Investigation of Adaptive Control Approaches to Mitigate 

Shock Impact With Piezoceramics (Armor) 

by Marthinus van Schoor and Jacob Pretorius 

ARL-CR-0581 November 2006 

prepared by 

Midé Technology Corporation 

200 Boston Avenue Suite 1000 

Medford, MA 02155 

under contract 

DAAD-19-02-D-001

Approved for public release; distribution is unlimited. 
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DESTRUCTION NOTICE⎯Destroy this report when it is no longer needed. Do not return it to 

the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-CR-0581 November 2006 

Investigation of Adaptive Control Approaches to Mitigate 

Shock Impact With Piezoceramics (Armor) 

by Marthinus van Schoor and Jacob Pretorius 

Midé Technology Corporation 

prepared by 

Midé Technology Corporation 

200 Boston Avenue Suite 1000 

Medford, MA 02155 

under contract 

DAAD-19-02-D-001

Approved for public release; distribution is unlimited.
ii 

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PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

 November 2006 

2. REPORT TYPE 

Final 

3. DATES COVERED (From - To) 

 July 2004 to April 2005 

5a. CONTRACT NUMBER 

 

5b. GRANT NUMBER

4. TITLE AND SUBTITLE 

 Investigation of Adaptive Control Approaches to Mitigate Shock Impact With 

 Piezoceramics (Armor) 

 5c. PROGRAM ELEMENT NUMBER

 

5d. PROJECT NUMBER 

 622618H80 

5e. TASK NUMBER 

6. AUTHOR(S) 

 Marthinus van Schoor and Jacob Pretorius (both of Midé) 

5f. WORK UNIT NUMBER 

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

 Midé Technology Corporation 

 200 Boston Avenue Suite 1000 

 Medford, MA 02155

8. PERFORMING ORGANIZATION 

 REPORT NUMBER 

 ARL-CR-0581 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) 

 U.S. Army Research Laboratory 

 Weapons and Materials Research Directorate 

 Aberdeen Proving Ground, MD 21005-5066

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S) 

12. DISTRIBUTION/AVAILABILITY STATEMENT 

 Approved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES 

The contracting officer’s representative (COR) is Tyrone Jones, U.S. Army Research Laboratory, ATTN: AMSRD-ARL-WMTA, Aberdeen Proving Ground, MD 21005-5066, telephone number (410) 278-6223. 

14. ABSTRACT 

The U.S. Army Research Laboratory sought a Short-Term Analysis Services (STAS) program funded through Army 

Research Office (ARO) with Midé in the research, design, and development of an adaptive control system to mitigate the 

shock wave impact on an isolation system during and after a ballistic event. This report documents the initial work 

performed by Midé. 

15. SUBJECT TERMS

 adaptive control; armor; piezoceramics; shock mitigation 

16. SECURITY CLASSIFICATION OF: 

19a. NAME OF RESPONSIBLE PERSON

 Tyrone Jones 

a. REPORT 

 UNCLASSIFIED 

b. ABSTRACT 

UNCLASSIFIED

c. THIS PAGE 

UNCLASSIFIED

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OF ABSTRACT 

SAR 

18. NUMBER 

OF PAGES 

60 19b. TELEPHONE NUMBER (Include area code) 

 410-278-6223 

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18
iii 

Contents 

List of Figures iv

List of Tables v

Acknowledgments vi

Executive Summary 1

1. Description of Work Completed During Phase I 3

1.1 Task 1: Develop and Understand Requirements ............................................................3 

1.1.1 Kick-off Meeting.................................................................................................3 

1.1.2 Test Setup for Preliminary Tests .........................................................................4 

1.1.3 Preliminary Test Definitions ...............................................................................4 

1.2 Task 2: Parametric Modeling .........................................................................................5 

1.3 Task 3: Absorber Optimization ....................................................................................10 

1.3.1 Finite Element Model Formulation ...................................................................10 

1.3.2 Anisotropic Materials ........................................................................................11 

1.3.3 Modeling of Piezoelectric Materials .................................................................13 

1.3.4 Linear Results....................................................................................................15 

1.3.5 ANSYS Finite Element Model..........................................................................20 

1.4 Task 4: Preliminary Experiments.................................................................................26 

1.4.1 Kevlar Plate Tests..............................................................................................26 

1.4.2 Integrated Piezo Tests .......................................................................................31 

1.5 Task 5: Shock Absorber Design...................................................................................36 

2. Conclusion and Future Work 38

3. References 39

Appendix A. MATLAB Main Code 41 

Distribution List 47 
iv 

List of Figures 

Figure 1. Finite element model. ..................................................................................................... 6 

Figure 2. First non-rigid resonant mode shape. ............................................................................. 6 

Figure 3. Second non-rigid resonant mode shape.......................................................................... 7 

Figure 4. Third non-rigid resonant mode shape............................................................................. 7 

Figure 5. Von Mises stress at 0.8 μs after the 1.56-gram projectile impacted the center of 

the plate at 450 m/s ................................................................................................................. 8 

Figure 6. Von Mises stress at 4 μs after the 1.56-gram projectile impacted the center of the 

plate at 450 m/s ....................................................................................................................... 8 

Figure 7. Von Mises stress at 8 μs after the 1.56-gram projectile impacted the center of the 

plate at 450 m/s ....................................................................................................................... 9 

Figure 8. Displacement and velocity (deformation) of impact point............................................. 9 

Figure 9. Displacement and velocity (deformation) of top surface directly above the impact 

point. ..................................................................................................................................... 10 

Figure 10. Deformation of a piezo cube when a voltage is applied across the 33 d (Z-) 

direction ................................................................................................................................ 15 

Figure 11. First mode shape of the ceramic-GRP composite target predicted by the Midé 

code. ...................................................................................................................................... 16 

Figure 12. Displacement and velocity (deformation) of impact point......................................... 16 

Figure 13. Displacement and velocity (deformation) of the top surface directly above the 

impact point .......................................................................................................................... 17 

Figure 14. Predicted von Mises stresses at 230 microseconds after impact ................................ 17 

Figure 15. First mode shape of the ceramic-GRP composite target predicted by the Midé 

code. ...................................................................................................................................... 18 

Figure 16. Displacement and velocity (deformation) of impact point......................................... 18 

Figure 17. Displacement and velocity (deformation) of the top surface directly above the 

impact point .......................................................................................................................... 19 

Figure 18. Predicted von Mises Stresses at 230 micro-seconds after impact .............................. 19 

Figure 19. The meshed ANSYS model........................................................................................ 21 

Figure 20. A typical result from the ANSYS analysis illustrating the nodal displacement 

in the z direction.................................................................................................................... 21 

Figure 21. Comparison of high speed video and the ANSYS model. ......................................... 22 

Figure 22. Voltage output from the PA1 piezo sensor during the ballistic test........................... 25 

Figure 23. Voltage output from the PA1 piezo sensor in the ANSYS simulation....................... 26 

Figure 24. Kevlar displacement test setup. .................................................................................. 27

Figure 25. Test setup as viewed from the gun barrel................................................................... 27 
v 

Figure 26. The gun, left and side view of the eddy gauge, metal strip and Kevlar target, 

right....................................................................................................................................... 28 

Figure 27. Setup before test number 2646................................................................................... 29 

Figure 28. Failure during test 2646.............................................................................................. 29 

Figure 29. Failure of test 2647..................................................................................................... 30 

Figure 30. The impact point is well above the position of the 075-inch metal disk in 

test 2648................................................................................................................................ 30 

Figure 31. Delaminating of the 0.75-inch metal disk during test 2649. ..................................... 31 

Figure 32. Failure of test 2650 was attributable to the dislodging of the metal disk.................. 31 

Figure 33. Four layers of piezoelectric elements with various electric configurations were 

bonded to the target as shown on the left............................................................................. 32 

Figure 34. Pre and post-test 2652 pictures of the QuickPack and PowerAct sensors. ................ 33 

Figure 35. Results from the eddy current gauge.......................................................................... 34 

Figure 36. Output from PA1 ........................................................................................................ 34 

Figure 37. Output from QP1 ........................................................................................................ 35 

Figure 38. Output from PA2 ........................................................................................................ 35 

Figure 39. Output from QP2 ........................................................................................................ 36 

Figure 40. Displacement of the center node in response to the ballistic event............................ 37 

Figure 41. Displacement of the center node in response to the ballistic event when a 

structural interference wave is generated by the piezoelectric elements in response 

to a high voltage pulse. ......................................................................................................... 37 

List of Tables 

Table 1. Material properties of the armor system.......................................................................... 5 

Table 2. Test sequence and failure mechanisms for a ballistic test conducted at ARL............... 29 

Table 3. Description of the integrated piezo tests........................................................................ 32 

Table 4. Details of the four encapsulated piezoelectric wafers bonded to the Kevlar plate........ 33 
vi 

Acknowledgments 

Midé would like to acknowledge the following ARL personnel for their contribution to this 

work: 

1. Mr. Tyrone Jones for the initiating the program and having the foresight to evaluate the 

use piezoelectric “smart” materials for shock mitigation during a ballistic event. Mr. 

