00 flush i/o buffers 

 1 t 0.0000E+00 dt 2.11E-03 flush i/o buffers 

 1 t 0.0000E+00 dt 2.11E-03 write d3plot file 

 2365 t 4.9983E+00 dt 2.11E-03 write d3plot file 

 4730 t 9.9986E+00 dt 2.11E-03 write d3plot file 

 5000 t 1.0570E+01 dt 2.11E-03 flush i/o buffers 

 7095 t 1.4999E+01 dt 2.11E-03 write d3plot file 

 9460 t 1.9999E+01 dt 2.11E-03 write d3plot file 

 10000 t 2.1141E+01 dt 2.11E-03 flush i/o buffers 

 11825 t 2.5000E+01 dt 2.11E-03 write d3plot file 

 14189 t 2.9998E+01 dt 2.11E-03 write d3plot file 

 15000 t 3.1713E+01 dt 2.11E-03 flush i/o buffers 

 16554 t 3.4998E+01 dt 2.11E-03 write d3plot file 

 18919 t 3.9999E+01 dt 2.11E-03 write d3plot file 

 20000 t 4.2284E+01 dt 2.11E-03 flush i/o buffers 

 21284 t 4.4999E+01 dt 2.11E-03 write d3plot file 

 23649 t 5.0000E+01 dt 2.11E-03 write d3plot file 

 23649 t 5.0002E+01 dt 2.11E-03 write d3dump01 file 
131

The user conducted their single- and double-flap calculations by reducing the time step 

via the *CONTROL_TIMESTEP method. Stable behavior was achieved in both their 

single- and double-flap calculations (consistent with the developer’s results). 

Based on these example calculations, the option recommended by the developer is to 

let LS-DYNA, by default, automatically calculate and use the stable time step. This 

means leaving ECDT as zero on the *CONTROL_CONTACT card. The default 

*CONTROL_CONTACT method selects the optimal time step throughout the run time of 

the calculation. On the other hand, with the *CONTROL_TIMESTEP option, the user 

must review the run-time diagnostics, then stop and rerun the calculation with a reduced 

time step.

Runs Conducted With Different Contact Surface Types 

The developer conducted both the single- and double-flap calculations with different 

contact surface formulations to further search for instabilities. LS-DYNA has 25 contact 

surface types. Four types were examined here: 

Eroding Single Surface: All calculations discussed in the previous paragraphs used 

this formulation. Instabilities, if they occurred, appeared as eroding wood post elements. 

The input specified seven parts to this contact surface (the neoprene on the impact 

cylinder, the three parts of the wood post, the two neoprene liners on each side of the 

post, and the rigid-concrete support). 

Single Surface: One double-flap calculation was conducted with this formulation. The 

calculation terminated early (at 2.9 ms) because of the negative volume of an element 

within the neoprene liner. The offending element is shown in figure 115. The liner is 

modeled as an elastic material. This calculation demonstrates that contact surface 

instabilities affect different parts of the mesh. The instability was not eliminated by 

reducing the time step below that needed for contact surface stability. 

The developer also checked the *CONTACT_SINGLE_SURFACE performance using 

an older version of LS-DYNA (beta version 970, revision 1553). The calculation did not 

run past the initialization stage. Instead, the calculation terminated at time zero with 

error messages stating that 30 nodes on the post had out-of-range velocities. LS-DYNA 

was unable to list the velocities, so it was expected that they were effectively infinite. 

The bogie does not even impact the post until about 0.5 ms, so these infinite velocities 

suggest a stability problem. No additional effort was made to diagnose this problem. 
132

(a) Post with liners (b) View of liner (c) View of post 

Figure 115. Unstable behavior of an elastic element in the neoprene liner. 

Nodes-to-Surface: One calculation was conducted with the addition of a 

*CONTACT_NODES_TO_SURFACE request in an attempt to keep the liner nodes at 

the sharp contact from penetrating the post segments (see figure 116). Penetration was 

observed. The calculation remained stable whether or not the time step exceeded that 

for stable contact behavior. 

Separate Surfaces for Each Contact: A single-flap calculation was conducted with the 

*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE algorithm for parts in direct 

contact with each other. The behavior was similar to that shown in figure 116(b), with 

the liner penetrating the post. The behavior was stable if the time step was set below 

that for contact surface stability. 

