January 2015 

NASA/CR–2015-218679 

Elemental Water Impact Test: Phase 1 

20-inch Hemisphere 

Gregory J. Vassilakos 

Analytical Mechanics Associates, Inc., Hampton, Virginia 
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January 2015 

NASA/CR–2014-218679 

Elemental Water Impact Test: Phase 1 

20-Inch Hemisphere 

Gregory J. Vassilakos 

Analytical Mechanics Associates, Inc., Hampton, Virginia 
Available from: 

NASA STI Program / Mail Stop 148 

NASA Langley Research Center 

Hampton, VA 23681-2199 

Fax: 757-864-6500 

Acknowledgments 

The author would like to recognize Dr. Karen Lyle, Steve Gayle, and Dr. Peter Gage for 

developing the plan for the test series and arranging the set-up of the test facility and 

fabrication of the test article. The author would like to thank David Stegall for his 

exhaustive efforts in providing test data and troubleshooting problems with the 

instrumentation and data acquisition system. The author would also like to thank 

Mercedes Reaves for the investigations into coupling stiffness and gravitational preload 

that she performed using 3-D models of the hemisphere. The author would also like to 

recognize Claude Bryant for bringing attention to the Cappelli and Wilkinson equations 

and for his efforts in troubleshooting problems with the 2-D axisymmetric model. 

The use of trademarks or names of manufacturers in this report is for accu rate reporting and does not constitute an 

official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and 

Space Administration. 
iii

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iv

Abstract 

Spacecraft are being designed based on LS-DYNA simulations of water landing impacts. The Elemental 

Water Impact Test (EWIT) series was undertaken to assess the accuracy of LS-DYNA water impact 

simulations. Phase 1 of the EWIT series featured water impact tests of a 20-inch hemisphere dropped 

from heights of 5 feet and 10 feet. The hemisphere was outfitted with an accelerometer and three 

pressure gages. The focus of this report is the correlation of analytical models against test data. Three 

analytical models were used: 

1. Closed-Form Solution 

2. 2-D Axisymmetric LS-DYNA Model 

3. 3-D Quarter Symmetry LS-DYNA Model 

The closed form solution was found to over-predict the peak acceleration. The peak pressure from the 

closed-form solution is infinite; however, the solution does provide a reasonable prediction for the latetime pressure decay. 

The 2-D axisymmetric LS-DYNA model was evaluated for a broad range of modeling parameters. The 

two parameters that were found to be the most critical were mesh density and fluid-structure coupling 

stiffness. The 2-D model provided reasonable predictions for the acceleration histories. Pressure 

histories were poorly predicted; however, reasonable predictions were obtained for the impulse as 

determined by integrating the pressure history. Increasing mesh density resulted in better predictions for 

the late-time pressure decay, but did not improve the predictions of the early-time peak pressure. 

The 3-D quarter symmetry LS-DYNA model was used for further evaluations of mesh density and fluid 

structure coupling stiffness. The 3-D model produced predictions for the acceleration histories that 

better matched the test data than the 2-D model. The pressure histories from the 3-D model were equally 

as poor as the 2-D model. Again, the impulse was predicted far more accurately than the pressure. 

The following guidelines were proposed for defining the fluid mesh density and fluid-structure coupling 

stiffness for LS-DYNA simulations. These guidelines might not be feasible for spacecraft water landing 

design simulations due to limits in available computer resources. 

1. The element size of the fluid mesh should be no larger than 1/200th of the radius of curvature of the 

structure. 

2. The coupling stiffness curve should be established based on the maximum expected coupling pressure 

at a penetration equal to 1/10th the size of the fluid elements. 

Guidelines were also offered for judging the adequacy of the fluid-structure coupling definition. 

1. The coupling stiffness is too soft if the peak coupling pressure is toward the middle of the contact 

patch rather than at the perimeter. 

2. The coupling stiffness is too soft if the acceleration time history exhibits oscillations that can be 

related to the structure bouncing on the coupling surface. 

3. The coupling stiffness is too stiff if the coupling pressure distribution appears as a checkerboard 

pattern of isolated pressure spikes. 

4. The coupling stiffness is too stiff if the coupling pressure histories appear as a series of isolated 

spikes. 
v

Table of Contents 

1. Introduction ........................................................................................................................................ 1

2. Simulations .......................................................................................................................................... 1

2.1. LS-DYNA......................................................................................................................................... 1

2.2. ALE Solution Parameters ................................................................................................................. 1

2.3. Element Section Parameters ............................................................................................................. 2

2.4. Material Parameters .......................................................................................................................... 2

2.5. Equation of State Parameters ............................................................................................................ 2

2.6. Fluid Structure Coupling Parameters ............................................................................................... 2

2.7. Boundary Conditions ........................................................................................................................ 2

2.8. Gravity and Atmospheric Preload .................................................................................................... 3

3. Tests ..................................................................................................................................................... 3

3.1. Test Configuration ............................................................................................................................ 3

3.2. Test Article ....................................................................................................................................... 4

3.3. Test Results ...................................................................................................................................... 5

4. Simulation Models .............................................................................................................................. 8

4.1. Closed-Form Solution ...................................................................................................................... 8

4.2. 2-D LS-DYNA Simulation ............................................................................................................... 9

4.3. 3-D LS-DYNA Simulation ............................................................................................................. 11

5. Test and Simulation Correlation .................................................................................................... 13

5.1. Closed-Form Results ...................................................................................................................... 13

5.2. 2-D LS-DYNA Results ................................................................................................................... 15

5.3. 3-D LS-DYNA Results ................................................................................................................... 30

6. Establishing Simulation Parameters without Test Data ............................................................... 38

6.1. Width of Pressure Pulse .................................................................................................................. 38

6.2. Establishing Mesh Density and Coupling Stiffness........................................................................ 39

6.3. Evaluating Model Performance without Test Data ........................................................................ 40

7. Conclusions and Recommendations ............................................................................................... 43

References .................................................................................................................................................. 44

Appendix A: Two-Dimensional Axisymmetric Model ......................................................................... 45

Appendix B: Three-Dimensional Quarter Model ................................................................................ 48
vi

List of Figures 

Figure 1. Test Set-Up ..................................................................................................................... 4

Figure 2. Hemisphere Configuration ............................................................................................. 4

Figure 3. Pressure Transducer Locations ....................................................................................... 5

Figure 4. Raw Acceleration Histories for 5-foot Drops ................................................................. 5

Figure 5. Filtered Acceleration Histories for 5-foot Drops............................................................. 6

Figure 6. Raw Acceleration Histories for 10-foot Drops ............................................................... 6

Figure 7. Filtered Acceleration Histories for 10-foot Drops .......................................................... 7

Figure 8. Pressure Histories for 5-foot Drops ................................................................................ 8

Figure 9. Pressure Histories for 10-foot Drops .............................................................................. 8

Figure 10. Two-Dimensional Axisymmetric Model .................................................................... 10

Figure 11. Mesh Variants for Two-Dimensional Axisymmetric Model ...................................... 11

Figure 12. Three-Dimensional Quarter Model ............................................................................ 12

Figure 13. 0.025-inch Fluid Element Mesh Variant .................................................................... 13

Figure 14. Closed-Form Solution Acceleration History for 5-foot Drop .................................... 14

Figure 15. Closed-Form Solution Acceleration History for 10-foot Drop .................................. 14

Figure 16. Closed-Form Solution Pressure History for 5-foot Drop ........................................... 15

Figure 17. Closed-Form Solution Pressure History for 10-foot Drop ......................................... 15

Figure 18. Acceleration Histories for 5-foot Drop for 0.025-inch Element Size ........................ 16

Figure 19. Acceleration Histories for 5-foot Drop for 0.05-inch Element Size .......................... 16

Figure 20. Acceleration Histories for 5-foot Drop for 0.1-inch Element Size ............................ 17

Figure 21. Acceleration Histories for 10-foot Drop for 0.025-inch Element Size ...................... 17

Figure 22. Acceleration Histories for 10-foot Drop for 0.5-inch Element Size .......................... 18

Figure 23. Acceleration Histories for 10-foot Drop for 0.1-inch Element Size .......................... 18

Figure 24. Peak Accelerations for Mesh and Coupling Stiffness Variants for 5-foot Drops ...... 19

Figure 25. Peak Acceleration for Mesh and Coupling Stiffness Variants for 10-foot Drops ...... 19

Figure 26. Pressure in Fluid versus DBFSI Pressure at Coupling Surface .................................. 20

Figure 27. Pressure Histories for 5-foot Drop for 0.025-inch Element Size ............................... 21

Figure 28. Pressure Histories for 5-foot Drop for 0.05-inch Element Size ................................. 21

Figure 29. Pressure Histories for 5-foot Drop for 0.1-inch Element Size ................................... 22

Figure 30. Pressure Histories for 10-foot Drop for 0.025-inch Element Size ............................. 22

Figure 31. Pressure Histories for 10-foot Drop for 0.05-inch Element Size ............................... 23

Figure 32. Pressure Histories for 10-foot Drop for 0.1-inch Element Size ................................. 23