Jones provided Midé with armor mechanic background and experimental ballistic tests 

results. 

2. Mr. William Gooch for overall program support. 

3. Mr. Neil Gniazdowski for setup and use of measuring and recording equipment. 

4. Mr. Matt Burkins for setup and use of the ballistic laboratory and conducting tests. 
1 

Executive Summary 

Midé Technology Corporation was approached by the U.S. Army Research Laboratory (ARL) to 

investigate the effect of using the unique effects of piezoelectric materials in order to reduce the 

magnitude of the ballistic shock of ballistic events. The program was set up to develop a threedimensional (3-D) structural analysis code to simulate the effect of the piezo materials on the 

displacement of a Kevlar1 29 laminate armor plate. These models were to be calibrated via 

simple ballistic tests. Once the code was calibrated, an optimization and design effort would be 

completed in order to perform proof-of-concept tests. 

Upon receiving the orthotropic material properties of the Kevlar 29 composite, Midé’s research 

and development, which specializes in smart materials, decided to use a MATLAB2-based finite 

element approach that accurately models the 3-D anisotropic behavior of the armor. The model 

also included the ability to model piezoelectric material and its interaction with the Kevlar 

material. 

Some delays in the process forced the testing to be postponed until very late in the program. 

This reduced the amount of time available for the calibration and optimization of the model. As 

an alternative, Midé agreed to integrate some of its off-the-shelf packaged piezoelectric actuators 

with Kevlar composite targets in order to test the effects of the ballistic events on the materials. 

This step was scheduled for the Phase I Option, and so certain tasks from Phase I moved into the 

option and vice versa. 

Further difficulties in obtaining reliable data from the ballistic tests hindered calibration of the 

model. At this stage it was decided to simulate the tests that were conducted in ANSYS3, a 

commercial finite element analysis package. Correlation between the model and high speed video 

data, as well as data from the piezoelectric tests, was obtained as far as possible. The model was 

then used to investigate the effect of creating a destructive surface wave on reducing the maximum 

displacement of the impact point. Early, un-calibrated and un-optimized results indicate that a 

27% reduction in the displacement of the impact point is possible when a high voltage pulse is 

delivered to a certain arrangement of piezoelectric materials. 

These results are encouraging but should be validated by testing. Calibration of the model is 

scheduled early in the option. The model is ready to be optimized as soon as the calibration 

parameters are updated. This optimization will assist in a rapid design cycle to ensure that 

testing of an integrated system will still be performed during the option. 

 1

Kevlar is a registered trademark of E. I. DuPont de Nemours & Co., Inc. 

2

MATLAB is a registered trademark of The MathWorks. 

3ANSYS, which is not an acronym, is a registered trademark of ANSYS, Inc. 
2 

The following is a summary of the achievements under each of the tasks as outlined in the work 

breakdown structure of the Phase I proposal. 

Task 1: Develop and Understand Requirements 

Midé had a productive “kick-off” meeting with the technical monitor at Aberdeen Proving 

Ground (APG). The meeting restated the objectives of the program, and the schedule and plan 

for the coming months were agreed upon. The technical monitor also provided Midé with 

literature and defined test parameters. Midé further received detailed specifications for the 

Kevlar plate to be used during the program. 

Task 2: Parametric Modeling 

A 3-D finite element model was constructed to study the anisotropic behavior of the armor 

material. This code was verified with previously published results and was used to understand 

the behavior of the armor system. 

Task 3: Absorber Optimization 

This task involved the integration of piezoelectric materials into the model. The voltage output 

and visual displacement correlations from the integrated model were validated with the limited 

experimental data available. Actuation control techniques, piezoelectric material size and 

placement, piezoelectric shunting techniques and other shock mitigation schemes need to be 

explored in a post-Phase I option. 

Task 4: Preliminary Experiments 

Ballistic experiments using polypropylene bullets shot at Kevlar targets at 1000 m/s were 

performed at APG. These tests include shots at targets with piezoelectric materials integrated 

into them. Some useful data were obtained during the tests, and more tests are scheduled in the 

period between the end of Phase I and the start of the option. 

Task 5: Shock Absorber Design 

A piezoelectric material configuration, size and actuation scheme was chosen to investigate the 

effect of producing a destructive surface wave in the Kevlar to reduce the displacement of the 

impact point. The result of this modeling effort was a 27% reduction in the translation of the 

impact point. This result is encouraging, but it must be noted that the model is not calibrated and 

that the result can only be verified with experiments in a post-Phase I option. 
3 

1. Description of Work Completed During Phase I 

This section reports about the progress that was made under each of the proposed tasks. The 

original tasks are listed in the beginning of each chapter in italics.

1.1 Task 1: Develop and Understand Requirements 

In this task, Midé worked with the U.S. Army Research Laboratory (ARL) to define a set of shock 

absorber requirements. ARL’s experience and understanding of the dynamics of a ballistic 

impact were used to develop these requirements and to transfer knowledge to Midé personnel. 

1.1.1 Kick-off Meeting 

Midé had a productive meeting with the technical point of contact (TPOC) at Aberdeen Proving 

Ground (APG), Maryland. The meeting focused on the scheduling of tasks and the definition of 

the problem. 

1.1.1.1 Problem Definition 

Current bulletproof vest systems include a ceramic plate with a woven Kevlar 29 backing. The 

ceramic plate breaks up the bullet and reduces it to small pieces. The Kevlar backing then catches 

these pieces of ceramic and bullet, thus preventing them from penetrating the skin of the Soldier. 

Midé gained a better understanding of the mechanics of the ballistic protection system. A main 

concern for personnel protection is the amount of displacement at the back of the armor system 

after a ballistic event. This displacement can cause damage to organs if not contained, often 

resulting in incapacitation the Soldier. 

This displacement is a direct result from arresting the mass of target and penetrator that travels 

through the armor system after a ballistic event. The main focus of this project was to reduce the 

amount of displacement at the back of the armor protection system. Midé realized that the 

ballistic event has two components that need to be addressed. 

First, the energy of the shock wave needs to be dissipated. Piezoceramics have been successfully 

applied to a number of high frequency-damping problems. Part of the program focused on how 

to effectively employ these ceramics so that maximum energy dissipation and damping can 

occur. 

The second component is the momentum translation from the high speed, lightweight bullet to 

the slowly moving, higher mass armor vest. Ideally, the armor system translates all the momentum 

into a very slow moving mass that contacts a wide area of the body, thereby reducing the pressure 

on the body and minimizing the displacement of the body tissue. 
4 

A successful armor protection system will deal effectively with both these components in order 

to reduce the damage to the body. 

The TPOC also supplied Midé with information about previous ballistic tests with ceramic and 

composite targets, evaluation of different periodic cellular materials and blunt trauma effects 

after low-velocity ballistic impacts. 

1.1.2 Test Setup for Preliminary Tests 

The approach to Task 1 was as follows: 

1. Non-perforating small arms ballistic experiments that focused on collecting shock wave 

and displacement data off the back face of the target were conducted. These preliminary 

tests confirm the non-perforating test velocity for the test projectile into the target. The 

data that were collected are as follow: 

• Back face displacement versus time for 0- to 150-kHz range. 

• Shock wave speed and possibly shock wave pressure. 

• Maximum back face displacement. 

2. Another experimental setup used was the composite panel attached to a steel plate and 

measured the force transmitted during the projectile impact with a load cell. Here would be 

an example of a worst case scenario of the force transmitted to the panel because of the 

coupling of the steel plate. 

3. The data were obtained with the following transducers: 

• A crush gauge (or piezo pin transducers) with signal conditioning was initially used to get 

an initial measurement of the maximum back face displacement off the back of the target. 

