nilakantan gaurav

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UNIVERSITY OF CINCINNATI

Date:___________________

I, _________________________________________________________,

hereby submit this work as part of the requirements for the degree of:

in:

It is entitled:

This work and its defense approved by:

Chair: _______________________________

_______________________________

_______________________________

_______________________________

_______________________________

08/03/2006

Gaurav Nilakantan

Master of Science

Mechanical Engineering

Design and Development of an Energy Absorbing Seat and Ballistic

Fabric Material Model to reduce Crew Injury caused by Acceleration

from Mine/IED blast

Dr. Ala Tabiei

Dr. Jay Kim

Dr. David Thompson


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DESIGN AND DEVELOPMENT OF AN ENERGY ABSORBING SEAT AND

BALLISTIC FABRIC MATERIAL MODEL TO REDUCE CREW INJURY

CAUSED BY ACCELERATION FROM MINE/IED BLAST

A Thesis submitted to the

Division of Research and Advanced Studies

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE

in the Department of Mechanical, Industrial and Nuclear Engineering

of the College of Engineering

2006

by

Gaurav Nilakantan

Bachelor of Engineering (B.E.)

Visveswaraiah Technological University, India, 2003

Committee Chair: Dr. Ala Tabiei


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Abstract

Anti tank (AT) mines pose a serious threat to the occupants of armored vehicles.

High acceleration pulses and impact forces are transmitted to the occupant

through vehicle-occupant contact interfaces, such as the floor and seat, posing

the risk of moderate injury to fatality.

The use of an energy absorbing seat in conjunction with vehicle armor plating

greatly improves occupant survivability during such an explosion. The axial

crushing of aluminum tubes over a steel rail constitutes the principal energy

absorption mechanism. Concepts to further reduce the shock pulse transmitted

to the occupant are introduced during the study, such as the use of a foam

cushion and an inflatable airbag cushion.

The explicit non-linear finite element software LS-DYNA© is used to perform all

numerical simulations. Vertical drop testing of the seat structure with the

occupant are performed for comparison with experimental data after which

simulations are run, that utilize input acceleration pulses comparable to a mine

blast under an armored vehicle. The occupant is modeled using a 5th percentile

HYBRID III dummy. Data such as lumbar load, neck moments, hip and knee

moments, and head and torso accelerations are collected for comparison with

known injury threshold values to assess injury.

Numerical simulations are also conducted of the impact of a dummy’s feet by

a rigid wall whose upward motion is comparable to an armored vehicle’sreaction to a mine blast directly underneath it. A 50 th percentile HYBRID III

dummy is used in various seated positions. The input pulses that control the

motion of the rigid wall are varied in a step wise manner to determine the effect

on extent of injury. Data such as hip and knee moment, femoral force and foot

acceleration are collected from the dummy and compared to injury threshold


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values from various references. By numerically simulating the mine blast under a

vehicle, the significant cost of conducting destructive full scale tests can be

avoided.

A simple numerical formulation is presented, to predict the deceleration

response during dynamic axial crushing of cylindrical tubes. The formulation

uses an energy balance approach and is coded in the high level language

MATLAB©. It can track the histories of plastic work, kinetic energy, and dynamic

crushing load during the crushing process, and finally yields the peak

acceleration magnitude, which can then be calibrated and used for injury

assessment and survivability studies by comparing with allowable values for

human occupants. Further, the geometric and material properties of the tube

can be varied to study its response during the dynamic axial crushing.

The impact resistance of high strength fabrics makes them desirable in

applications such as protective clothing for military and law enforcement

personnel, protective layering in turbine fragment containment, armor plating of

vehicles, and other similar applications involving protection resistance against a

high velocity projectile. Such fabrics, especially Kevlar©, Zylon©, and Spectra©,

can be used in the energy absorbing seat as a cushion cover for the high

density foam, to prevent tearing by unexpected shrapnel during an explosion

underneath the armored vehicle. The protective fabric can also be used as a

protective vest for the dummy occupant and as a liner inside the vehicle hull. A

material model has been developed to realistically simulate ballistic impact of

loose woven fabrics with elastic crimped fibers. It is based upon a

micromechanical approach that includes the architecture of the fabric and the

phenomenon of fiber reorientation, and excludes strain rate sensitivity as the

yarns are simplified as elastic members. The material model is implemented as

a FORTRAN© subroutine and integrated into the explicit, non-linear dynamic

finite element code LSDYNA© as a user-defined material model (UMAT). Results


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of axial fabric tests run in LSDYNA© using this material model agree well with

other models. This justifies the use of a simplistic, computationally inexpensive

material model to realistically simulate ballistic impact.