Figure 33. Pressure Histories for 5-foot Drop for 10 x Curve 10 Mesh Variants........................ 24

Figure 34. Pressure Histories for 10-foot Drop for 10 x Curve 10 Mesh Variants...................... 24

Figure 35. Peak Pressure for Mesh and Coupling Stiffness Variants for 5-foot Drops ............... 25

Figure 36. Peak Pressure for Mesh and Coupling Stiffness Variants for 10-foot Drops ............. 25

Figure 37. Impulse for Mesh and Coupling Stiffness Variants for 5-foot Drops ........................ 26

Figure 38. Impulse for Mesh and Coupling Stiffness Variants for 10-foot Drops ...................... 26

Figure 39. Pressure Contours for Coupling Stiffness Variants for 5-foot Drop ........................... 27

Figure 40. Peak Filtered Accelerations for Sensitivity Study Variants ....................................... 28

Figure 41. Peak Pressures for Sensitivity Study Variants............................................................ 29

Figure 42. Pressure Pulse Caused by a 0.02-inch Divot .............................................................. 30

Figure 43. Acceleration History for 5-foot Drop Simulations ..................................................... 31
vii

Figure 44. Acceleration History for 10-foot Drop Simulations ................................................... 31

Figure 45. Pressure Histories for 5-foot Drop Simulations ......................................................... 32

Figure 46. Pressure Histories for 10-foot Drop Simulations ....................................................... 33

Figure 47. Pressure Distribution at 0.001 seconds after Impact for 5-foot Drop Simulations .... 34

Figure 48. Pressure Distribution at 0.001 seconds after Impact for 10-foot Drop Simulations .. 35

Figure 49. Acceleration Histories for Mesh Variants for 5-foot Simulations.............................. 36

Figure 50. Acceleration Histories for Mesh Variants for 10-foot Simulations............................ 36

Figure 51. Pressure Histories for Mesh Variants for 5-foot Simulations .................................... 37

Figure 52. Pressure Histories for Mesh Variants for 10-foot Simulations .................................. 37

Figure 53. Pressure Transducer Arrangement ............................................................................. 38

Figure 54. Pressure Histories for Multiple Pressure Transducers................................................ 39

Figure 55. Description of Penetration and Leakage ..................................................................... 41

Figure 56. Symptoms of an Excessively Soft Coupling Stiffness ............................................... 42

Figure 57. Symptoms of Excessively High Coupling Stiffness ................................................... 43

List of Tables 

Table 1. Parameters Varied for Sensitivity Study ........................................................................ 28

Table 2. Pressure Transducer Locations ...................................................................................... 38

Table 3. Pressure Pulse Width Estimate ...................................................................................... 39

Table 4. Recommendations for Element Size and Coupling Stiffness ........................................ 40
1

1. Introduction 

Spacecraft are being designed based on LS-DYNA [1] simulations of water landing impacts. The 

Elemental Water Impact Test (EWIT) series was undertaken to assess the accuracy of LS-DYNA water 

impact simulations. Phase 1 of the EWIT series featured water impact tests of a 20-inch hemisphere 

dropped from heights of 5 feet and 10 feet. 

2. Simulations 

2.1. LS-DYNA

LS-DYNA is a general purpose transient dynamic finite element code capable of simulating complex real 

world problems. LS-DYNA’s strength is in the modeling of impact problems. An explicit time 

integration scheme is used in which there is no equilibrium check and iteration of the solution between 

time steps. This approach works only because the time step is restricted to be smaller than the shortest 

stress wave transit time for any element in the model. 

The modeling of contact between bodies in LS-DYNA is accomplished via a penalty method. Contact is 

detected when the nodes of one body pass through the face or edges of the elements of another body. 

Preloaded penalty springs are then inserted to push the bodies apart. One consequence of this approach is 

one body must always penetrate another body before contact is detected. Another consequence is that 

there is a finite contact stiffness at the interface between the bodies that is entirely nonphysical. 

LS-DYNA has a limited capability to model a fluid using Arbitrary Lagrangian-Eulerian (ALE) meshes. 

In the ALE approach, each time step begins with a mesh that is conceptually similar to the Lagrangian 

meshes used to model structures. LS-DYNA determines the deformation of the fluid that occurs during 

the time step, then moves, or advects, the mesh back to its original configuration and treats the fluid as 

having moved through the mesh. The result is that the nodes of the mesh do not move. Instead, the 

volume fraction of the fluid in each element is changed. The fluid in the ALE mesh can flow, compress, 

and impart momentum; however, the ALE mesh does not offer a full Navier-Stokes fluid flow solution. 

LS-DYNA features many parameters that can be adjusted in modeling of fluid-structure interaction 

problems. An overarching parameter is the mesh density. As with all finite element codes, a smaller 

element size generally produces results that are more accurate. In addition to mesh density, there are 

many other solution parameters that can be selected. Several of these are discussed in the following 

sections. 

2.2. ALE Solution Parameters 

The *CONTROL_ALE card includes several parameters, most of which should be allowed to take default 

values. The number of solution cycles per mesh advection step, NADV, should ideally be specified as 1, 

though it can be set to a higher value if necessary to reduce solution time. Various options for the mesh 

advection method, METH, are available. The developer recommends METH=2, which is second order 

accurate. Other options can be tried if necessary to reduce solution time. Several parameters are 

available for mesh advection smoothing. The developer warns that the smoothing algorithm is not based 

in physics. It is recommend that smoothing be turned off, AFAC=-1. 
2

2.3. Element Section Parameters 

For a 2-D mesh, *SECTION_ALE2D offers two axisymmetric element formulations. ELFORM=14 is 

area weighted and ELFORM=15 is volume weighted. The code developer strongly recommends 

ELFORM=14. For a 3-D mesh, *SECTION_SOLID offers two treatments of an air space above a fluid. 

ELFORM=11 allows the air to be treated as a fluid with its own equation of state. ELFORM=12 treats 

the air as a void space. The code developer recommends ELFORM=11. 

2.4. Material Parameters 

Fluids with an equation of state utilize *MAT_NULL. The most important material property for the 

impact problem is the material density, RO. The tensile pressure cutoff, PC, is typically set to either zero 

or a very small negative number. If the air is treated as a void space (ELFORM=12), it may be desirable 

to set PC equal to negative one atmosphere (-14.7 psi) in order to mimic the fact that cavitation does not 

occur until the pressure drops to zero absolute pressure. The LS-DYNA Keyword User’s Manual [2] 

implies that a non-zero value must be specified in order for the fluid to be able to cavitate. 

2.5. Equation of State Parameters 

The two most commonly used equations of state for water are *EOS_GRUNEISEN and 

*EOS_LINEAR_POLYNOMIAL. *EOS_GRUNEISEN is required for water at high pressure as would 

occur in the simulation of an underwater explosion. For the range of pressures seen in the water impact 

problem, the two options provide similar relationships between pressure and volumetric strain. 

*EOS_LINEAR_POLYNOMIAL is readily usable for both water and air. 

2.6. Fluid Structure Coupling Parameters 

The *CONSTRAINED_LAGRANGE_IN_SOLID card features many options. The default for the 

number of fluid-structure coupling points on the surface of each structural element, NQUAD, is a 2 x 2 

array of coupling points. If the structural elements are larger than the fluid elements, a larger number of 

NQUAD points should be specified. Perhaps the most important coupling parameter is the coupling 

stiffness, PFAC. If PFAC is a positive value, the coupling stiffness is based on the solution time step and 

the mass of the nodes on either end of the penalty coupling springs. The default is PFAC=0.1. A 

negative value for PFAC points to a user-specified coupling stiffness curve. The curve specifies the 

coupling pressure as a function of the distance the fluid penetrates past the coupling surface. The user can 

also specify the fluid element minimum volume fraction at which coupling is activated, FRCMIN. The 

default is FRCMIN=0.5. Problems with excessive penetration of fluid into the structure can be addressed 

by reducing FRCMIN; however, there is no firm physical basis for this. Simulations with low values of 

FRCMIN have been observed to show the fluid moving away from the structure prematurely. 

2.7. Boundary Conditions 

The typical approach for modeling a water or soil block in an impact problem is to restrain the sides and 

bottom of the mesh in the directions normal to each face. The problem with this approach is that stress 

waves are reflected when they reach the mesh boundary. Usually, dispersion of the stress waves results in 

negligible pressure amplitude by the time the stress wave arrives back in the area of the impact. An 

alternative approach is to designate a layer of elements along the sides and bottom of the mesh as ambient 
3

pressure reservoir elements. This is done via the ambient element type option, AET=4, on the 

*SECTION cards. The ambient pressure reservoir elements allow material to flow in and out of the mesh 

while holding the pressure constant. 

2.8. Gravity and Atmospheric Preload 

It is customary in water and soil impact problems to initialize gravity at 1g instantaneously at the start of a 

simulation. The result is that stress waves oscillate through the material throughout the solution duration. 