• An eddy current gauge was set up at the back of the panel to give a displacement versus 

time reading and works for the 0- to 150-kHz frequency range. Velocity was obtained 

through post-processing differentiation. 

• A polyvinylidene fluoride transducer was used to measure the shock wave speed from the 

front face to the back face of the target and the shock wave pressure. 

4. The data acquisition system was four, four-channel digital oscilloscopes. 

1.1.3 Preliminary Test Definitions 

The properties of the materials that were used in the preliminary tests and some of the test 

parameters are listed in table 1. 
5 

Table 1. Material properties of the armor system. 

Parameters 

Target - Kevlar Units Value

Volume cm3 331.84 

Size (L , W, t) cm 

mm 

L=W=22.86 

t=6.35 

Material Density g/cm3 1.44 

Poisson’s Ratio (in-plane) -- 0.12 

Poisson’s Ratio (out-of-plane) -- 0.4 

Material Stiffness - x and y directions GPa 24.1 

Material Stiffness - z direction GPa 10.4 

Fiber Shear Strength GPa 0.24 

Matrix (Delamination Shear) Strength MPa 48 

Material Compression Strength GPa 0.35 

Thru Thickness Crush Strength MPa 69 

Right cylinder projectile Penetrator – Polypropylene Plastic Units Value 

Diameter mm 12.57 

Length g 14.78 

Weight g 1.56 

Density g/cm3 0.91 

Velocity (at impact) m/s 300-up 

Tensile strength at yield MPa 35.85 

Tensile elongation at break % 600 

Tensile modulus GPa 1.65 

Flexural modulus GPa 1.59 

Flexural strength MPa 48.26 

Notched izod impact strength J/m 60 

1.2 Task 2: Parametric Modeling 

In this task, Midé worked with ARL to develop a parametric model with which the performance 

of a shock absorber design was evaluated and validated. 

Upon receiving the orthotropic material properties of the Kevlar, Midé decided to use a MATLAB4

-

based finite element approach that accurately models the 3-D anisotropic behavior of the armor. 

The code is attached as appendix A. This code was verified as far as possible and it was used to 

understand the dynamics of the impact and the resultant stresses that a piezo mitigation system 

must address. Figure 1 shows the model and figures 2 through 4 are the first three flexible modes 

predicted by the model. Results of an impact simulation are in figures 5 through 7 and time 

responses in figures 8 and 9. 

 4MATLAB is a registered trademark of The MathWorks. 
6 

Figure 1. Finite element model. 

Figure 2. First non-rigid resonant mode shape. 
7 

Figure 3. Second non-rigid resonant mode shape. 

Figure 4. Third non-rigid resonant mode shape. 
8 

Figure 5. Von Mises stress at 0.8 μs after the 1.56-gram projectile impacted the center of the 

plate at 450 m/s. (Note that the top surface is not deformed yet and that the damage is 

limited to the impact point.) 

Figure 6. Von Mises stress at 4 μs after the 1.56-gram projectile impacted the center of the plate 

at 450 m/s. (The stress on the top surface has increased but little or no deformation is 

visible. The maximum top surface Von Mises Stress is around 155 MPa.) 
9 

Figure 7. Von Mises stress at 8 μs after the 1.56-gram projectile impacted the center of the plate 

at 450 m/s. (Clear deformation is visible at this point with the top surface near 350 MPa.) 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

x 10-4

0

1

2

3

x 10-3

Z-Displacement of Impact Point (m

Time (seconds)

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

x 10-4

-200

0

200

400

600

Time (seconds)

Z-Velocity of Impact Point (m/s)

Figure 8. Displacement and velocity (deformation) of impact point. 
10 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

x 10-4

0

1

2

3

x 10-3

Time (seconds)

Z-Displacement of Back (m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

x 10-4

-200

0

200

400

600

Time (seconds)

Z-Velocity of Back (m/s)

Figure 9. Displacement and velocity (deformation) of top surface directly above 

the impact point. 

1.3 Task 3: Absorber Optimization 

The models of Task 2 were used to establish a design, to optimize the design, and to estimate the 

performance of the design. 

1.3.1 Finite Element Model Formulation 

Midé uses the National Center for Supercomputing Applications structural analysis system 

Nastran5

, which is a finite element analysis program. Nastran does not have a piezoelectric 

element in its library. Initially, the cost of ANSYS which does have a piezoelectric element was 

considered prohibitive, so Midé decided to evaluate the performance of different geometries of 

active (piezo) and passive materials, with its MATLAB-based finite element code. It is easier to 

generate many models in MATLAB compared to the alternative of using Nastran to generate the 

finite element models and then importing the finite element models into MATLAB where the 

active elements can be modeled. 

The Midé MATLAB finite element code is based on the hybrid stress finite element that has 

excellent accuracy even if the elements are distorted. This sub-section provides a quick review 

of the formulation of hybrid stress finite elements. 

 5Nastran is a trademark of the National Center for Supercomputing Applications. 
11 

In the hybrid finite element model, the strain-stress relationship is 

ε = Sσ (1) 

The stress is expressed in terms of the undetermined stress parameters β : 

σ = Pβ (2) 

From the strain-displacement (q) relations, 

ε = Bq (3) 

The Hellinger-Reissner functional ( ∏R ) 

( ) i

R ij ij ij i i

V S

∏= − + − ⎡ ⎤ B dV u T dS σ σε ∫ ∫ ⎣ ⎦ (4) 

with ( ) 1

2

T T T

R ∏ =− + − β ββ HG Q q Bq (5) 

where Q are the external forces and where 

T

V

= P SPdV H ∫ (6) 

T

V

= B PdV G ∫ (7) 

The operations / 0 ∂∏ ∂ = R r β yield 

1 β α − = H G (8) 

Eliminating β and substituting 

1 α B q − = (9) 

we obtain k Q q = (10) 

where the stiffness matrix is given by 

18 18 18 6 6 6 6 18

1 1 24 6 6 18 18 6 6 24

24 18 18 18 18 24 18 6 6 6 6 18

T

x x x x Intg

T T

T T xx x x

x x x x x x Intg

H PSP W

B P PB

G H G PSP W

J J

− −

= ⎡ ⎤ ⎣ ⎦

= = ⎡ ⎤ ⎣ ⎦ k

 (11) 

where 18 6 6 24

18 24

T

T x x

x Intg

V

P B G B PdV W

J = = ∫ (12) 

1.3.2 Anisotropic Materials 

The first modification of the existing MATLAB code was to include in the model the ability to 

use anisotropic materials. Given the Jacobian of an element, 
12 

xyz

x x

xyz

y y

xyz

z z

ξ ξξξ

η ηηη

ζ ζζζ

⎧ ⎫⎡ ⎤ ∂ ∂∂∂ ⎧ ∂ ⎫ ⎧⎫ ∂ ⎪ ⎪⎢ ⎥ ⎪ ⎪ ⎪⎪ ∂ ∂∂∂ ∂ ∂ ⎪ ⎪⎢ ⎥ ⎪ ⎪ ⎪⎪

∂ ∂∂∂ ∂ ∂ ⎪ ⎪ ⎪⎪ ⎨ ⎬ ⎨⎬ ⎨⎬ = = ⎢ ⎥ ∂ ∂∂∂ ∂ ∂ ⎪ ⎪ ⎪⎪ ⎪⎪ ⎢ ⎥

∂ ∂∂∂ ∂ ∂ ⎢ ⎥

⎢ ⎥ ⎩ ⎭⎣ ⎦ ∂ ∂∂∂ ∂ ∂ ⎩⎭ ⎩⎭

J (13) 

The orientation of element in the global coordinate system, given its nodal connectivity numbering, 

can be determined as the normalized inverse of the Jacobian: 

1

1

−

− = J T

J (14) 

Given the definition of the compliance matrix S , 

( )

( )

( )

1 000

1 000

1 000

2 1

000 0 0

2 1

000 0 0

2 1

000 0 0

yx zx

xx yy zz

xy zy

xx yy zz x x

xz yz y y

xx yy zz z z

yz yz yz

zx zx xx

xy xy zx

yy

xy

zz

E EE

EE E

E EE

E

E

E

ν ν

ν ν

ε σ

ν ν ε σ

ε σ

γ τ ν

γ τ

γ τ ν

ν

⎡ ⎤

⎢ ⎥ − −

− −

⎧ ⎫

⎪ ⎪

⎪ ⎪ − − ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ = + ⎪ ⎪

⎪ ⎪

⎪ ⎪ ⎪ ⎪ ⎩ ⎭ +

+

⎣ ⎦

x

y

z

yz

zx

xy

σ

σ

σ

τ

τ

τ

⎧ ⎫ ⎧⎫ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪

⎨ ⎬ ⎨⎬ =

⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪

⎩⎭ ⎩⎭ ⎪ ⎪ ⎪⎪

S (15) 