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Acknowledgements

I am indebted to my advisor Prof. Ala Tabiei for giving me a chance to work with

him on all his fascinating research, for believing in me and constantly guiding

and encouraging me.

I express my utmost gratitude to my parents S. Nilakantan and Nirmala

Nilakantan for all that they have done for me, for all their love, support, sacrifice,

and encouragement.

I sincerely thank committee members, Prof. Jay Kim, and Prof. David Thompson

for their presence on my committee and their suggestions.

I am also grateful to the University of Las Vegas-Nevada for funding part of this

research, as well as the Ohio Supercomputing Center for their high-speed

computing support.

I thank my colleague Srinivasa Vedagiri Aminijikarai for all his technical advice

and support.


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Contents

a. List of Figures…………………………………………………………………………….... i

b. List of Tables……………………………………………………………………………….. vi

1. Introduction 1

1.1 Background………………………………………………………………………….. 1

1.2 Literature Review…………………………………………………………………….. 2

1.2.1 Energy Absorbing Seat………………………………………………….. 2

1.2.2 Foot Impact during IED/Mine blast…………………………………….. 4

1.2.3 Human Injury Criteria……………………………………………………. 5

1.2.4 Dynamic Axial Crushing of Circular Tubes……………………………. 13

1.2.5 Ballistic Impact of Dry Woven Fabrics…………………………………. 14

1.3 Scope of Work……………………………………………………………………….. 26

1.4 Outline of Thesis……………………………………………………………………… 27

2. Energy Absorbing Seat 29

2.1 Preliminary Design…………………………………………………………………… 29

2.2 Dynamic Axial Crushing of the Aluminum Tubes………………………………… 32

2.2.1 Techniques to reduce the initial crushing load of a tube…………... 36

2.3 Additional energy absorbing elements…………………………………………… 39


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2.3.1 Low Density Foam Cushion…………………………………………….. 39

2.3.2 Airbag Cushion………………………………………………………….. 42

2.4 Shock Pulses Applied to the Structure…………………………………………….. 44

2.4.1 Impact After Free Fall…………………………………………………… 44

2.4.2 Mine Blast………………………………………………………………… 45

2.5 Filtering of Data……………………………………………………………………… 46

2.6 Validation of Initial EA Seat Simulations…………………………………………… 47

3. Results and Discussion: Energy Absorbing Seat 49

3.1 Test Matrix…………………………………………………………………………….. 49

3.2 Simulation Setup…………………………………………………………………….. 50

3.3 EA seat with GEBOD dummy subjected to vertical drop testing………………. 51

3.4 EA seat with HYBRID III dummy subjected to vertical drop testing…………….. 54

3.5 EA seat with GEBOD dummy subjected to mine blast testing…………………. 56

3.6 EA seat with HYBRID III dummy subjected to mine blast testing……………….. 59

3.7 Improved Modeling of the EA seat structure…………………………………….. 60

3.8 Effect of Aluminum Yield Strength on the Simulations…………………………... 61

3.9 Stages of Crushing of the Aluminum Crush Tube………………………………... 62

3.9.1 Stages of crushing for the original EA seat model……………………

63

3.9.2 Stages of crushing for the improved EA seat model………………... 64


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3.9.3 Shape of the Crushed Tube when Modeled with Solid Elements….. 64

3.10 Final EA Seat Design for use in full scale Vertical Drop Testing and mine

Blast Testing………………………………………………………………………………. 65

3.10.1 Vertical Drop Testing…………………………………………………… 66

3.10.2 Mine Blast Testing………………………………………………………. 68

3.11 New EA Mechanism……………………………………………………………….. 69

3.12 Conclusions………………………………………………………………………… 71

3.13 Scope for Further Work…………………………………………………………….. 73

4. Impact of Foot during IED/Mine Blast 74

4.1 Numerical Setup and Methodology………………………………………………. 74

4.2 Numerical Results and Discussion…………………………………………………. 78

4.2.1 Hybrid III dummy in a sitting straight position…………………………. 80

4.2.2 Hybrid III dummy in a driving position…………………………………. 84

4.3 Parametric Study…………………………………………………………………….. 89

4.4 Conclusions………………………………………………………………………….. 93

4.5 Scope for Further Work……………………………………………………………… 94

5. Dynamic Axial Crushing of Circular Tubes: Numerical Formulation 95

5.1 Need for a Simple Numerical Formulation……………………………………….. 95

5.2 Theory and Formulation…………………………………………………………….. 97

5.3 Results and Discussion……………………………………………………………… 107

5.4 Conclusions………………………………………………………………………….. 114


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5.5 Scope for further work………………………………………………………………. 115