This typically has negligible effect on the solution as the amplitude of the pressure oscillations is similar 

to the hydrostatic head at the base of the mesh, which is much less than the pressure due to the impact. A 

more accurate method is to ramp gravity to 1g prior to the impact. The result is a stable hydrostatic stress 

state in the material provided that the ramp time is much longer than the time required for a stress wave to 

propagate through the depth of the mesh. If there is no atmospheric overpressure, the pressure in the 

material at the surface will be zero, which could allow material to cavitate prematurely. If the air is 

treated as a void (ELFORM=12), premature cavitation can be prevented by setting the tensile cutoff 

pressure on the *MAT_NULL input, PC, equal to negative one atmosphere (-14.7 psi). If the air is 

modeled as a fluid (ELFORM=11), the *INITIAL_HYDROSTATIC_ALE and 

*ALE_AMBIENT_HYDROSTATIC options can be used to preload the air and water meshes with 

atmospheric and hydrostatic pressure. For the *INITIAL_HYDROSTATIC_ALE and 

*ALE_AMBIENT_HYDROSTATIC options, *EOS_LINEAR_POLYNOMIAL must be used to define 

the equation of state for the air and water. 

3. Tests

3.1. Test Configuration 

The drop tests were performed in a 15-foot diameter above-ground swimming pool located in the Room 

123 high-bay area of Building 1293A at NASA Langley Research Center (LaRC). The depth of the water 

in the pool was approximately four feet. The test pool was located inside a 24-foot diameter aboveground swimming pool to catch any over splash. A foam pad was placed under the liner at the bottom of 

the inner pool to cushion bottom impacts. The test article was suspended above the test pool on a boom 

extended from a forklift. A line hanging from the test article was used to measure the drop height. The 

test set-up is illustrated in Figure 1. 
4

Figure 1. Test Set-Up

3.2. Test Article 

The test article was a hemispherical aluminum shell with an outside diameter of 20 inches. The general 

configuration of the test article is illustrated in Figure 2. The hemisphere had a shell thickness of 0.19 

inches and was filled with bismuth ballast to an approximate depth of 2.5 inches at the apex. Eight 

phenolic ribs served as internal attachment points for instrumentation, which included an accelerometer at 

the center and three pressure transducers at a distance of approximately 2.25 inches from the apex. The 

locations of the pressure transducers are illustrated in Figure 3. An aluminum lid with a thickness of 0.25 

inches served to keep water away from the instrumentation. The hemisphere was lifted into position for 

the drop test via three lift points at the perimeter of the lid. The weight of the hemisphere with 

instrumentation was 48 lb. 

Figure 2. Hemisphere Configuration 
5

Figure 3. Pressure Transducer Locations 

3.3. Test Results 

Three tests were performed at a 5-foot drop height and three were performed at a 10-foot drop height. For 

comparison with simulation data, the acceleration histories were filtered using a 180 Hz Butterworth filter 

to remove the vibratory structural response. Figures 4 and 5 show raw and filtered acceleration histories 

for the 5-foot drops. Figures 6 and 7 show the acceleration histories for the 10-foot drops. An artifact of 

the filtering is a small negative dip in acceleration prior to impact.

Figure 4. Raw Acceleration Histories for 5-foot Drops 
6

Figure 5. Filtered Acceleration Histories for 5-foot Drops

Figure 6. Raw Acceleration Histories for 10-foot Drops 

180 Hz Butterworth Filter
7

Figure 7. Filtered Acceleration Histories for 10-foot Drops 

Histories from the pressure transducers for the 5-foot and 10-foot drops are shown in Figures 8 and 9. 

The sampling rate for both pressure and acceleration data was 50,000 Hz. The TDAS PRO data 

acquisition system used for the tests is equipped with an analog anti-aliasing filter with a cutoff frequency 

of 4300 Hz. The anti-aliasing filter can be bypassed, but it was used for these tests. The sampling rate 

was relatively high for this type of test; however, the duration of the pressure peaks is so short that even 

this relatively high sampling rate provides just a few points to define the pressure peaks. As a 

consequence, some of the pressure histories exhibit truncated peaks. Even for the pressure histories that 

do not show truncated peaks, it is inevitable that the data points sampled during the test did not capture 

the absolute pressure peak. 

One pressure history from each test that does not show a truncated peak was chosen for comparison 

against simulation data. The chosen pressure histories are Gage 3 of Test 1, Gage 3 of Test 2, and Gage 

2 of Test 3 for the five-foot drops, and Gage 1 of Test 4, Gage 2 of Test 5, and Gage 3 of Test 6 for the 

ten-foot drops. The peaks of the pressure histories do not occur simultaneously due to small angles of 

pitch that exist upon impact of the hemisphere with the water. In the figures, the relative timings of the 

peaks are as they occurred during the test. For comparisons between tests, the pressure histories have 

been arbitrarily shifted so that several peaks from different tests align. 

180 Hz Butterworth Filter
8

Figure 8. Pressure Histories for 5-foot Drops 

Figure 9. Pressure Histories for 10-foot Drops 

4. Simulation Models 

4.1. Closed-Form Solution 

A closed-form solution for the acceleration and pressure histories of a sphere impacting water was 

developed by A.P. Cappelli and J.P.D. Wilkinson [3]. The equations are as follows. 
9

A = − (4 √2 ρ 

V0

5/2R

3/2t1/2

M

) (1 + γ)

−2 Equation 1

P =

√2ρV0

3/2R

1/2[1−γ(2−3r2

c

2

)]

πt1/2(1−r

2

c

2

)

1/2

(1+γ)2

− 

ρV0

2

2(1+γ)2

[1 + 4r2

2c2

(1 − r

2

c

2

)

−1] Equation 2

c = (2 R V0 t)

1/2 Equation 3

γ =

8√2ρ(RV0t)

3/2

3M

 Equation 4

Where: A = Acceleration 

 P = Pressure 

 ρ = Water Mass Density 

 V0 = Initial Velocity 

 M = Mass 

 R = Radius of Curvature at Impact Point 

 r = Polar Distance from Impact Point 

 c = Maximum Radius of Wetted Shell Surface 

 t = Time after Impact 

 γ = Non-Dimensional Parameter 

 

Cappelli and Wilkinson note problems with Equation 2. The predicted pressure is singular at the time 

that the contact patch radius, c, reaches the polar distance, r, which results in the equation producing no 

real answer for the highest pressure at a given polar distance. Cappelli and Wilkinson recommend 

dropping the second term of the pressure equation as it is small everywhere except for a negative 

singularity at the perimeter of the contact patch. Cappelli and Wilkinson further note that the remaining 

term of the pressure equation predicts nonphysical negative pressure in the late time. 

4.2. 2-D LS-DYNA Simulation 

A model of a two-dimensional axisymmetric slice of the penetromter was used to evaluate the sensitivity 

of the acceleration and pressure to several LS-DYNA parameters. The model configuration is illustrated 

in Figure 10. 
10

Figure 10. Two-Dimensional Axisymmetric Model 

The hemisphere was treated as linear elastic. Aluminum material properties were specified for the shell 

and the cover. The internal ballast was bismuth. The material density of the bismuth ballast was adjusted 

to achieve the desired total weight of 48 lb. The water was modeled with an equation of state. The air 

was treated as a vacuum. Gravity was ramped to 1g during the first 0.01 seconds to obtain a stable 

hydrostatic pressure state in the water prior to impact. The initial height and velocity of the hemisphere 

were adjusted so that impact occurred at the desired velocity at 0.01 seconds. The LS-DYNA cards that 

describe the coupling stiffness, material properties, and initial conditions are provided in Appendix A. 

Three mesh variants of the model were used with element edge lengths of 0.1, 0.05, and 0.025 inches in 

the area of the initial contact for both the hemisphere shell and the water. The meshes are illustrated in 

Figure 11. 
11

Figure 11. Mesh Variants for Two-Dimensional Axisymmetric Model 

The pressure transducers used for the tests had a diameter of approximately one-eighth inch. For the 

simulations, coupling pressure was recorded using the DBFSI option in LS-DYNA. The pressure was 

averaged for the elements that span 0.1 inches at the pressure transducer location. This was one element 

for the 0.1-inch mesh, two elements for the 0.05-inch mesh, and four elements for the 0.025-inch mesh. 

The baseline coupling stiffness was designated Curve 10. Curve 10 featured 100 psi at a penetration of 

0.005 inches. Simulations were also performed with variants of Curve 10 with the stiffness scaled by 

factors of 0.1, 10, and 100. 

4.3. 3-D LS-DYNA Simulation 

A three-dimensional quarter model of the hemisphere was used for further evaluations of coupling 

stiffness and mesh density. The three-dimensional model was considered necessary because the 2-D and 

3-D sections of the LS-DYNA code were written by different developers. The theory is the same for 

both, but there is no certainty that the implementation behaves in exactly the same manner, so there is no 

certainty that the findings concerning one modeling approach are directly applicable to the other. The 

three-dimensional model is illustrated in Figure 12.
12

Figure 12. Three-Dimensional Quarter Model

The hemisphere was treated as rigid. Both the air and the water were modeled with equations of state. 