The compliance matrix S in the element coordinate system is 

[ ]

[ ] ( )

( )

( )

[ ]

[ ] 6 6 6 6 6 6 6 6

6 6 6 6 6 6 6 6

1 000

1 000

1 000

0 0

0 0 2 1

000 0 0

2 1

000 0 0

2 1

000 0 0

yx zx

xx yy zz

xy zy

xx yy zz

xz yz

T

xx yy zz x x x x

x yz x x x

xx

zx

yy

xy

zz

E EE

EE E

E EE

E

E

E

ν ν

ν ν

ν ν

ν

ν

ν

⎡ ⎤

⎢ ⎥ − −

− −

− −

⎡⎤ ⎡⎤ = ⎢⎥ ⎢⎥

+ ⎣⎦ ⎣⎦

+

+

⎣ ⎦

T T

S

T T (16) 
13 

1.3.3 Modeling of Piezoelectric Materials 

The next step in expanding the capabilities of the MATLAB code was to determine the voltage 

generated by the piezo elements when deformed and the deformation they induce when a voltage 

is applied. A piezoelectric material is transversely isotropic. In the Institute of Electrical and 

Electronics Engineers Standard (STD-176-1978), the relationship among dielectric displacement 

(D), mechanical stress (T), the electric field (E) and mechanical strain is (S)

1 11 15

2 22 15

3 33 31 31 33

1 31 11 12 13

2 31 12 22 23

3 33 13 23 33

4 15 44

5 15 55

6 66

000000 0

0 0000 00

00 000

00 000

00 000

00 000

0 0000 00

000000 0

00000000

T

T

T

EEE

EEE

EEE

E

E

E

D d

D d

D ddd

S dsss

S dsss

S dsss

S d s

S d s

S s

ε

ε

ε

⎧ ⎫ ⎡ ⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪ ⎪ ⎪ ⎨ ⎬ =

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪ ⎩ ⎭ ⎣

%

%

%

1

2

3

1

2

3

4

5

6

E

E

E

T

T

T

T

T

T

⎤ ⎧ ⎫

⎢ ⎥ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎦ ⎩ ⎭

 (17) 

where ε is the permittivity of the material and it is assumed to be isothermal. In engineering 

notation, 

1 11 15

2 22 15

3 33 31 31 33

1 31 11 12 13

2 31 12 22 23

3 33 13 23 33

4 15 44

5 15 55

6 66

000000 0

0 0000 00

00 000

00 000

00 000

00 000

0 0000 00

000000 0

00000000

T

T

T

EEE

EEE

EEE

E

E

E

d

d

ddd

dSSS

dSSS

dSSS

d S

d S

S

λ ε

λ ε

λ ε

ε

ε

ε

ε

ε

ε

⎧ ⎫ ⎡ ⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪ ⎪ ⎪ ⎨ ⎬ =

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪ ⎩ ⎭ ⎣

%

%

%

1

2

3

1

2

3

4

5

6

E

E

E

σ

σ

σ

σ

σ

σ

⎤ ⎧ ⎫

⎢ ⎥ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎦ ⎩ ⎭

 (18) 

This can be re-written in block matrix form as 

9 9

T E

x

e E

e S

λ ε

ε σ

⎧ ⎫ ⎡ ⎤ ⎧⎫ ⎨ ⎬ ⎨⎬ = ⎢ ⎥ ⎩⎭ ⎣ ⎦ ⎩⎭

% (19) 

where the coupling coefficient is now e and c represents stiffness. 

{} {} [ ]{ }

1

2

1 11 1 15

3

2 22 2 15

4

3 33 3 31 31 33

5

6

00 0000 0

0 0 0 0 0 00

0 0 0 00

E d

E d

E ddd

E e

σ

σ

λ ε

σ

λ ε

σ

λ ε

σ

σ

λε σ

⎧ ⎫ ⎪ ⎪

⎡ ⎤ ⎪ ⎪ ⎧⎫ ⎧ ⎫⎧ ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎨ ⎬ ⎨ ⎬ ⎨ ⎬⎨ ⎬ = + ⎢ ⎥ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎢ ⎥ ⎩⎭ ⎩ ⎭⎩ ⎭ ⎣ ⎦ ⎪ ⎪ ⎪ ⎪ ⎪⎩ ⎭⎪

= + ⎡ ⎤ ⎣ ⎦

%

%

%

%

 (20) 
14 

[ ] { }

{ } [ ] {} {}

1 11 13 13 1

2 12 22 23 2

3 13 23 33 3

4 44 4

5 55 5

6 66 6

000

000

000

000 00

0000 0

00000

EEE

EEE

EEE T

E

E

E

T E

SSS

SSS

SSS

e E

S

S

S

eE S

ε σ

ε σ

ε σ

ε σ

ε σ

ε σ

ε σ

⎧⎫ ⎧ ⎫ ⎡ ⎤

⎪⎪ ⎪ ⎪ ⎢ ⎥

⎨⎬ ⎨ ⎬ = +

⎪⎪ ⎪ ⎪

⎪ ⎪ ⎢ ⎥⎪ ⎪ ⎩⎭ ⎩ ⎭ ⎣ ⎦

= + ⎡ ⎤ ⎣ ⎦

 (21) 

The piezo can be a sensor ( λ = 0), which yields the following equations: 

( )

( )

1

1

0

TE T E

Ee E e

eE S e e S

λ ε σ εσ

ε σ εσ σ

−

−

= + = ⇒ =−

= + =− +

% %

% (22) 

or it can be driven by an applied electric field: 

applied

T E

applied

E e

eE S

λ ε σ

ε σ

= +

= +

%

 (23) 

T

applied e E is a forcing term and can be included in the finite element model as n virtual work terms. 

This was implemented in the MATLAB code. 

Place this in the Hellinger-Reissner functional: 

( )

( )

1

2

1

2

TT T T

R ij Applied

V

T TT T T

e E dV B

B

β β σ βα α

β ββ βα α β

∏ =− + + −

=− + + −

H JQ ∫

H FJ Q

 (24) 

Where F T T

V

E P e dVE = ∫ F (25) 

This yields a new “forcing” term: 

1 1

18 3 3 1 24 6 6 18

3 1

1

3 1

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

T T T

E x x x x

xx

T

x

yy

zz

xx

T T T

x

yy

zz

EB J E

t

V

t

t

t

V

t

t

β

β

α

− −

−

= = ⎡⎤ ⎡⎤ ⎣⎦ ⎣⎦

⎡ ⎤

⎢ ⎥

⎢ ⎥

⎢ ⎥ = ⎢ ⎥

⎢ ⎥

⎢ ⎥

⎢ ⎥

⎢ ⎥ ⎣ ⎦

⎡ ⎤

⎢ ⎥

⎢ ⎥

⎢ ⎥ = ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥

⎢ ⎥

⎢ ⎥

⎢ ⎥ ⎣ ⎦

QF F

F

GH F

 (26) 
15 

The active strain is 

λ 33 31 36 61 x E e x xx = ε σ % + (27) 

when there is an applied field and without an applied field, the generated field is 

( )

( )

1

1

0

TE T E

Ee E e

eE S e e S

λ ε σ εσ

ε σ εσ σ

−

−

= + = ⇒ =−

= + =− +

% %

% (28) 

Note that the same coordinate transformation needs to be performed if the material properties are 

aligned along the element coordinate system. 

Figure 10 is a simple example where a voltage was placed over an element in the Z-direction (the 

33 d direction). 

Figure 10. Deformation of a piezo cube when a voltage is applied 

across the 33 d (Z-) direction. (The bottom corners are 

fixed and the cube expands in the Z-direction while 

contracting in the X- and Y-directions. The constraints 

introduce stresses in the cube.) 