6. Ballistic Impact of Woven Fabrics 116

6.1 Description of the Material Model………………………………………………… 116

6.2 The Representative Volume Cell of the Model…………………………………... 116

6.3 Elastic Model………………………………………………………………………… 118

6.4 Numerical Results - Fabric Strip Testing…………………………………………… 125

6.4.1 Elastic model fabric strip test………………………………………….. 127

6.4.2 Viscoelastic model fabric strip test……………………………………. 129

6.4.3 Comparison between Elastic and Viscoelastic model results……… 130

6.5 Conclusions………………………………………………………………………….. 132

6.6 Scope for Further Work……………………………………………………………… 133

Appendix I

Source code for the numerical formulation of dynamic axial crushing of circular

tubes………………………………………………………………………………………. 134

Appendix II

Source code for the incremental constitutive equation used in the Elastic

material model to derive the stress-strain relationship………………………………. 146

References……………………………………………………………….. 148


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i

List of Figures

Chapter 1

1.1 Crashworthy seat for commuter aircraft………………………………... 3

1.2 Evaluation of an OH-58 pilot’s seat……………………………………… 4

1.3 Dummy lower leg models used in the lower leg impact studies…….. 5

1.4 Numerical dummies developed by LSTC………………………………. 5

1.5 Axially crushed aluminum tube………………………………………….. 14

1.6 Numerical simulation of ballistic impact of fabric in LSDYNA………… 22

Chapter 2

2.1 Preliminary EA seat design………………………………………………... 29

2.2 Specifications of the rail substructure…………………………………… 31

2.3 Stress Vs. Strain curve for the aluminum crush tubes………………….. 32

2.4 Static and dynamic axial crushing load of cylindrical aluminum

tubes with a D/t ratio of 30.7……………………………………………... 35

2.5 Annular grooves on a circular crush tube………………………………. 36

2.6 Weakening the FE mesh of the crush tube…………………………….. 37

2.7 Heat treatment curve used during the annealing process…………… 38

2.8 Static performance of plain and wasted tubes……………………….. 38

2.9 Nominal stress Vs. strain curve for the low density foam material……. 39

2.10 Gravity settling of the dummy against the foam cushion…………….. 40

2.11 Contoured foam cushion headrest to minimize head injury…………. 41

2.12 Effect of foam cushion on HYRBID III head acceleration……………... 41

2.13 FE mesh of the EA seat with airbag cushion and GEBOD dummy…... 43

2.14 Input parameters of the airbag cushion………………………………... 44

2.15 Acceleration pulse used in vertical drop testing………………………. 45

2.16 Acceleration pulse representing a mine blast…………………………. 46

2.17 Filtering of data……………………………………………………………. 47


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ii

List of Figures… continued

2.18 Validation of initial EA seat simulations………………………………….. 48

Chapter 3

3.1 EA seat with a GEBOD dummy………………………………………….. 50

3.2 EA seat with a HYBRID III dummy………………………………………… 51

3.3 Results of EA Seat with GEBOD dummy subject to vertical drop

testing……………………………………………………………………….. 53

3.4 Results of EA Seat with HYBRID III dummy subject to vertical drop

testing……………………………………………………………………… 563.5 Results of EA Seat with GEBOD dummy subject to mine blast testing.. 58