Gravity was initiated instantaneously and options within LS-DYNA were employed to initiate the air at 

one atmosphere and the water at one atmosphere plus hydrostatic pressure. The initial height of the 

hemisphere above the water was set so that impact occurred immediately after the start of the simulation. 

The bottom and outermost layers of elements of the water and air meshes were defined as reservoir 

elements. The reservoir elements allow material to flow in or out of the mesh in order to maintain 

constant pressure at the boundary. The LS-DYNA cards that describe the coupling stiffness, material 

properties, and initial conditions are provided in Appendix B.

Three water meshes were used. The baseline mesh featured an element size of 0.1 inches near the initial 

impact. The overall mesh radius was 15 inches, the air height was 1.2 inches, and the water depth was 

13.2 inches. The first variant featured an element size of 0.05 inches near the initial impact and the same 

overall mesh radius and depth as the baseline mesh. The second variant was created by halving the 

dimensions of the 0.05-inch mesh. This resulted in an element size of 0.025 inches near the initial impact 

and an overall mesh radius of 7.5 inches, an air height of 0.6 inches, and a water depth of 6.6 inches. The 

0.025-inch element model is illustrated in Figure 13. Due to the limited extent of the mesh, the 0.025-

inch element model was suitable only for short duration simulations to determine early-time impact 

response.

15”

13.2”

1.2”
13

Figure 13. 0.025-inch Fluid Element Mesh Variant

For all simulations, the element size for the hemisphere was 0.1 inches, which is similar to the size of the 

pressure transducer used in the tests. Pressures from the simulations were recorded for a single element 

using the DBFSI option.

The baseline coupling stiffness was designated Curve 12. Curve 12 featured 100 psi at a penetration of 

0.01 inches. This was half the stiffness of the baseline Curve 10 used for the 2-D simulations. The 

rationale for halving the coupling stiffness for the 3-D simulations was that the baseline 3-D mesh 

featured elements with edge lengths twice as large as the baseline 2-D mesh. For the baseline mesh with 

an element size of 0.1 inches, simulations were performed with variants of Curve 12 that were scaled by 

factors of 0.1 and 10 for the stiffness. Simulations were also performed with the coupling stiffness 

default, PFAC = 0.1. LS-DYNA determines the default coupling stiffness based on the stiffness required 

to achieve a vibration period equal to the critical time step size for solution stability. 

5. Test and Simulation Correlation 

5.1. Closed-Form Results 

Accelerations for the closed-form solution for the 5-foot and 10-foot drops are plotted with test data in 

Figures 14 and 15. The test data was filtered using a 180-Hz Butterworth filter to eliminate vibratory 

structural response not represented in the analytical models. The closed-form solution exhibits no noise 

and requires no filtering. The results show that the closed-form solution substantially over predicted the 

peak acceleration. This is partly due to the closed-form solution not taking into account the reduction in 

the velocity that occurs as a consequence of the deceleration during the early stages of the impact. For the 

5-foot drop, the velocity would have reduced from 215 in/sec at impact to 168 in/sec at 0.01 seconds after 

impact. For the 10-foot drop, the velocity would have reduced from 304 in/sec to 206 in/sec.
14

Figure 14. Closed-Form Solution Acceleration History for 5-foot Drop

Figure 15. Closed-Form Solution Acceleration History for 10-foot Drop

The closed-form solution pressure histories are plotted with test data in Figures 16 and 17. The closedform solution is asymptotic at the perimeter of the contact patch, but provides a reasonable prediction of 

the pressure decay.

Test Data Filtered at 180 Hz

Test Data Filtered at 180 Hz
15

Figure 16. Closed-Form Solution Pressure History for 5-foot Drop

Figure 17. Closed-Form Solution Pressure History for 10-foot Drop

5.2. 2-D LS-DYNA Results 

Acceleration histories for the three mesh variants are compared to test accelerometer histories in Figures 

18 through 20 for the 5-foot drops and Figures 21 through 23 for the 10-foot drops. All acceleration 

histories were filtered using a 180-Hz Butterworth filter and were time-shifted to facilitate comparison. 

The figures for the 5-foot drops show close agreement with the test results. For the 10-foot drops, the 

simulations over-predicted the acceleration peak. Both the 5-foot and 10-foot drops show the simulations 

had a much slower acceleration decay rate in the late time, after approximately 0.008 seconds. 
16

Figure 18. Acceleration Histories for 5-foot Drop for 0.025-inch Element Size

Figure 19. Acceleration Histories for 5-foot Drop for 0.05-inch Element Size

180 Hz Butterworth Filter

180 Hz Butterworth Filter
17

Figure 20. Acceleration Histories for 5-foot Drop for 0.1-inch Element Size

Figure 21. Acceleration Histories for 10-foot Drop for 0.025-inch Element Size

180 Hz Butterworth Filter

180 Hz Butterworth Filter
18

Figure 22. Acceleration Histories for 10-foot Drop for 0.5-inch Element Size

Figure 23. Acceleration Histories for 10-foot Drop for 0.1-inch Element Size

The acceleration histories show that the filtered peak acceleration is relatively insensitive to both the 

mesh density and the coupling stiffness for the range of element sizes and coupling stiffnesses considered. 

This is illustrated in the bar charts shown in Figure 24 for the 5-foot drops and Figure 25 for the 10-foot 

180 Hz Butterworth Filter

180 Hz Butterworth Filter
19

drops. The tests produced filtered peaks of approximately 11g for the 5-foot drops and 22g for the 10-

foot drops.

Figure 24. Peak Accelerations for Mesh and Coupling Stiffness Variants for 5-foot Drops

Figure 25. Peak Acceleration for Mesh and Coupling Stiffness Variants for 10-foot Drops

Pressure histories were extracted from the LS-DYNA simulations using the DBFSI option, which 

translates the coupling forces into an interface pressure. The DBFSI pressure does not necessarily match 

the pressure seen in the fluid. This is illustrated in Figure 26 for a 5-foot drop of the 0.025-inch mesh 

model with the 10 x Curve 10 coupling stiffness. The DBFSI pressure reflects the actual loading on the 

coupling surface whereas the fluid pressure represents the pressure at the center of the elements of the 

fluid mesh. The relative mesh densities for the fluid and structure along with the density of the fluid 
20

coupling points on the structure (NQUAD) all factor into how closely the pressure in the fluid matches 

the interface pressure. Further mesh refinement would lead to better agreement between the pressure in 

the fluid and the pressure at the coupling surface.

Figure 26. Pressure in Fluid versus DBFSI Pressure at Coupling Surface 

Pressure histories for the three mesh variants are compared to test pressure histories in Figures 27 through 

29 for the 5-foot drops and Figures 30 through 32 for the 10-foot drops. The pressure histories are 

unfiltered. Pressure histories for the 10 x Curve 10 simulations are shown in Figure 33 for the 5-foot 

drops and Figure 34 for the 10-foot drops. The simulation pressure histories have been averaged over an 

edge length of 0.1 inches, which approximates the pressure transducer size of 0.125 inches. The 

simulation results show that refining the mesh results in better agreement with the test data for the late 

time decay of the pressure history; however, there is no convergence in matching the peak pressure of the 

test data.
21

Figure 27. Pressure Histories for 5-foot Drop for 0.025-inch Element Size 

Figure 28. Pressure Histories for 5-foot Drop for 0.05-inch Element Size
22

Figure 29. Pressure Histories for 5-foot Drop for 0.1-inch Element Size

Figure 30. Pressure Histories for 10-foot Drop for 0.025-inch Element Size 
23

Figure 31. Pressure Histories for 10-foot Drop for 0.05-inch Element Size

Figure 32. Pressure Histories for 10-foot Drop for 0.1-inch Element Size
24

Figure 33. Pressure Histories for 5-foot Drop for 10 x Curve 10 Mesh Variants

Figure 34. Pressure Histories for 10-foot Drop for 10 x Curve 10 Mesh Variants

The pressure histories show that the peak pressure is highly sensitive to both the mesh density and the 

coupling stiffness. The results also show that this sensitivity is reduced as the mesh is refined; however, 

this does not mean that the peak pressures from the simulations converge toward the peak pressures from 

the test. This is illustrated in the bar charts shown in Figure 35 for the 5-foot drops and Figure 36 for the 
25

10-foot drops. The tests produced peak pressures of approximately 120 psi for the 5-foot drops and 200 

psi for the 10-foot drops.

Figure 35. Peak Pressure for Mesh and Coupling Stiffness Variants for 5-foot Drops

Figure 36. Peak Pressure for Mesh and Coupling Stiffness Variants for 10-foot Drops

Figures 37 and 38 show the impulse at the pressure transducer locations from the LS-DYNA simulations. 

The impulse was calculated by integrating the pressure history for the first 0.01 seconds following impact. 

Despite the drastic differences in the shapes of the pressure histories, the impulse is relatively insensitive 

to the mesh density and the coupling stiffness. The impulse varies between 0.069 psi-sec and 0.073 psisec for the simulations of the 5-foot drops and between 0.112 psi-sec and 0.117 psi-sec for the simulations 

of the 10-foot drops. This explains why the acceleration histories were very similar despite drastic 
26

differences in the pressure histories. For simulation of the response of the overall structure, the exact 

profile of the pressure pulse is probably not important as long as the impulse is correct; however, the 

profile of the pressure pulse may be important for the design of small penetrations or crushable materials.