Parametric Studies 

Six additional calculations were conducted using the default *CONTROL_CONTACT 

method with the *CONTACT_ERODING_SINGLE_SURFACE formulation to ensure that 

changes in input do not result in additional instabilities. No instabilities occurred in any 

of the calculations. Some of the more interesting calculations are discussed here: 

Elastic Post: A single-flap calculation was conducted with the post modeled with elastic 

material model 1, rather than wood material model 143. The behavior remained stable. 

Additionally, the neoprene liner penetrated the elastic post at the sharp corner in the 

breakaway region, similar to the contact behavior calculated with the wood post (see 

figure 116). 
133

 (a) Elastic material 1 post (b) Wood material 143 post 

Figure 116. The liner penetrates the post when the post is modeled with either 

elastic or wood material models. 

Post-Peak Hardening: By default, the wood model simulates perfectly plastic behavior 

in compression (Ghard = 0.0). An option is available for hardening via the Ghard

parameter. One double-flap calculation with moderate post-peak hardening was run 

using a value of Ghard = 0.5. The calculation remained stable. Deformed configurations 

are given in figure 117. Note that the post breaks earlier in time with post-peak 

hardening than with perfect plasticity (compare figures 113 and 117). 

 (a) 5 ms (b) 10 ms (c) 25 ms (d) 50 ms 

Figure 117. The post breaks earlier when modeled with post-peak hardening 

(default saturated grade 1 pine properties with Ghard = 0.5). 

Penetration Penetration 
134

Douglas Fir: All calculations previously discussed were conducted with default 

properties for pine. One calculation was conducted with default properties for Douglas 

fir (without rate effects or post-peak hardening). Deformed configurations are shown in 

figure 118. The post breaks completely in two by 15 ms. Slight damage is evident in the 

impact region. The calculation remained stable. 

 (a) 5 ms (b) 10 ms (c) 15 ms (d) 50 ms 

Figure 118. The post breaks by 15 ms in this Douglas fir simulation (default 

saturated grade 1 properties without rate effects). 

Impact Velocity: All of the calculations previously discussed were conducted at a bogie 

vehicle impact velocity of 9.63 m/s (22 mi/h). An additional set of calculations at 

29.5 m/s (66 mi/h) was also conducted. These included the double-flap calculation 

without rate effects, with rate effects, and with a variation in the wood material 

properties. All calculations remained stable. Example calculations without and with rate 

effects are shown in figures 119 and 120, respectively. Fringes of damage are shown in 

figure 121. 
135

(a) 5 ms (b) 10 ms (c) 15 ms (d) 36 ms 

Figure 119. Bogie impact at 29.5 m/s for a grade 1 wood post modeled without 

rate effects (grade 1 default saturated pine properties). 

(a) 4 ms (b) 10 ms (c) 15 ms (d) 34 ms 

Figure 120. Bogie impact at 29.5 m/s for a saturated grade 1 wood post modeled 

with rate effects (default pine properties). 
136

 (a) 4 ms (b) 10 ms (c) 15 ms (d) 34 ms 

Figure 121. Fringes of damage for bogie impact at 29.5 m/s (default properties for 

saturated grade 1 pine with rate effects). 

Runs Conducted With Rigid Sleeve 

The developer reproduced one double-flap calculation with a modified bogie and 

post/liner/support model that was originally created by the user and analyzed in 

figure 92. The liner and support were removed and replaced with a rigid sleeve with 

smoothed flaps. The bogie was also simplified. 

The calculation exhibited unstable behavior with or without a time-step reduction below 

that needed for stable contact surface behavior. The unstable behavior was erosion at 

the bottom of the wood post (as shown in figures 122 and123). An examination of the 

stress histories in the first element to erode indicated that all six stress components 

experienced sudden high stresses that exceeded the strengths of the wood. This 

caused the element to soften and erode. This erosion initiated almost immediately (at 

0.002 ms). The time of erosion was less than the 0.005-ms wave transit time across a 

single 25-mm wood element. It was also substantially less than the wave transit time 

from the bogie impact point to the bottom of the post (about 0.3 ms). In addition, it took 

about 0.5 ms for the bogie vehicle to impact the post because there was an initial 

separation between the bogie vehicle and the post. This time discrepancy indicated that 

forces other than those caused by bogie impact were loading the elements. 

9.900e-001 

8.910e-001 

7.950e-001 

6.930e-001 

5.940e-001 

4.950e-001 

3.960e-001 

2.970e-001 

1.980e-001 

9.900e-002 

0000e-000
137

 (a) Model (b) 0.002 ms (c) 0.0065 ms 

Figure 122. Unstable behavior in the developer’s rigid-sleeve calculation. 