1.3.4 Linear Results 

The finite elements were programmed in FORTRAN (Formula Translator) and linked with 

MATLAB executable files. The model was used to examine the performance of the ceramic−glassreinforced plastic (GRP) composite targets of Straβburger, Senf, Burkins, and Gooch (1996). This 

section reports the results where the material behavior was assumed to be linear. The next step was 

to perform a nonlinear large deformation analysis where elements in which the stresses exceed 
16 

failure criteria are eliminated from the analysis. Figure 11 shows the linear first mode predicted by 

the Midé code. Note that for these results, clamped boundary conditions were assumed in the 

model. The total target mass is predicted to be 11.40 kg or 25.08 lb. 

The model was also used to examine the behavior of the target if the boundary conditions were 

assumed to be simply supported. 

Figure 11. First mode shape of the ceramic-GRP composite target predicted by the Midé code. 

(Boundary conditions were clamped.) 

0 100 200 300 400 500 600 700

-10

0

10

20

30

Time (micro-seconds)

Z-Displacement of Impact Point (m

m

0 100 200 300 400 500 600 700

-500

0

500

1000

Time (micro-seconds)

Z-Velocity of Impact Point (m/s)

Figure 12. Displacement and velocity (deformation) of impact point. (Boundary 

conditions were clamped.) 
17 

0 100 200 300 400 500 600 700

-10

-5

0

5

10

Time (micro-seconds)

Z-Displacement of Back (mm)

0 100 200 300 400 500 600 700

-200

-100

0

100

200

Time (micro-seconds)

Z-Velocity of Back (m/s)

Figure 13. Displacement and velocity (deformation) of the top surface directly above the 

impact point. (Boundary conditions were clamped.) 

Figure 14. Predicted von Mises stresses at 230 microseconds (μs) after impact. (Boundary conditions 

were clamped.) 
18 

Figure 15. First mode shape of the ceramic-GRP composite target predicted by the Midé code. (Boundary 

conditions were simply supported.) 

0 50 100 150 200 250 300 350

-10

0

10

20

30

Time (micro-seconds)

Z-Displacement of Impact Point (m

m

0 50 100 150 200 250 300 350

-500

0

500

1000

Time (micro-seconds)

Z-Velocity of Impact Point (m/s)

Figure 16. Displacement and velocity (deformation) of impact point. (Boundary conditions 

were simply supported.) 
19 

0 50 100 150 200 250 300 350

-5

0

5

10

Time (micro-seconds)

Z-Displacement of Back (mm)

0 50 100 150 200 250 300 350

-150

-100

-50

0

50

100

Time (micro-seconds)

Z-Velocity of Back (m/s)

Figure 17. Displacement and velocity (deformation) of the top surface directly above the 

impact point. (Boundary conditions were simply supported.) 

Figure 18. Predicted von Mises stresses at 230 micro-seconds after impact. (Boundary conditions 

were simply supported.) 
20 

As expected, the linear analysis was substantially different from the results reported in Straβburger 

et al. (1996). However Midé code can now predict the voltages generated by piezo-materials and 

is ready for studies of how the piezo-elements can be used to reduce the deformation of the back 

plate. 

1.3.5 ANSYS Finite Element Model 

Initially, Midé considered the cost of obtaining ANSYS specifically for this program to be 

prohibitive. Another Midé program had the funds available and decided to purchase the FEA 

package. This allowed Midé to generate an alternate finite element model for this program. The 

advantages of using ANSYS instead of the MATLAB model are as follow: 

• A finer grid can be modeled. 

• The actual models can be created in a solid modeling program and imported into the FEA 

package. 

• Optimization is supported. 

• Highly detailed piezoelectric models are available. 

• Memory management schemes in ANSYS allow for more detailed analysis. 

• Time history and animation plots are easily obtained. 

It was thus decided at a late stage in the program to change to the ANSYS model. 

1.3.5.1 ANSYS Model Description 

Figure 19 illustrates the meshed ANSYS model. The model consists of tetrahedral elements for 

the Kevlar parts and solid bricks for the piezo parts. Figure 19 shows the model in a deformed 

state. The model’s boundary conditions are placed at three nodes on every corner on the piezo 

side of the Kevlar plate in every direction. A simple assumption was to model the bullet impact 

as an initial velocity on the nodes surrounding the center of the plate with a 0.5-inch diameter. 

This velocity was set at 1000 m/s. 

The piezo elements were constrained so that all the elements on their top and bottom (attached to 

the Kevlar) surfaces were electrically connected to each other. This had the same effect as placing 

an electrode over these surfaces and modeled the QuickPack6 and PowerAct sensors and actuators 

well. 

A typical result of the analysis is shown in figure 20. Here, the elements are deformed and highlighted according to their displacement in the z direction (direction the bullet is traveling). The 

shock waves can clearly be seen on the surface, causing the displacements. 

 6QuickPack and PowerAct are trademarks of Midé Technology Corporation. 
21 

Figure 19. The meshed ANSYS model. 

Figure 20. A typical result from the ANSYS analysis illustrating the nodal displacement 

in the z direction. 
22 

1.3.5.2 Time Step Displacement Comparisons 

The following series of images compares the displacement output of the ANSYS model to that of 

the high speed video camera for test 2649. The high speed video camera has a shutter speed of 

121 μs/frame. The model was run with a 10-μs interval. Every 12th step of the output of the 

model is shown in table 2. The plate is c-clamped to the holder and struck on the face contacting 

the frame. The impact is below the black tape. 

It is interesting to note how the model captures the initial ballistic event, causing the sharp bubble 

in the Kevlar, and the secondary wave that displaces the Kevlar from the frame. This comparison 

shows that the model is somewhat representative of reality. Unfortunately, real displacement data 

were not available and a true calibration of the model was not possible. 

 

 

Figure 21. Comparison of high speed video and the ANSYS model. 
23 

 

 

 

 

Figure 21. (continued). 
24 

 

 

 

 

Figure 21. (continued). 
25 

1.3.5.3 Voltage Generation Comparison 

This section presents a brief comparison between the results obtained from the only good sensor 

(PA1) in the tests described in section 1.4.2. This sensor was the only one that produced data 

with some value. A part of the sensor’s output is shown in figure 22, where the figure zooms in 

on the first millisecond of data for comparison with the ANSYS model. The result of the voltage 

output of the piezo wafer, placed at the same spot as the PA1 sensor is shown in figure 23. 

Although the two plots differ in many ways, there are some remarkable resemblances: 

• Both have a dominant frequency of ~6.5 kHz. 

• The maximum voltage for the first peak is ~900 V. 

• A similar high frequency content is superimposed on the dominant frequency. 

• There is a general increase in voltage over the first 1 ms of the event. 

Although these similarities are vague, it is encouraging to realize that these similarities exist 

without the model being calibrated. It may be safe to assume that trends that are identified by 

the model might be achievable in reality. 

Figure 22. Voltage output from the PA1 piezo sensor during the ballistic test. 
26 

Figure 23. Voltage output from the PA1 piezo sensor in the ANSYS simulation. 

1.4 Task 4: Preliminary Experiments 

Small experiments were designed and conducted to verify critical elements of the design. The 

experimental results were used to update and verify the parametric models. 

Midé and the ARL decided to combine testing of the baseline Kevlar sheets and preliminary 

piezoelectric sensor devices. The piezoelectric tests were scheduled for the option, but since the 

test facilities were available, it was decided to evaluate the piezoelectric devices during a 

ballistic event and move the design and optimization research to a next phase effort. 

1.4.1 Kevlar Plate Tests 

Six tests were conducted to determine the displacement of the Kevlar sheets in response to the 

impact of a high velocity polypropylene bullet. 

1.4.1.1 Test Setup 

The test setup schematic is shown in figure 24. The controller initiates the event by sending an 

electric pulse to the gun. This pulse activates the firing pin of the gun and ignites the charge. 

The charge propels the polypropylene bullet through the gun’s barrel (figure 26) and toward the 

Kevlar target (figure 25). On the way to the target, the bullet passes through the trigger. The 

trigger sends a signal to the controller that commands the oscilloscope and the laptop (high-speed 

camera) to start recording. The eddy displacement gauge (figure 26) records the displacement of 
27 

the metal strip, and the laptop computer records the sequence of events that follows the impact of 

the bullet. 

Figure 24. Kevlar displacement test setup. 

Figure 25. Test setup as viewed from the gun barrel. 

Kevlar 

Plate 

Camera 

Trigger
28 

 

Figure 26. The gun, left and side view of the eddy gauge, metal strip and Kevlar 

target, right. 