3.6 Results of EA Seat with HYBRID III dummy subject to mine blast

testing……………………………………………………………………….. 60

3.7 Improved modeling of the EA seat structure…………………………… 61

3.8 Effect of Aluminum yield strength on the simulations…………………. 62

3.9 Stages of tube crushing for original seat model………………………. 63

3.10 Stages of tube crushing for improved seat model……………………. 64

3.11 Shape of the crushed tube modeled with solid elements……………. 65

3.12 Final model of the EA seat structure…………………………………….. 66

3.13 Deceleration pulses………………………………………………………. 66

3.14 Dynamic axial crushing force of the tube, and Dummy-seat

contact force……………………………………………………………… 67

3.15 Contact force between the foot and floor…………………………….. 67

3.16 Acceleration pulses……………………………………………………….. 68

3.17 Dynamic axial crushing force of the tube, and Dummy-seat

contact force……………………………………………………………… 68

3.18 Contact force between the foot and floor…………………………….. 69

3.19 New honeycomb EA mechanism………………………………………. 70


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iii


3.20 Interior view of the EA mechanism……………………………………… 71

Chapter 4

4.1 Experimental setup of lower leg impact……………………………….. 74

4.2 Numerical setup in ‘Sitting Straight’ position……………………………. 75

4.3 Numerical setup in ‘Driving’ position…………………………………….. 76

4.4 Prescribed velocity of the wall…………………………………………… 77

4.5 Validation of femur axial compressive force with test db2a…………. 78

4.6 Validation of foot acceleration with test db2a………………………… 794.7 Validation of femur axial compressive force with test db3a…………. 79

4.8 Validation of foot acceleration with test db3a………………………… 80

4.9 Foot (z) acceleration……………………………………………………… 81

4.10 Hip flexion-extension moment for wall speeds 1 ft/s - 15 ft/s…………. 82

4.11 Hip flexion-extension moment for wall speeds 25 ft/s - 35 ft/s………... 82

4.12 Lower leg (z) acceleration………………………………………………... 83

4.13 Femur axial compressive force………………………………………….. 83

4.14 Knee flexion-extension moment………………………………………… 84

4.15 Foot (z) acceleration……………………………………………………… 85

4.16 Hip flexion-extension moment…………………………………………… 86

4.17 Lower leg (z) acceleration………………………………………………... 86

4.18 Femur axial compressive force………………………………………….. 87

4.19 Knee flexion-extension moment…………………………………………. 87

4.20 Ankle dorsi-plantar flexion moment for wall speeds 1 ft/s - 10 ft/s…… 88

4.21 Ankle dorsi-plantar flexion moment for wall speeds 15 ft/s - 35 ft/s….. 88

4.22 Variables used in the parametric study…………………………………. 89


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iv


4.23 Variation of peak foot acceleration with peak wall speed for a

dummy in a driving position……………………………………………… 914.24 Variation of peak femur force with peak wall speed for a dummy in

a driving position…………………………………………………………... 92

4.25 Variation of peak femur force with wall speed and knee angle for

various dummy positions…………………………………………………. 92

Chapter 5

5.1 Applied deceleration pulse simulating impact after freefall…………. 985.2 Formation of a basic folding element………………………………….. 100

5.3 Comparison of impactor velocity time history…………………………. 108

5.4 Comparison of energy transformation during the impact event……. 109

5.5 Comparison of dynamic crushing load………………………………... 110

5.6 Velocities from the numerical formulation……………………………… 111

5.7 Unfiltered EA seat acceleration data…………………………………… 111

5.8 FFT of the relative velocity of the EA seat………………………………. 112

5.9 Comparison of acceleration response…………………………………. 112

5.10 Comparison of peak acceleration magnitude………………………... 113

Chapter 6

6.1 Representative Volume Cell (RVC) of the model……………………… 117

6.2 Pin-joint bar mechanism………………………………………………….. 118

6.3 One Element Elasticity Model……………………………………………. 118

6.4 Equilibrium position of the central nodes……………………………….. 120

6.5 Yarn stress-strain response of viscoelastic model……………………… 124

6.6 Yarn stress-strain response of elastic model……………………………. 124

6.7 Numerical setup of fabric axial strip test………………………………... 125


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v


6.8 Von-Mises stress distribution for strip with 30 s-1 strain rate…………… 126

6.9 Axial strip tests of Elastic model………………………………………….. 1286.10 Bias strip tests of Elastic model…………………………………………… 129

6.11 Axial strip tests of Viscoelastic model……………………………………. 129

6.12 Bias strip tests of Viscoelastic model…………………………………….. 130

6.13 Comparison of bias tests of elastic and viscoelastic models at

different strain rates……………………………………………………….. 131

6.14 Comparison of axial tests of elastic and viscoelastic models at

different strain rates……………………………………………………….. 132


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vi

List of Tables

Chapter 1

1.1 Human tolerance limits to acceleration ……………………………….. 61.2 Abbreviated Injury Scale (AIS) and sample injury types for two body