A similar computation was performed for the pressure histories from the tests. The impulse for the 5-foot 

drops was 0.116 psi-sec for Gage 3 of Test 1 and 0.0.084 psi-sec for Gage 3 of Test 2. The impulse for 

the 10-foot drops was 0.122 psi-sec for Gage 2 of Test 5 and 0.119 psi-sec for Gage 3 of Test 6. The 

pressure histories for Gage 2 of Test 3 and Gage 1 of Test 4 were not long enough to determine the 

impulse for the full period.

Figure 37. Impulse for Mesh and Coupling Stiffness Variants for 5-foot Drops

Figure 38. Impulse for Mesh and Coupling Stiffness Variants for 10-foot Drops
27

In addition to the effect the coupling stiffness has on the peak of the pressure history, it also affects the 

shape of the pressure contours within the fluid. Also, a coupling stiffness that is too soft can result in 

substantial penetration of fluid through the fluid-structure interface. This is illustrated in Figure 39 for the 

simulation of a 5-foot drop of the 0.05-inch mesh. The 0.1 x Curve 10 coupling stiffness produces 

smooth pressure contours but shows significant penetration of the fluid into the structure. The 100 x 

Curve 10 coupling stiffness shows no penetration, but the pressure contours show multiple isolated 

patches of high pressure. For the 100 x Curve 10 coupling stiffness, the impact occurs as a series of 

localized hits rather than as one continuous impact.

 

Figure 39. Pressure Contours for Coupling Stiffness Variants for 5-foot Drop

Sensitivity studies were performed for several simulation parameters. The parameters varied are listed in 

Table 1. The baseline simulation for the study was the 0.05-inch element model dropped from 5 feet. An 

exception was made for the divot model, which was based on the 0.025-inch element model in order to 

provide a finer mesh for defining the divot. Bar charts illustrating the peak filtered acceleration and peak 

0.1 x Curve 10

(Substantial 

Penetration) 1.0 x Curve 10

10 x Curve 10 100 x Curve 10

Penetration
28

pressure are shown in Figures 40 and 41. Most of these parameters had relatively little effect on the peak 

filtered acceleration and peak pressure. 

Table 1. Parameters Varied for Sensitivity Study

Parameter Description Baseline

ELFORM Element formulation for 2-D 

axisymmetric mesh.

14

EOS_GRUNEISEN Form of the equation of state for 

the water.

EOS_LINEAR_POLYNOMIAL

FRCMIN Volume fraction at which a fluid 

element is considered to be 

coupled to the structure.

0.5

METH Method for advecting fluid mesh 

between solution time steps.

3

PC Tensile cutoff pressure for fluid. 14.7 psi

Instantaneous Gravity Method of applying gravity. Gravity ramped over 0.01 seconds 

prior to impact.

Rigid Model Treating the hemisphere model 

as rigid rather than flexible.

Flexible model.

61.3 lb Model Weight of hemisphere. 48.0 lb

Divot Adding a divot with a depth of 

0.02 inches in way of the 

pressure transducer location.

No divot.

Figure 40. Peak Filtered Accelerations for Sensitivity Study Variants
29

Figure 41. Peak Pressures for Sensitivity Study Variants

Regarding these parameters, the following should be noted.

- ELFORM=15 does not compute the stress correctly and should not be used according to 

the LS-DYNA developers at LSTC. 

- The value of FRCMIN should be changed with caution as a low value can result in the 

fluid mesh moving before the impacting object arrives. 

- METH=2 is described in the LS-DYNA Keyword User’s Manual [2] as “second order 

accurate”, whereas METH=1 and METH=3 (Baseline) are described as “first order 

accurate”.

- PC=-14.7 is used to mimic the overpressure of the atmosphere. The result is that the 

water at the surface of the fluid mesh does not cavitate until a tensile pressure of 14.7 psi 

is reached. 

- Initiating gravity instantaneously results in an oscillating pressure field in the fluid 

whereas ramping gravity results in a stable hydrostatic pressure field.

- The measured weight of the hemisphere was 48 lbs. The 61.3 lb weight was based on the 

basic geometry assuming that the bismuth was sold rather than machined away to 

accommodate instrumentation.

Increasing the weight of the hemisphere would be expected to reduce the peak deceleration. This is 

consistent with the simulation results. The reduced deceleration would result in a modestly higher 

velocity at the time that the pressure pulse reaches the transducer location, which would be expected to 

result in a higher pressure peak. The simulation showed negligible change in the peak pressure. The 

effect of the increased weight on the pressure history was so small that no clear effect was perceptible in 

the simulation.

The idea of adding a divot to the simulation model stemmed from the difficulty of obtaining a perfectly 

flush mounting for a pressure transducer in the test article. For the 2-D axisymmetric model, the 
30

representation of a recessed transducer mounting as a divot was not exactly correct as the divot actually 

represented an axisymmetric groove; however, the effect was expected to be similar. The 0.02-inch divot 

resulted in a significant spike in the pressure as the water passed over it. This is illustrated in Figure 42 

for a 5-foot drop of the 0.025-inch mesh with the 10 x Curve 10 coupling stiffness. This was consistent 

with findings from experiments with pressure transducers that showed that slightly recessing the pressure 

transducer resulted in a higher pressure reading.

Figure 42. Pressure Pulse Caused by a 0.02-inch Divot

The conclusion from the results from the 2-D model was that the most important parameters for the study 

of test versus analysis correlation are mesh density and coupling stiffness. Other parameters either have 

little effect or lack any physical basis for making a change. As a consequence, mesh density and coupling 

stiffness were the focus of further studies performed with the three-dimensional model of the hemisphere.

5.3. 3-D LS-DYNA Results 

A series of coupling stiffness variants for the baseline mesh (0.1-inch elements) were analyzed. In 

Figures 43 and 44, the acceleration histories for the 5-foot and 10-foot drops are compared to test data. 

For both drop heights, the simulation acceleration histories correlate well with the test data. The variant 

with the lowest coupling stiffness (0.1 x Curve 12) shows oscillatory behavior, which resulted from the 

hemisphere bouncing on the coupling surface.
31

Figure 43. Acceleration History for 5-foot Drop Simulations

Figure 44. Acceleration History for 10-foot Drop Simulations

180 Hz Filter

180 Hz Filter
32

The pressure histories from the simulations are compared to test data in Figures 45 and 46. The 

simulation pressure histories show a strong sensitivity to coupling stiffness. The baseline coupling 

stiffness (Curve 12 x 1) shows the closest match to the peak pressures measured in the test; however, the 

shape of the curve from the simulation does not match the shape of the curves from the test.

Figure 45. Pressure Histories for 5-foot Drop Simulations
33

Figure 46. Pressure Histories for 10-foot Drop Simulations

For simulations of the 5-foot drops, the impulse during the first 0.01 seconds after impact varied between 

0.052 psi-sec for the Curve 12 x 10 variant and 0.067 psi-sec for the Curve 12 x 1 variant. For the 5-foot 

drop test data, the range was 0.084 psi-sec to 0.116 psi-sec. For simulations of the 10-foot drops, the 

impulse varied between .098 for the Curve 12 x 10 variant and 0.100 for the PFAC Default variant. For 

the 10-foot drop test data, the range was 0.119 psi-sec to 0.122 psi-sec.

Figures 47 and 48 illustrate the distribution of the coupling pressure in the simulations of the 5-foot and 

10-foot drops. The softest coupling stiffness (0.1 x Curve 12) produced a broad pressure patch without a 

well-defined “Coliseum Effect” ring of high pressure at its perimeter. The highest coupling stiffness 

(PFAC Default) produced a scattering of high pressure spikes rather than continuous rings of pressure.
34

Figure 47. Pressure Distribution at 0.001 seconds after Impact for 5-foot Drop Simulations

Curve 12 x 0.1

PFAC Default Curve 12 x 10

Curve 12 x 1
35

Figure 48. Pressure Distribution at 0.001 seconds after Impact for 10-foot Drop Simulations

Simulations were run for fluid mesh variants with element sizes of 0.05 inches and 0.025 inches. The 

element size of the hemisphere was 0.1 inches for all simulation variants. The 0.05-inch fluid mesh was 

created by subdividing the 0.1-inch elements of the baseline fluid mesh. The 0.025-inch fluid mesh was 

created by halving the dimensions of the 0.05-inch mesh. As a consequence, the 0.025-inch fluid mesh 

has just half the overall extent of the 0.1-inch and 0.05-inch fluid meshes. For the 0.025-inch fluid mesh, 

the hemisphere began to interact with the mesh boundary at approximately 0.002 seconds. This limited 

the 0.025-inch fluid mesh simulation to the very early time response.