1.4.1.2 Test Sequence 

Five tests were performed on the bare Kevlar sheets. Unfortunately, the metal strips used were 

not able to withstand the ballistic event. Only limited data from these tests were available, but 

none of them were useful to calibrate the model. Additional tests were mostly conducted in an 

attempt to improve the performance of the metal strips so that displacement data could be 

recorded. 

Table 2 summarizes the tests that were performed at APG. These tests can be divided into the 

displacement and piezo tests. The displacement tests were the originally scheduled tests for this 

part of the program. The results from these tests were to be used for the calibration of the FEA 

model. As stated before, the tests ended mostly in the destruction of the metal pieces needed by 

the measuring equipment, and thus, no usable data were obtained from them. 

Figures 27 to 32 show the failures of the different tests. Initially, the metal strips for the eddy 

current gauge were bonded to a protective layer that covered the Kevlar plate. The existence of 

this layer was only discovered after test 2647. Although this layer was removed for the subsequent tests, the bonding layer between the metal and the Kevlar was not strong enough to withstand the ballistic event. Ensuing tests will have the metal integrated with the Kevlar and this 

should solve the problem. The QuickPack and PowerAct tests produced some useful data and 

these tests are described in some more detail next. 

Eddy

Gauge Metal 

Strip 

Kevlar 

Plate 
29 

Table 2. Test sequence and failure mechanisms for a ballistic test conducted at ARL. 

Test No. Description Failure Mechanism 

2646 Displacement test. Three 2-inch metal tape strips Metal tape ruptures 

2647 Displacement test. Metal sheet bonded to structure Metal sheet ruptures 

2648 Displacement test; 0.75-inch-diameter metal tape 

placed under the impact point. 

Metal disc intact; data not useful for calibration 

of model. 

2649 Displacement test; 0.75-inch-diameter metal disc 

bonded to structure. 

Disk blown off structure. 

2650 Displacement test; 0.75-inch-diameter thin metal 

disc bonded to structure 

Thin disk blown off structure. 

2651 Multi layer piezo test. Piezos bonded to protective layer. Piezos 

delaminated from structure. 

2652 QuickPack and PowerAct piezo wafer test. Sensors bonded to protective layer. QuickPacks 

failed structurally. One PowerAct intact. 

Figure 27. Setup before test number 2646. 

Figure 28. Failure during test 2646. (Note 

how the tape tears in all directions, 

indicating severe strain-related 

failure of the metal.) 
30 

Figure 29. Failure of test 2647. (Again, the rupture of 

the metal sheet indicated that the strain 

limit of the material was exceeded 

significantly.) 

Figure 30. The impact point is well above the position 

of the 0.75-inch metal disk in test 2648. 

(The impact does not dislodge the tape, 

indicating that a smaller area might have a 

chance of surviving the high differential 

strain environment of the ballistic test.) 
31 

Figure 31. Delaminating of the 0.75-inch metal disk 

during test 2649. 

Figure 32. Failure of test 2650 was attributable to the 

dislodging of the metal disk. 

1.4.2 Integrated Piezo Tests 

Although tests with piezoelectric elements are part of the option for this program, Midé decided to 

combine these tests with the Kevlar plate tests. The main reason for this is to fail early and learn 

lessons in order to succeed later. In order to accomplish this, two sets of piezoelectric sensors and 

actuators were bonded to the Kevlar surface. As stated earlier, the surface was covered with a 

“peel-off” protective layer, the existence of which was only discovered during the tests at ARL. 

Thus, the piezoelectric materials were actually bonded to the protective peel-off layer. 

Disk
32 

Two Kevlar plates were instrumented with piezos for tests 2651 and 2652. The first set of piezoelectric elements consisted of four layers of piezoelectric arrays. Each layer consisted of six rows 

of piezos that were made from three separate 1.8-inch by 0.83-inch by 0.006-inch piezoelectric 

wafers, coupled in parallel to each other. The second set of piezos consisted of two sets of Midé’s 

PA10N PowerAct and QP10N QuickPack actuators. The description and summary of the tests are 

given in table 3. 

Table 3. Description of the integrated piezo tests. 

Test No. Description Failure Mechanism 

2651 Multi layer piezo test. Piezos bonded to protective layer. Piezos delaminated from structure. 

2652 QuickPack and PowerAct 

piezo wafer test. 

Sensors bonded to protective layer. QuickPacks failed structurally. 

One PowerAct intact. 

Because of the presence of the protective layer, the initial shock was enough to remove the piezos 

from the Kevlar, and no useful data were obtained. It is not deemed necessary to describe the test 

and the configurations or the results at any length. 

 

Figure 33. Four layers of piezoelectric elements with various electric configurations were bonded to the target 

as shown on the left. (Unfortunately, because of the presence of a protective layer, the piezos were 

not bonded to the structure and the failure [right] resulted during test 2651. No useful data were 

obtained.) 

The second piezo tests had four encapsulated piezoelectric wafers bonded to the Kevlar plate. 

The test setup is shown in figure 34. Two QuickPack QP10Ns and PowerAct PA10Ns were 

placed opposite each other as shown. The details of the sensors are listed in table 4. A short 

description of the two types of actuators is available at http://www.mide.com. 
33 

 

 

Figure 34. Pre- and post-test 2652 pictures of the QuickPack and PowerAct sensors. 

Table 4. Details of the four encapsulated piezoelectric wafers bonded to the Kevlar plate. 

Sensor No. Description Wafer Size (in.) Serial No. Piezo Material Capacitance (nF) 

PA1 Conformable wafer 1.83 x .83 x 0.01 PA11201 PZT5A 41.7 

PA2 Conformable wafer 1.83 x .83 x 0.01 PA11010 PZT5A 45 

QP1 Rigid wafer 1.83 x .83 x 0.01 QP11205 PZT5A 54.4 

QP2 Rigid wafer 1.83 x .83 x 0.01 QP11214 PZT5A 52.6 

Although the wafers were bonded to the protective layer, some useful data were obtained from the 

sensors. These results are shown in figures 35 through 39 and were used in the modeling section 

to compare with the predicted output from the sensors. The picture on the left of figure 34 shows 

the effect that the ballistic event had on the sensors. PA1 is the only sensor that remained intact. 

All the other sensors were destroyed by the event. It was expected that the high strains would 

crack the rigid QuickPacks. The failure of the one PowerAct can only be explained by the fact 

that it was bonded to the protective layer, which delaminated during the event, causing the 

PowerAct to be accelerated away from the surface and to experience abnormal bending. 

Figure 35 shows the results from the eddy current gauge. The 0.75-inch metal strip was removed 

form the Kevlar plate by the ballistic event. This caused a spike in the gauge data and indicated 

the time of impact. No further useful data can be derived from the signal. 

PA1 

PA2 

QP1 

QP2 

PA2 PA1 

QP1

QP2
34 

Figure 35. Results from the eddy current gauge. (This result is indicative of the failure of the metal strip to remain on the Kevlar 

composite plate. However, it indicated the initial event at 

0.1 sec after trigger, which is useful for analysis of the 

piezoelectric signals.) 

Figure 36 shows the signal obtained from PA1. This is the only useful piece of data available 

from the entire test series. This trace was further analyzed in the modeling section where it was 

compared with the ANSYS model. Here, we can note a few features of the signal. The first 

resonant mode is at 140 Hz. The initial impact is sensed but does not drive the signal to the 

limit. The shock arriving around 0.01 second after impact drives the signal out of range, 

indicating that this is the main event. 

Figure 36. Output from PA1. (The continuous trace after the event 

indicates that these are useful data. The spike at 0.11 sec 

exceeded the limits of the oscilloscope.) 
35 

Figure 37 shows the result form QP1. The impact cracked the piezo into a number of smaller 

pieces. The data show this as the different, disconnected pieces generate their individual signals 

that are combined in the trace. This combined signal appears as a random trace, as can be seen 

in figure 37. 

Figure 37. Output from QP1. (It is clear that the sensor produced random 

signal because the wafer was cracked.) 

Figures 38 and 39 show what happens when the wafer becomes dislodged from the Kevlar. The 

ballistic wave pushes the piezo, having momentum, back. This causes the element to bend and 

completely break off, as can be seen in the left picture of figure 34. The output voltage traces 

from the elements indicate an initial charge that then bleeds off after the piezo is destroyed. 