regions………………………………………………………………………. 7

1.3 HIC for various dummy sizes……………………………………………… 9

1.4 Critical values for various dummies used in the calculation of NIC…. 11

1.5 Recommended injury criteria for landmine testing……………………. 13

Chapter 2

2.1 Dimensions and material properties of the cylindrical aluminum

tubes used………………………………………………………………….. 33

2.2 Axial crushing parameters of the cylindrical aluminum tubes used…. 35

Chapter 3

3.1 Test matrix for EA seat design…………………………………………….. 49

Chapter 5

5.1 Human tolerance limits to acceleration………………………………… 96

5.2 Characteristics of the shell and impactor………………………………. 107

Chapter 6

6.1 Material and geometric properties of the Kevlar© fabric strip……….. 127


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1

Chapter 1

Introduction

1.1 Background

Efforts are continually underway to maximize occupant safety during

peacekeeping efforts. Anti Tank (AT) mines and Improvised Explosive Devices

(IED) pose a serious threat to the occupants of armored vehicles. High

acceleration pulses and impact forces are transmitted to the occupant through

vehicle-occupant contact interfaces, such as the floor and seat, posing the risk

of moderate to fatal injury. The use of an energy absorbing (EA) seat in

conjunction with vehicle armor plating greatly improves occupant survivability

during such an explosion. The U.S. Army does not currently have an effective EA

seat in use. The only additional protection offered to the occupant so far is the

seat cushion.

The design of such an EA seat will need to include a suitable energy absorbing

device that proves to be both effective and feasible to incorporate into current

armored vehicle designs. The EA seat will then need to be rigorously tested

against explosive ordnance. The dynamic axial crushing of aluminum tubes is

an extensively used energy absorbing element in crashworthiness studies

because of numerous advantages such as high energy absorption and a

reasonably constant operating force.

The occupant lower leg impact by the vehicle floor during an IED explosion is

also of interest in occupant survivability studies. There currently exists very little

experimental data of lower leg impact, and consequently the injury

mechanisms are still not fully understood and validation of numerical studies

becomes difficult.


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2

Efforts are also on to accurately model the ballistic impact of high strength

fabrics and to understand their complex behavior by virtue of their fabric

architecture. Such fabrics have high applicability to occupant safety, especially

for their anti-penetration resistance to projectiles. Different models have been

presented over the years, but a single comprehensive model that captures all

the fabric phenomena during ballistic impact does not currently exist. Simplistic

models however have been presented that capture the most important

features with good accuracy and at the least computational expense.

With the advent of supercomputing and advanced commercial finite element

codes, the emphasis is on conducting numerical simulations of real world

phenomena, to reduce the high costs of destructive testing while still preserving

the accuracy of the problem. This is the rationale behind this research which

involves conducting numerical simulations of mine blast testing of the energy

absorbing seat, occupant lower leg impact by the vehicle floor during the

explosion of an IED, and the development of a material model to realistically

simulate ballistic impact.

1.2 Literature Review

1.2.1 Energy Absorbing Seat

Concepts that are used in the crashworthiness analysis of aircraft seats are quite

similar to those used in crew protection against mine blasts. In 1988, Fox [1]

performed a feasibility study for an OH-58 helicopter energy attenuating crew

seat. Energy attenuating concepts included a pivoting seat pan, a guided

bucket, and a tension seat. In 1989, Simula Inc. prepared an Aircraft Crash

Survival Design Guide [2] for the Aviation Applied Technology Directorate. The

guide outlined various injury criteria, and energy absorbing devices amongst


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3

other such related topics. In 1990, Gowdy [3] designed a crashworthy seat for

commuter aircraft using a wire bending energy absorber design as seen in

Figure 1.3. This design was sub-optimal but provided satisfactory results for

vertical decelerations between 15-32 Gs.

Figure 1.1 Crashworthy seat for commuter aircraft [3]

In 1993, Laananen [4] performed a crashworthiness analysis of commuter

aircraft seats during full scale impact using SOM-LA (Seat Occupant Model –

Light Aircraft). He concluded that those current designs did not meet the then

standards for occupant safety and that vertical direction energy absorbing

devices needed to be implemented. In 1994, Haley Jr. [5] evaluated a retrofit

OH-58 pilot’s seat to study its effectiveness in preventing back injury, as seen in

Figure 1.2. In 1996, Alem et al. [6] evaluated an energy absorbing truck seat to

evaluate its effectiveness in protection against landmine blasts. In 1998, the

Night Vision and Electronic Sensors Directorate published a report on Tactical

Wheeled Vehicles and Crew Survivability in Landmine Explosions [7]. Keeman [8]

has briefly summarized the approach adopted during the design of vehicle

crashworthy structures that utilize joints and thin walled beams. In 2002, Kellas [9]

designed an energy absorbing seat for an agricultural aircraft using the axial

crushing of aluminum tubes as the primary energy absorber.