For the 0.05-inch fluid mesh, the coupling stiffness was made twice as stiff as the Curve 12 baseline. For 

the 0.025-inch fluid mesh, coupling stiffness was made four times as stiff as the Curve 12 baseline. The 

increase in coupling stiffness for the finer meshes was motivated by the belief that the maximum 

allowable penetration distance should be a function of the fluid element size rather than an absolute 

dimension. Also, the number of fluid coupling points (NQUAD) was increased from 2 for the 0.1-inch 

baseline fluid mesh to 3 for the 0.05-inch fluid mesh and 6 for the 0.025-inch fluid mesh. This was 

necessary to avoid the smaller fluid elements slipping between the coupling points of the 0.1-inch 

elements of the hemisphere. 

Curve 12 x 0.1

PFAC Default Curve 12 x 10

Curve 12 x 1
36

Acceleration histories for the 5-foot and 10-foot drops for the fluid mesh variants are compared to test 

data in Figures 49 and 50. The 0.025-inch fluid mesh is not included in the acceleration comparison 

because the hemisphere begins interacting with the fluid mesh boundary before the peak acceleration was 

reached. The results show that the refinement from a 0.1-inch mesh to a 0.05-inch mesh makes negligible 

difference in the acceleration histories.

Figure 49. Acceleration Histories for Mesh Variants for 5-foot Simulations

Figure 50. Acceleration Histories for Mesh Variants for 10-foot Simulations

Pressure histories for the fluid mesh variants are compared to test data in Figures 51 and 52. The pressure 

histories show that the baseline 0.1-inch mesh offers the best prediction for the peak pressure, but does 

not follow the pressure decay curves from the tests and has a second peak that is not physically 

reasonable. Refinement to a 0.05-inch mesh reduces the pressure peak below the value from the tests and 

results in a pressure history that oscillates about the pressure decay curves from the tests. Further 

180 Hz Butterworth Filter

180 Hz Butterworth Filter
37

refinement to a 0.025-inch mesh further reduces the peak pressure and results in a pressure history that 

closely follows the pressure decay curves from the tests. 

Figure 51. Pressure Histories for Mesh Variants for 5-foot Simulations

Figure 52. Pressure Histories for Mesh Variants for 10-foot Simulations

The simulation results for the 3-D model had peak filtered accelerations that were very similar to the test 

results. For the 5-foot drops, the simulations under-predicted the peak accelerations by less than 15%. 

For the 10-foot drops, the simulations modestly over-predicted the peak accelerations. The acceleration 

results support the use of a 15% allowance for design for loads that are proportional to the acceleration. 

The same cannot be concluded for the pressure histories. The peak pressures can be either over-predicted 

or under-predicted based on the mesh density and the coupling stiffness. 
38

6. Establishing Simulation Parameters without Test Data 

6.1. Width of Pressure Pulse 

A series of tests were performed with additional pressure transducers mounted in the hemisphere. The 

time required for the pressure pulse to propagate from one transducer location to another provides an 

indication of the speed at which the pressure pulse travels. This can be used in conjunction with the 

observed time duration of the pressure pulse to estimate of the width of the pressure pulse. Figure 53 

shows the arrangement of pressure transducers. Table 2 lists the coordinates of the pressure transducers.

Figure 53. Pressure Transducer Arrangement

Table 2. Pressure Transducer Locations

Sensor ID X (in) Y (in)

MS1 0.8125 2.125

MS2 1.250 -3.1875

MS3 0.875 -2.0625

PCB1 -0.875 -2.0625

PCB2 3.0625 0.875

PCB3 -1.750 -4.1875

The histories for the pressure transducers for a 10-foot drop are shown in Figure 54. The peak pressure 

decreases, and the time duration increases, as the pressure pulse moves away from the apex. Table 3 

provides an estimate of the width of the pressure pulse based on the time duration of the pulse and the 
39

velocity of the pulse as determined from the arrival time at subsequent transducer locations. The 

calculation suggests a pulse width of approximately 0.2 inches, which is approximately 1/50th of the 

radius of the hemisphere. 

Figure 54. Pressure Histories for Multiple Pressure Transducers 

Table 3. Pressure Pulse Width Estimate 

Gage Arrival 

Time 

(sec)

X (in) Y (in) Radius 

(in)

Velocity 

(in/sec)

Pulse 

Width 

(sec)

Pulse 

Width 

(in)

PCB1 4.711 -0.875 -2.0625 2.2404 986.17 0.0002 0.197

MS2 4.7122 -1.25 -3.1875 3.4238 857.41 0.0002 0.171

PCB3 4.7135 -1.75 -4.1875 4.5385 - - -

6.2. Establishing Mesh Density and Coupling Stiffness 

The ability of the model to adequately simulate the pressure pulse is dependent on having a mesh density 

that adequately describes the shape of the pressure pulse. If it is assumed that a minimum of four 

elements are needed across the width of the pressure pulse, and it is estimated that the width of the 

pressure pulse is approximately 1/50th of the radius of curvature of the structure, then the fluid element 

size should be no larger than 1/200th of the radius of curvature. This leads to a fluid element size of 0.05 

inches for the hemisphere. This is the element size for the middle mesh variant for the 2-D axisymmetric 

model. It is half the element size of the baseline 3-D quarter model.
40

The approach recommended by LSTC in the LS-DYNA Keyword User’s Manual [2] for defining the 

coupling stiffness curve is as follows.

“The curve consists of {0,0} as the first point and {maximum allowable penetration (MAP), estimated 

maximum coupling pressure (EMCP)} as a second point. MAP may be a small penetration with respect to 

the minimum ALE element width (maybe 10% or less). EMCP can be estimated from a maximum fluid 

pressure observed from a previous run when leakage first occurs. This curve may be scaled to vary the 

stiffness of the coupling spring. The approach is to gradually increase the coupling stiffness until leakage 

stops. The best coupling stiffness is one which provides just enough force to prevent leakage and not 

more”

LSTC subsequently amended this recommendation in e-mail and verbal communications. The amended 

recommendation is to base EMCP on the maximum pressure observed in a simulation with the PFAC 

default (PFAC = 0.1). There remains ambiguity as to whether this is the peak pressure seen anywhere in 

the model or at a presumed pressure transducer location and whether it should be the pressure seen in the 

fluid or at the fluid-structure interface. LS-DYNA does permit the specification of different fluidstructure coupling definitions (*CONSTRAINED_LAGRANGE_IN_SOLID) for different regions of the 

model; however, the coupling definition cannot be changed during the simulation. 

For the hemisphere, the recommended mesh density and coupling stiffness are described in Table 4.

Table 4. Recommendations for Element Size and Coupling Stiffness

Parameter Criteria Value

Radius of Curvature, R Known Dimension 10 in

Fluid Element Size, L L = R/200 0.05 in

Maximum Allowable 

Penetration, MAP

MAP = L/10 0.005 in

Estimated Maximum Coupling 

Pressure, EMCP

From LS-DYNA simulation 

with PFAC = 0.1

100 psi

The maximum pressure is expected to be more than 10 psi but less than 1000 psi, so 100 psi was chosen 

as an order of magnitude estimate for EMCP. This resulted in a curve that is identical to Curve 10 (100 

psi at 0.005 inch) used for the 2-D axisymmetric model. It is twice as stiff as Curve 12 (100 psi at 0.01 

inch) used for the 3-D quarter model. It is recognized that even with these guidelines, the peak pressure is 

not likely to be predicted with a high degree of accuracy.

6.3. Evaluating Model Performance without Test Data 

When test data is unavailable, the analyst must make judgments on the performance of the fluid-structure 

interaction to determine whether the coupling stiffness is too high or too low. Through the course of these 

and other simulations, several aspects of the model performance have been observed that provide 

indications regarding whether the behavior of a simulation is physically reasonable.

One way to assess the adequacy of the fluid-structure interaction is to observe the degree of penetration 

and leakage through the structure. The following distinction is made between penetration and leakage.
41

- Penetration is fluid that passes through the coupling interface but is still resisted by the 

coupling force.

- Leakage is fluid that escapes through the coupling interface and is not resisted by the 

coupling force.

Figure 55 illustrates the distinction between penetration and leakage.

Figure 55. Description of Penetration and Leakage

Since LS-DYNA utilizes a penalty method in which springs are added to resist the passage of material 

through the coupling interface, some degree of penetration must always occur in order for there to be a 

coupling force. Penetration can be reduced by increasing the coupling stiffness (PFAC). 

Leakage should not occur at a properly functioning fluid-structure interface. Leakage may occur if the 

relative mesh size is such that not every fluid element is resisted by coupling points on the structural 

elements. Leakage can be alleviated by increasing the density of the coupling points (NQUAD).

Two symptoms of an excessively soft coupling stiffness were observed. The first was a coupling pressure 

pattern that lacks a well-defined “Coliseum Effect” ring of high pressure at the outer perimeter of the 

contact patch. The second was low frequency oscillation of the acceleration history as a consequence of 

the oscillatory system created by the mass of the structure and the coupling stiffness. These symptoms 

are illustrated in Figure 56.
42

Figure 56. Symptoms of an Excessively Soft Coupling Stiffness

Two symptoms were also observed for an excessively stiff coupling stiffness. The first was an interface 

coupling pressure pattern that appears as a set of isolated point loads. The second was a pressure history 

that appears as a series of isolated high pressure spikes. These symptoms are illustrated in Figure 57.