Figure 38. Output from PA2. (The sensor breaks immediately after 

the initiating event, bleeding its charge to the oscilloscope.)
36 

Figure 39. Output from QP2. (This sensor also has a catastrophic failure, 

thus the bleed-off of the initial signal.) 

1.5 Task 5: Shock Absorber Design 

With the parametric model developed in Task 2 and updated in Task 4, design a detailed 

sandwiched piezoelectric shock absorption system that can be fabricated and tested in the 

option. 

The ANSYS model was used to determine the effect of sending a high voltage pulse to piezo 

wafers that were placed around the impact point in order to create a disturbance wave. It was 

hypothesized that this disturbance wave might reduce the displacement of the cone at the impact 

point and thus diminish injuries and damage during a ballistic event. 

The model was used to simulate the effect that 0.5-inch-thick piezo wafers might have on the 

displacement of the Kevlar composite plate. It is common practice to limit the electric field in a 

piezo to 20 V/mil. This was the maximum field that was used in the model. Again, the initial 

conditions of the model were to constrain the corners of the Kevlar plate to zero movement and 

to add an initial velocity of 1000 m/s to the node in a 0.5-inch diameter around the center of the 

plate. Two simulations were run, one with the voltage pulse and one without for comparison. 

Figure 40 shows the displacement of the center node only in response to the ballistic event. The 

node is displaced a maximum of 230 micro-strains 0.38 ms after bullet impact. Figure 41 shows 

the displacement of the same node, but this time with a destructive wave generated by the piezos. 

The maximum displacement is 180 micro-strains 0.39 ms after the ballistic event. This is a 27% 

reduction in displacement. It is further interesting to note the high frequency element present in 

the piezo-actuated simulation. This high frequency element can be responsible for the reduction 

in the center node amplitude. 
37 

Figure 40. Displacement of the center node in response to the ballistic event. 

Figure 41. Displacement of the center node in response to the ballistic event when a 

structural interference wave is generated by the piezoelectric elements in 

response to a high voltage pulse. 
38 

These are encouraging results, but caution must be exercised. The actual meaning of the displacement units can only be determined when the model is calibrated. This calibration, and only this 

calibration, will quantify these results. 

Once the model is calibrated, the ANSYS model can be used to find the best way to reduce the 

displacement of the center node. The model is now set up so that the following variables can 

easily be changed in order to find the optimal solution: 

• Piezo size 

• Piezo placement 

• Electric field 

• Waveform 

• Amplitude 

• Piezo material 

• Piezo coupling 

• Control scheme 

2. Conclusion and Future Work 

The option was initially created to build and test a Kevlar composite plate with piezos integrated 

into the plate. The tests evaluated the optimal solution as determined by the modeling of Phase I. 

As stated earlier, problems with obtaining reliable data reduced the effectiveness of the modeling 

in Phase I. Some of the option work was completed by testing integrated piezos, but again, the 

impact of the tests was reduced by the unavailability of reliable displacement data. 

Efforts are under way to improve the displacement data. The models have been created and are 

ready to be optimized. The period between the end of Phase I and the start of the option will be 

used to improve the displacement data. This will enable Midé to complete the optimization very 

early in the option, so that the prototypes can be built and tested without disrupting the program 

further. 
39 

3. References 

1. Institute of Electrical and Electronics Engineers. IEEE Standard on Piezoelectricity; STD176-1978; New York, 1978. 

2. Straβburger, E.; Senf, H.; Burkins, M. S.; Gooch W. A. Dynamic Impact Resistance of 

Ceramic-GRP Composite Targets. Presented at the 16th International Symposium on 

Ballistics, San Francisco, CA, September 23-27, 1996. 
40 

INTENTIONALLY LEFT BLANK. 
41 

Appendix A. MATLAB Main Code 

% Construct a lumped paramater model of a bullet impact 

close all 

clear all 

pack 

% SIMULATION 

Delt_Frac=0.02; 

% Delt_Frac=0.1; 

Nstep=4000; 

zeta=2e-10; % Damping ratio 

% zeta=0*1e-17; % Damping ratio 

iplt=1; % Plot option (0 = No plots) 

number_node=0; % = 1: Plot the node numbers 

number_element=0; % = 1: Plot the element numbers 

Nskip=20; % Number of steps between animation plots 

Deformation_Scale=1; % Scaling factor for the deformation 

Case_Name='APG'; 

save_opt=1; % = 1; Save the plots in jpg format 

movie_opt=1; % = 1; Save a movie of the impact response 

stress_opt=1; % Calculate the stresses 

% GEOMETRY 

Nx = 13; % Number of elements in the planar direction 

Ny = Nx; 

Lx = 0.2286; % Lenght or width of the armor protection 

Nz = 5; % Number of elements in the thickness direction 

Lz = .00635; % Thickness 

Ly = Lx; % Consider a square plate 

Ly = Lx; % Just a strip to better match the stiffness 

MidNod=fix(Nx/2); 

Iimpact=MidNod+MidNod*Nx+1; 

Ibehind=Iimpact + Nx*Ny*(Nz-1); 

delx=Lx/(Nx-1); 

dely=Ly/(Ny-1); 

delz=Lz/(Nz-1); 

% BULLET 

Bullet_Velocity=600; % Bullet impact velocity 

Bullet_Mass=.00156; % Bullet mass 

% MATERIAL PROPERTIES 

EyoungXX=24.1E9; 
42 

EyoungYY=24.1E9; 

EyoungZZ=10.4E9; 

nhuzx=0.12; 

nhuyz=0.12; 

nhuxy=0.4; 

Density=1440; 

fprintf('\n Total Mass = %6.2f kg or %6.2f lb \n',Density*Lx*Ly*Lz,Density*Lx*Ly*Lz*2.2); 

% Construct the coordinates 

ii=0; 

for k=1:Nz 

 for j=1:Ny 

 for i=1:Nx 

 ii=ii+1; 

 Coord(ii,1)=(i-1)*delx; 

 Coord(ii,2)=(j-1)*dely; 

 Coord(ii,3)=(k-1)*delz; 

 end 

 end 

end 

Nnode=ii; 

% Construct the "Nodal" Connectivity 

% First in the X-direction 

ielem = 0; 

for k=1:Nz-1 

 for j=1:Ny-1 

 for i=1:Nx-1 

 ielem = ielem+1; 

 Nconec(ielem,1)=(k-1)*Nx*Ny + (j-1)*Nx + i; 

 Nconec(ielem,2)=(k-1)*Nx*Ny + (j-1)*Nx + i + 1; 

 Nconec(ielem,3)=(k-1)*Nx*Ny + j*Nx + i + 1; 

 Nconec(ielem,4)=(k-1)*Nx*Ny + j*Nx + i; 

 Nconec(ielem,5)=k*Nx*Ny + (j-1)*Nx + i; 

 Nconec(ielem,6)=k*Nx*Ny + (j-1)*Nx + i + 1; 

 Nconec(ielem,7)=k*Nx*Ny + j*Nx + i + 1; 

 Nconec(ielem,8)=k*Nx*Ny + j*Nx + i; 

 end 

 end 

end 

Nelem=ielem; 

Alive=ones(Nelem,1); 

% Plot the grid on a non-equal axes grid 

if(iplt~=0);plot_model_8;end 
43 

NGP = 3; 

% Now calculate and construct the finite element model 

KMat=sparse(zeros(3*Nnode,3*Nnode)); 

TMat=sparse(zeros(3*Nnode,3*Nnode)); 

MMat=sparse(zeros(3*Nnode,1)); 

for ielem=1:Nelem 

 for j=1:8 

 XI(j,1) = Coord(Nconec(ielem,j),1); 

 YI(j,1) = Coord(Nconec(ielem,j),2); 

 ZI(j,1) = Coord(Nconec(ielem,j),3); 

 end 

 [STIFM1 ,JAC] = ANSTFSOL (XI ,YI ,ZI ,EyoungXX ,EyoungYY ,EyoungZZ ,... 

 nhuxy ,nhuyz ,nhuzx ,NGP ); 

 [EMASS ,JAC ,XCG ,YCG ,ZCG ,TMASS] = MASSOL (XI ,YI ,ZI ,Density ,NGP ); 

 

 for i=1:8 

 IC = Nconec(ielem,i); 

 for k1=1:3 

 IC2=(IC-1)*3+k1; 

 ICS = (i - 1)*3 + k1; 

 for j=1:8 

 IR = Nconec(ielem,j); 

 for k2=1:3 

 IR2 = (IR - 1 )*3 + k2; 