 

 (a) Model (b) State 1 (c) State 2 (d) State 3 

Figure 123. Unstable behavior in the user’s rigid-sleeve calculation. 

An examination of the LS-DYNA diagnostics revealed 40 contact surface warnings. One 

example warning is shown in figure 124. It indicates that there was an initial penetration 

through a contact surface. Initial penetration is penetration detected by the LS-DYNA 

code before the start of the simulation. In other words, the contact surfaces were 

improperly set up. The LS-DYNA code moves any nodes that experience initial 

penetration before starting the simulation. In this case, the node was moved 18.2 mm. 

The developer did not see any value in conducting additional calculations with this 

mesh, so no attempt was made to correct the contact surface problem. 
138

Figure 124. LS-DYNA diagnostics indicate that a contact surface is improperly 

positioned and requires movement of nodes prior to running the simulation. 

Runs Conducted With Different LS-DYNA Releases 

Version 960 Using Interface: No instabilities occurred in the developer’s calculations, 

in which the wood model was interfaced with LS-DYNA as a user-defined material 

model. All runs were conducted on a Compact Alpha system using UNIX. In addition, 

penetration at the sharp corner between the liner and the wood post was not nearly as 

significant as that calculated with beta version 970, revision 1877 (PC using Windows). 

This is demonstrated by comparing figure 125 with figure 116.

C

 (a) 25 ms (b) 38 ms 

Figure 125. The liner does not penetrate the post in calculations conducted with 

LS-DYNA, version 960. 

*** Warning - initial penetration through contact surface

 interface # = 2 

 interface type = 5 

 moved node = 9998 

 closest node = 15078 

 segment = 1372 

 penetration = -0.1658895E+02 

 normal = 0.0000000E+00 0.1000000E+01 0.0000000E+00 

 node 9998 old x,y,z = 0.1005000E+03 0.5841105E+02 -0.7810679E+03 

 node 9998 s,t = -0.6009506E+00 -0.1000000E+01 

 segment data: 

 15014 0.9999900E+02 0.7500000E+02 -0.7760000E+03 

 15077 0.9999900E+02 0.7500000E+02 -0.8014000E+03 

 15078 0.7499900E+02 0.7500000E+02 -0.8014000E+03 

 15015 0.7499900E+02 0.7500000E+02 -0.7760000E+03 

 *** Warning-node 9998 of contact interface 2 moved -0.182E+02 
139

Beta Version 970, Revision 1553: With one exception, instabilities did not occur in the 

developer’s calculations (with or without time-step reduction), all of which used the wood 

model implemented as material model 143. The exception was an error termination 

following initialization when the *CONTACT_SINGLE_SURFACE formulation was 

requested. The error was out-of-range velocities applied to the nodes of the wood post 

at time zero, even though the post was not impacted by the bogie until about 0.5 ms. 

Beta Version 970, Revision 1877: Instabilities sometimes occurred in the developer’s

calculations if the critical time step for contact stability was violated. One instability also 

occurred in the liner if the *CONTACT_SINGLE_SURFACE formulation was requested, 

even though the time step was set below that needed for contact surface stability. 

Summary 

In summary, all calculations except one exhibited stable behavior when conducted with 

the time step set below that needed for stable contact surface behavior. Instabilities 

may (but do not always) occur if the time step for stable contact surface behavior is 

exceeded. Instabilities are not identical and reproducible from computer platform to 

computer platform. 

The one instability that we were unable to control occurred in the elastic liner when 

using the *CONTACT_SINGLE_SURFACE formulation. However, having instability with 

one type of surface is not an insurmountable problem. With more than 25 contact 

surface types available in the LS-DYNA code, the user has a variety of methods 

available to specify and control contact surface stability and penetration. 

141

18 REFERENCES 

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Software Technology Corporation, Livermore, CA, 2001. 

2. Murray, Y.D., Manual for LS-DYNA Wood Material Model 143, Report No. FHWAHRT-04-097, Federal Highway Administration, 2004. 

3. Lewis, B.A., Manual for LS-DYNA Soil Material Model 147, Report No. FHWAHRT-04-095, Federal Highway Administration, 2004. 

4. Reid, J.D., B.A. Coon, B.A. Lewis, S.H. Sutherland, and Y.D. Murray, Evaluation of 

LS-DYNA Soil Material Model 147, Report No. FHWA-HRT-04-094, Federal 

Highway Administration, 2004. 

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