180 Hz Filter

Early time pressure 

distribution lacks a 

well-defined 

“Coliseum Effect” 

ring at the 

perimeter of the 

contact patch.

Acceleration history 

exhibits oscillations 

due to ringing of the 

contact force.
43

Figure 57. Symptoms of Excessively High Coupling Stiffness

These criteria can be used to evaluate coupling stiffnesses that are at the extremes. Unfortunately, this 

still leaves a broad range of coupling stiffnesses that are either too stiff or too soft but give results that are 

not obviously wrong.

7. Conclusions and Recommendations 

The results for the hemisphere model demonstrate that LS-DYNA can accurately predict acceleration 

histories for a broad range of mesh densities and coupling stiffnesses. The prediction of pressure histories 

is a more difficult problem. LS-DYNA predictions of pressure histories improve as the fluid mesh is 

refined; however, the required mesh size for a real world problem may be impractical due to large model 

size requiring excessive disk space and unacceptably long run times. 

Pressure history 

appears as a series 

of isolated spikes.

Pressure 

distribution appears 

as a series of 

isolated point loads.
44

The simulation results for the 3-D hemisphere model had peak filtered accelerations that were very 

similar to the test results. For the 10-foot drops, the simulations modestly over-predicted the peak 

accelerations. For the 5-foot drops, the simulations under-predicted the peak accelerations by less than 

15%. This supports the use of a 15% allowance for design for loads that are proportional to the 

acceleration. The same cannot be concluded for the pressure histories. The peak pressures can be either 

over-predicted or under predicted based on the mesh density and the coupling stiffness.

In the absence of test data, the analyst must make a judgment regarding whether the fluid-structure 

coupling interface is performing adequately. The following guidelines are proposed.

1. The element size of the fluid mesh should be no larger than 1/200th of the radius of 

curvature of the structure.

2. The coupling stiffness curve should be established based on the maximum expected 

coupling pressure at a penetration equal to 1/10th the size of the fluid elements.

It is recognized that the above guidelines may result in an impractical model size with impractical run 

time and that the pressure histories are not likely to be realistic even if the guidelines are followed. As a 

consequence, the following guidelines for judging the adequacy of the performance of the coupling 

surface are offered.

1. The coupling stiffness is too soft if the peak coupling pressure is toward the middle of the 

contact patch rather than at the perimeter.

2. The coupling stiffness is too soft if the acceleration time history exhibits oscillations that 

can be related to the structure bouncing on the coupling surface.

3. The coupling stiffness is too stiff if the coupling pressure distribution appears as a 

checkerboard pattern of isolated pressure spikes.

4. The coupling stiffness is too stiff if the coupling pressure histories appear as a series of 

isolated spikes. 

References 

[1] Hallquist, J.O., “LS-DYNA Theoretical Manual”, LSTC Livermore, 1998.

[2] “LS-DYNA Keyword User’s Manual, Version 971,” Livermore Software Technology 

Corporation, May 2007. 

[3] Cappelli, A.P. and Wilkinson, J.P.D., “Study of Apollo Water Impact, Final Report, Volume 2, 

Dynamic Response of Shells of Revolution during Vertical Impact into Water – No Interaction,” 

NASA CR 92020, North American Aviation, Inc., Space Division, May 1967. 
45

Appendix A: Two-Dimensional Axisymmetric Model 

The following are the LS-DYNA cards that control the material properties, contact, and initial conditions 

for the axisymmetric model. These particular cards are for the 0.05-inch mesh for the 10-foot drop with 

the Curve 10 x 1 coupling stiffness. Node numbers and the number of set segments for pressure output 

differ depending on the mesh density. 

*KEYWORD 800000000

$ IMPACT AT_0.01 SECONDS

$ RAMPED GRAVITY

$ ELFORM=14 FOR AIR AND WATER

$ VARIABLE D3PLOT TIME STEP

*TITLE

2-D Axisymmetric Model of 20" Hemisphere 

*CONTROL_TERMINATION

$ ENDTIM ENDCYC DTMIN ENDENG ENDMAS

 0.0200 0.0 0.0 0.0 

$*CONTROL_PARALLEL

$4

*CONTROL_HOURGLASS

 1 0.1 

*CONTROL_ENERGY

$# HGEN RWEN SLNTEN RYLEN

 2 2 

*CONTROL_OUTPUT

$# NPOPT NEECHO NREFUP IACCOP OPIFS IPNINT IKEDIT IFLUSH 

 1 3 

$# IPRTF

 0 

$ 

$*DATABASE_RBDOUT

$ 0.0000020

*DATABASE_NODOUT

 0.0000020 

*DATABASE_HISTORY_NODE

$ id1 id2 id3 id4 id5 id6 id7 id8

 4000020 4000024 4001553 4001557 4001975 

*DATABASE_BINARY_D3PLOT

$# dt lcdt beam npltc 

 0.0000200 7778 

*DEFINE_CURVE

 7778 0 1.0 1.0 0.0 0.0 0 

 0.00000 0.002000 

 0.00990 0.002000 

 0.01000 0.000020 

 0.01210 0.000020 

 0.01212 0.002000 

 0.02000 0.002000 

*DATABASE_BINARY_D3THDT

 999.999 

$ 

*SET_MULTI-MATERIAL_GROUP_LIST 

$ 3=Vacuum 2=Soil

 123 

 2 

*ALE_MULTI-MATERIAL_GROUP 

 2 1 

 3 1 

$ 

*SET_PART_LIST

 1 

 2 3 

*SET_PART_LIST

 11

 1 11 12 21 22 

*CONTROL_ALE

$ DCT NADV METH AFAC BFAC CFAC DFAC EFAC

 3 1 3 -1.0 

$ START END AAFAC VFACT PRIT EBC PREF NSIDBEC
46

$ 

*CONSTRAINED_LAGRANGE_IN_SOLID_EDGE

$# slave master sstyp mstyp nquad ctype direc mcoup

 11 1 0 0 3 4 2 -123

$# start end pfac fric frcmin norm normtyp damp

 0 0 -10 0 0 0 0 0 

$# cq hmin hmax ileak pleak lcidpor nvent iblock

 0 0 0 0 0.1 

$# iboxid ipenchk intforc ialesof lagmul pfacmm thkf

 0 0 1 0 0 

$ 

*DEFINE_CURVE

$ lcid sidr sfa sfo

 10 1.0 1.00 

 0.000 0.0 

 0.005 100.0 

$ 

*SECTION_SHELL

$ SID ELFORM SHRF NIP PROPT IRID ICOMP SETYP

 1 14 0.83333 1 

$ T1 T2 T3 T4 NLOC MAREA IDOF EDGSET

 1. 1. 1. 1. 

*SECTION_SHELL

$ SID ELFORM SHRF NIP PROPT IRID ICOMP SETYP

 98 14 0.83333 1 

$ T1 T2 T3 T4 NLOC MAREA IDOF EDGSET

 1. 1. 1. 1. 

*SECTION_SHELL

$ SID ELFORM SHRF NIP PROPT IRID ICOMP SETYP 

 99 14 0.83333 1 

$ T1 T2 T3 T4 NLOC MAREA IDOF EDGSET

 1. 1. 1. 1. 

*SECTION_ALE2D

$ SID ALEFORM AET ELFORM

 2 11 14 

*SECTION_ALE2D

$ SID ALEFORM AET ELFORM

 3 11 14 

$ 

*PART

Vacuum 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 2 3 3 0 3 0 

$ 

*PART

Water 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 3 2 2 2 2 0 

$ 

*PART

Hemisphere 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 1 1 1 0 1 0 

SET SEGMENT 11 ELEMENT

 11 1 1 0 1 0 

SET SEGMENT 12 ELEMENT 

 12 1 1 0 1 0 

SET SEGMENT 21 ELEMENT

 21 1 1 0 1 0 

SET SEGMENT 22 ELEMENT

 22 1 1 0 1 0 

Bismuth

 98 98 98 0 1 0 

Cover

 99 99 99 0 1 0 

$ 

$ 

*MAT_VACUUM

$ mid rho

 3 1.116E-11 

*MAT_NULL

$ mid ro pc mu terod cerod ym pr 

 2 9.3365e-5 -14.7 1.6300E-7 0.0000000 0.0000000 

*MAT_ELASTIC

 1 0.000253 10.2E6 0.33 0 
47

*MAT_ELASTIC

 98 0.0006279 4.6E6 0.33 0 

*MAT_ELASTIC

 99 0.000253 10.2E6 0.33 0 

$ 

*EOS_LINEAR_POLYNOMIAL

 2 0.0000000 3.11574e5 0.0000000 0.0000000 0.0000000 0.0000000 

 0.0 1.0 

$ 

*Hourglass

$ HGID IHQ QM

 3 1 1.E-6 

 2 1 1.E-6 

 1 1 0.1 

*SET_NODE_LIST_GENERATE

$ sid

 111 

$ b1beg b1end

 4000001 4100000 

*INITIAL_VELOCITY

$ nsid

 111 

$ vx vy vz vxr vyr vzr 

 0. -302.48 0. 