 IRS = (j - 1)*3 + k2; 

 KMat(IR2,IC2) = KMat(IR2,IC2) + Alive(ielem)*STIFM1 (IRS ,ICS ); 

 end 

 end 

 end 

 end 

 

 for i=1:8 

 ID = Nconec(ielem,i); 

 for k1=1:3 

 ID2=(ID-1)*3+k1; 

 MMat(ID2) = MMat(ID2) + EMASS (i ); 

 end 

 end 

end 

for i=1:Nnode*3 

 TMat(i,:)=KMat(i,:)/MMat(i); 

end 

% TMat(1:3,1:3) 

[phi,eval]=eig(full(TMat)); 

[Freq,iord]=sort(sqrt(real(diag(eval)))/(2*pi)); 

for i=1:Nnode*3 
44 

 phi1(:,i)=phi(:,iord(i)); 

end 

phi=phi1; 

clear phi1 

delt=Delt_Frac/max(Freq); 

fprintf('\n\n Lowest Natural Frequency: %7.3f Hz \n\n',Freq(7)); 

save Restart TMat KMat MMat phi Freq 

wold=zeros(Nnode*3,1); 

wvold=zeros(Nnode*3,1); 

KE_Bullet=0.5*Bullet_Velocity*Bullet_Velocity*Bullet_Mass; 

Imparted_Velocity=sqrt(KE_Bullet*2/(MMat(Iimpact*3) + Bullet_Mass)); 

wold(Iimpact*3)=Imparted_Velocity*delt; 

wvold(Iimpact*3)=0; 

MMat(Iimpact*3)=MMat(Iimpact*3) + Bullet_Mass; 

MMat(Iimpact*3-1)=MMat(Iimpact*3-1) + Bullet_Mass; 

MMat(Iimpact*3-2)=MMat(Iimpact*3-2) + Bullet_Mass; 

for i=1:Nnode*3 

 TMat(i,:)=KMat(i,:)/MMat(i); 

end 

wvel=(wold-wvold)/(delt); 

% KE0=0.5*wvel'.*MMat'*wvel 

if(iplt~=0);plot_deformed_8;end 

w_store=zeros(Nstep,Nnode*3); 

Nstress=Nstep/Nskip; 

VMStress_store=zeros(Nstress,Nelem); 

wvel_store=w_store; 

istress=0; 

for itime=1:Nstep 

 Time(itime)=(itime-1)*delt; 

 wvel=(wold-wvold)/(delt); 

 wnew=+2*wold - wvold - delt*delt*TMat*wold - delt*delt*zeta*TMat*wvel; 

 

 w_store(itime,:)=wnew; 

 wvel_store(itime,:)=wvel; 

 wvold=wold; 

 wold=wnew; 

 

% Calculate the Kinetic Energy 

KE(itime)=0.5*wvel'.*MMat'*wvel; 

PE(itime)=0.125*(wold+wvold)'*KMat*(wold+wvold); 
45 

% Calculate the stresses around the impact point 

 if(mod(itime,Nskip) == 0); 

 fprintf(' Time Step %d \n',itime); 

 if (stress_opt == 1) 

 istress = istress + 1; 

 for ielem=1:Nelem 

 for j=1:8 

 XI(j,1) = Coord(Nconec(ielem,j),1); 

 YI(j,1) = Coord(Nconec(ielem,j),2); 

 ZI(j,1) = Coord(Nconec(ielem,j),3); 

 U(j*3-2,1) = wnew(Nconec(ielem,j)*3-2); 

 U(j*3-1,1) = wnew(Nconec(ielem,j)*3-1); 

 U(j*3,1) = wnew(Nconec(ielem,j)*3); 

 end 

 [SIGX ,SIGY ,SIGZ ,SIGXY ,SIGYZ ,SIGZX ,SIGVM ,JAC] = ... 

 ANSTRSOL (XI ,YI ,ZI ,U ,EyoungXX ,EyoungYY ,EyoungZZ ,nhuxy ,nhuyz ,nhuzx ,NGP ); 

 VMStress_store(istress,ielem)=SIGVM(9)/1E6; % In MPa 

% if(ielem==1); 

% U(1:16)' 

% VMStress_store(istress,:) 

% pause 

% end 

% if(ielem==4); 

% U(1:16)' 

% VMStress_store(istress,:) 

% pause 

% end 

 end 

 end 

 end 

end 

save Restart TMat KMat MMat phi Freq KE PE wvel_store w_store Time VMStress_store 

figure(2) 

subplot(211) 

plot(Time,w_store(:,Iimpact*3));xlabel('Time (seconds)');ylabel('Z-Displacement of Impact Point (m)') 

subplot(212) 

plot(Time,wvel_store(:,Iimpact*3));xlabel('Time (seconds)');ylabel('Z-Velocity of Impact Point (m/s)') 

figure(2) 

figure(3) 

subplot(211) 

plot(Time,w_store(:,Ibehind*3));xlabel('Time (seconds)');ylabel('Z-Displacement of Back (m)') 

subplot(212) 

plot(Time,wvel_store(:,Ibehind*3));xlabel('Time (seconds)');ylabel('Z-Velocity of Back (m/s)') 

figure(3) 
46 

figure(4) 

subplot(311) 

plot(Time,KE);xlabel('Time (seconds)');ylabel('Kinetic Energy (J)') 

subplot(312) 

plot(Time,PE);xlabel('Time (seconds)');ylabel('Potential Energy (J)') 

subplot(313) 

plot(Time,PE+KE);xlabel('Time (seconds)');ylabel('Total Energy (J)') 

figure(4) 

if(iplt~=0);animate_filled_8;end 
47 

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NO. OF 

COPIES ORGANIZATION

 1 OTO BREDA 

 M GUALCO 

 VIA VALDIOCCHI 15 

 I 19136 LA SPEZIA 

 ITALY 

 5 RAPHAEL BALLISTICS CTR 

 M MAYSELESS Y PARTOM 

 G ROSENBERG Z ROSENBERG 

 Y YESHURUN 

 BOX 2250 

 HAIFA 31021 

 ISRAEL 

 1 ROYAL MILITARY ACADEMY 

 E CELENS 

 RENAISSANCE AVE 30 

 B 1040 BRUSSELS 

 BELGIUM 

 1 ROYAL NETHERLANDS ARMY 

 J HOENEVELD 

 V D BURCHLAAN 31 

 PO BOX 90822 

 2509 LS THE HAGUE 

 NETHERLANDS 

 1 DEFENCE MATERIEL ADMIN 

 WEAPONS DIRECTORATE 

 A BERG 

 S 11588 STOCKHOLM 

 SWEDEN 

 2 SWEDISH DEFENCE RSCH ESTAB 

 DIVISION OF MATERIALS 

 S J SAVAGE J ERIKSON 

 S 172 90 STOCKHOLM 

 SWEDEN 

 3 SWEDISH DEFENCE RSCH ESTAB 

 L HOLMBERG B JANZON 

 P LUNDBERG 

 BOX 551 

 S 147 25 TUMBA 

 SWEDEN 

 1 TECHNION INST OF TECH 

 FACULTY OF MECH ENGINEERING 

 S BODNER 

 TECHNION CITY 

 HAIFA 32000 

 ISRAEL 

NO. OF 

COPIES ORGANIZATION

 3 TECHNISCHE UNIVERSITAT 

 CHEMNITZ ZWICKAU 

 A SCHROEDTER L KRUEGER 

 L MEYER 

 POSTFACH 

 D 09107 CHEMINITZ 

 GERMANY 

 2 TNO PRINS MAURITS LAB 

 H PESKES R IJSSELSTEIN 

 LANGE KLEIWEG 137 

 PO BOX 45 

 2280 AA RIJSWIJK 

 THE NETHERLANDS 

 6 CENTRE DE RECHERCHES 

 ET D’ETUDES D’ARCUEIL 

 D BOUVART C COTTENNOT 

 S JONNEAUX H ORSINI 

 S SERROR F TARDIVAL 

 16 BIS AVENUE PRIEUR DE 

 LA COTE D’OR 

 F 94114 ARCUEIL CEDEX 

 FRANCE 

 1 CDR EUROPEAN RSCH OFFICE 

 USARDSG (UK) 

 S SAMPATH 

 PSC 802 BOX 15 

 FPO AE 09499-1500