*LOAD_BODY_Y

 1 386.1 

*DEFINE_CURVE

 1 0 1.0 1.0 0.0 0.0 0 

 0.0 0.0 

 0.01 1.0 

 100.0 1.0 

$ 

*INCLUDE

2d_hemisphere_water_block_rev4_0p050.k 

*DEFINE_TRANSFORMATION

 100 

$ a1 a2 a3 a4 a5 a6 a7

TRANSL 0.0 13.04 0.

$ 

*INCLUDE_TRANSFORM 

2d_20inch_hemisphere_0p050.k 

$ idnoff ideoff idpoff idmoff idsoff idfoff iddoff

 4000000 4000000 

$ idroff

$ fctmas fcttim fctlen fcttem incout1

 1 

$ tranid 

 100 

$ 

*END
48

Appendix B: Three-Dimensional Quarter Model 

The following are the LS-DYNA cards that control the material properties, contact, and initial conditions 

for the three-dimensional quarter model. These particular cards are for the 0.1-inch mesh for the 10-

foot drop with the Curve 12 x 1 coupling stiffness. For the 0.05-inch mesh, the number of fluid-structure 

coupling points, NQUAD, is increased to 3. For the 0.025-inch mesh, NQUAD is increased to 6. 

*KEYWORD 800000000

*TITLE

3D QUARTER MODEL OF HEMISPHERE 

*CONTROL_TERMINATION

$ ENDTIM ENDCYC DTMIN ENDENG ENDMAS

 0.02 0.0 0.0 0.0 

*CONTROL_HOURGLASS

 1 0.1 

*CONTROL_ENERGY

$# HGEN RWEN SLNTEN RYLEN

 2 2 

*CONTROL_OUTPUT

$# NPOPT NEECHO NREFUP IACCOP OPIFS IPNINT IKEDIT IFLUSH

 1 3 

$# IPRTF

 0 

$ 

*DATABASE_GLSTAT

 0.0000020 

*DATABASE_MATSUM

 0.0000020 

*DATABASE_RBDOUT

 0.0000020 

*DATABASE_BINARY_D3PLOT

$# dt lcdt beam npltc 

 0.0002 

*DATABASE_BINARY_FSIFOR

$ dt

$ 0.0000200 7778 

 0.0002 

*DATABASE_BINARY_D3THDT

 999.999 

$ 

*SET_PART_LIST

 1 

 2 3 22 23 

*SET_PART_LIST

 222 

 2 22 

*SET_PART_LIST

 323 

 3 23 

*ALE_MULTI-MATERIAL_GROUP 

$ sid idtype

 222 0 

 323 0 

*SET_MULTI-MATERAIL_GROUP_LIST 

 123 

 2 

*CONTROL_ALE

$# dct nadv meth afac bfac cfac dfac efac

 2 1 2 -1.0 

$# start end aafac vfact prit ebc pref nsidebc

 14.7

$ 

*CONSTRAINED_LAGRANGE_IN_SOLID

$# slave master sstyp mstyp nquad ctype direc mcoup

 1 1 1 0 2 4 2 -123

$# start end pfac fric frcmin norm normtyp damp

 0 0 -12 0 0 0 0 0 

$# cq hmin hmax ileak pleak lcidpor nvent iblock 

 0 0 0 0 0.1 

$# iboxid ipenchk intforc ialesof lagmul pfacmm thkf
49

 0 0 1 0 0 

$ 

*DEFINE_CURVE 

$ lcid sidr sfa sfo

 12 1.0 1.00 

 0.000 0.0 

 0.010 100.0 

$ 

*SECTION_SHELL

$ sid elform shrf nip propt irid icomp setyp 

 1 1 0.8333333 

$ t1 t2 t3 t4 nloc marea idof edgset

 0.1875 0.1875 0.1875 0.1875 

*SECTION_SOLID

$ SID ELFORM AET

 2 11 

*SECTION_SOLID

$ SID ELFORM AET 

 3 11 

*SECTION_SOLID

$ SID ELFORM AET

 22 11 4 

*SECTION_SOLID

$ SID ELFORM AET

 23 11 4 

$ 

*PART

Hemisphere 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 1 1 1 

$ 

*PART

Vacuum 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 2 2 2 2 2 0 

$ 

*PART

Water 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 3 3 3 3 3 0 

$ 

*PART

Vacuum 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 22 22 2 2 2 0 

$ 

*PART

Water 

$ PID SECID MID EOSID HGID GRAV ADAPT TMID 

 23 23 3 3 3 0 

$ 

*MAT_NULL

$ mid rho pc mu terod cerod ym pr 

 2 1.127E-7 0.0 

*MAT_NULL

$ mid rho pc mu terod cerod ym pr

 3 9.3365e-5 0.0 1.6300E-7 0.0000000 0.0000000 

*MAT_RIGID

$ mid ro e pr 

 1 0.001075 1e+07 0.3 

$ cmo con1 con2

 1 5 7 

$ a1 a2 a3 v1 v2 v3

$ 

$*EOS_IDEAL_GAS

$$ eosid cv cp c1 c2 t0 v0 

$ 2 6.179E5 8.651E5 0.0 0.0 527.67 1.0

*EOS_LINEAR_POLYNOMIAL

$ eosid c0 c1 c2 c3 c4 c5 c6

 2 0.0 0.0 0.0 0.0 0.4 0.4 0.0 

$ e0 v0

 36.74 0.0 

$ 

*EOS_LINEAR_POLYNOMIAL
50

$ eosid c0 c1 c2 c3 c4 c5 c6

 3 14.7 3.11574e5 0.0000000 0.0000000 0.0000000 0.0000000 

$ e0 v0

 0.0 0.0 

$ 

*Hourglass

$ HGID IHQ QM

 2 1 1.E-6 

 3 1 1.E-6 

*SET_NODE_LIST_GENERATE

$ sid

 111 

$ b1beg b1end

 4000001 4900000 

*INITIAL_VELOCITY

$ nsid

 111 

$ vx vy vz vxr vyr vzr

 304.41 0. 0. 

*LOAD_BODY_X

 1 -386.1

*DEFINE_CURVE

 1 0 1.0 1.0 0.0 0.0 0 

 0.0 1.0 

 100.0 1.0 

*SET_PART_LIST

$ sid

 781 

$ pid1 pid2 

 2 3 

*INITIAL_HYDROSTATIC_ALE 

$ SID SIDTYPE VECID GRAVITY PBASE

 781 0 789 386.1 14.7 

$ NID MMGBELOW

 103067 1 

 44 2 

*SET_PART_LIST

$ sid

 782 

$ pid1 pid2 

 22 23

*ALE_AMBIENT_HYDROSTATIC

$ SID SIDTYPE VECID GRAVITY PBASE

 782 0 789 386.1 14.7 

$ NID MMGBELOW

 103067 1 

 44 2 

*DEFINE_VECTOR

$ vid xt yt zt xh yh zh cid 

 789 0. 0. 0. 1. 0. 0. 

$ 

*INCLUDE

water_air_quarter_0p1.k

*DEFINE_TRANSFORMATION

 100 

$ a1 a2 a3 a4 a5 a6 a7

TRANSL -10.01 0.0 0.0 

$ 

*INCLUDE_TRANSFORM

hemisphere_mesh_rev0.k 

$ idnoff ideoff idpoff idmoff idsoff idfoff iddoff

 4000000 4000000 

$ idroff

$ fctmas fcttim fctlen fcttem incout1

 1 

$ tranid

 100 

$ 

*END
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Elemental Water Impact Test: Phase 1 20-inch Hemisphere

5a. CONTRACT NUMBER

NNL12AA09C

 6. AUTHOR(S)

Vassilakos, Gregory J.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center 

Hampton, Virginia 23681 

 

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

Langley Technical Monitor: Robin C. Hardy

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Unclassified - Unlimited

Subject Category 31

Availability: NASA STI Program (757) 864-9658

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

Spacecraft are being designed based on LS-DYNA simulations of water landing impacts. The Elemental Water Impact Test 

(EWIT) series was undertaken to assess the accuracy of LS-DYNA water impact simulations. Phase 1 of the EWIT series 

featured water impact tests of a 20-inch spherical hemisphere dropped from heights of 5 feet and 10 feet. The hemisphere was 

outfitted with an accelerometer and three pressure gages. The focus of this report is the correlation of analytical models against 

test data. 

15. SUBJECT TERMS

Correlation; Coupling stiffness; Element size; Hemisphere; Impacts; LS-DYNA; Landing; Simulations; Water

18. NUMBER

 OF 

 PAGES

60

19b. TELEPHONE NUMBER (Include area code)

(757) 864-9658

a. REPORT

U

c. THIS PAGE

U

b. ABSTRACT

U

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 ABSTRACT

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Prescribed by ANSI Std. Z39.18

Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

10/01/2013 - 09/30/2014

5b. GRANT NUMBER

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5d. PROJECT NUMBER

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5f. WORK UNIT NUMBER

747797.06.13.06.32.04.03

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

NASA/CR-2015-218679

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