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4

Figure 1.2 Evaluation of an OH-58 pilot’s seat [5]

1.2.2 Foot Impact during IED/Mine blast

Joss [10] described how anti-personnel landmines have become a global

epidemic. Khan et al. [11] studied the type of hind foot injuries caused by

landmine blasts and surgical techniques available to treat it. Horst et al. [12]

experimentally and numerically studied occupant lower leg injury due to

landmine detonations under a vehicle. Horst and Leerdam [13] presented

further research being conducted into occupant safety for blast mine

detonations under vehicles. Dummies are used to study the lower leg impact,

and data such as accelerations and forces are measured along the lower leg,

from which injury criteria are assessed. Figure 1.3 shows some of the dummy leg

models used during these studies.

(a) (b) (c)


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5

(d) (e)

Figure 1.3 a) Prosthetic leg model b) MADYMI detailed leg c) MADYMO Thor Lxleg d) Interior view of the modeled leg e) HYBRID III Denton leg [13]

1.2.3 Human Injury Criteria

In order to determine the effectiveness of a design that protects occupants

against injury caused by crash and mine blasts, certain injury criteria need to be

defined. Occupant crash data such as forces, moments and accelerations are

collected from dummies used experimental tests and simulations and then

compared to these injury criteria to assess Occupant Survivability and Human

Injury. Figure 1.4 displays numerical dummies developed by LSTC for use in the

commercial finite element code LSDYNA©.

(a) (b)

Figure 1.4 a) GEBOD dummy b) HYBRID III dummy


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6

a) Generalized Human Tolerance Limits to Acceleration

Table 1.1 displays the human tolerance limits for typical crash pulses along

three mutually orthogonal axes, for a well restrained young male. These values

provide a general outline of the safe acceleration limit for a human during a

typical crash. However, the time duration of the applied acceleration pulse has

not been specified. Higher acceleration pulses can be sustained for shorter

durations compare to lower acceleration pulses for longer durations, thus the

time duration in question is important [14].

Direction of Accelerative

Force

Occupant’s Inertial Response Tolerance Level

Headward (+Gz) Eyeballs Down 25 G

Tailward (-Gz) Eyeballs Up 15 G

Lateral Right (+Gy) Eyeballs Left 20 G

Lateral Left (-Gy) Eyeballs Right 20 G

Back to Chest (+Gx) Eyeballs-in 45 G

Chest to Back (-Gx) Eyeballs-out 45 G

Table 1.1 Human tolerance limits to acceleration [14]

b) Injury Scaling

Injury scaling is a technique for assigning a numerical assessment or severity

score to traumatic injuries in order to quantify the severity of a particular injury.

The most extensively used injury scale is the Abbreviated Injury Scale (AIS)

developed by the American Association for Automotive Medicine and originally

published in 1971. The AIS assigns an injury severity of “one” to “six” to each injury

according to the severity of each separate anatomical injury. Table 1.2 provides

the AIS designations and gives examples of injuries for two body regions. The

primary limitation of the AIS is that it looks at each injury in isolation and does not

provide an indication of outcome for the individual as a whole. Consequently,

the Injury Severity Score (ISS) was developed in 1974 to predict probability of

survival.


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7

AIS Severity Head Spine

0 None - -

1 Minor Headache or Dizziness Acute Strain (no fracture ordislocation)

2 Moderate Unconsciousness less than 1 hr.,

Linear fracture

Minor fracture without any cord

involvement3 Serious Unconscious, 1-6 hrs., Depressedfracture

Ruptured disc with nerve rootdamage

4 Severe Unconscious, 6-24 hrs., Openfracture

Incomplete cervical cord syndrome

5 Critical Unconscious more than 24 hr,Large hematoma , (100cc)

C4 or below cervical completecord syndrome

6 Maximum Injury(virtually non-survivable)

Crush of Skull C3 or above complete cordsyndrome

Table 1.2 Abbreviated Injury Scale (AIS) and sample injury typesfor two body regions [14]

The ISS is a numerical scale that is derived by summing the squares of the three

highest body region AIS values. This gives a score ranging from 1 to 75. The

maximal value of 75 results from three AIS 5 injuries, or one or more AIS 6 injuries.

Probabilities of death have been assigned to each possible score. Table 1.2

provides the AIS designations and gives examples of injuries for two body

regions. [14]

c) Dynamic Response Index (DRI)

The DRI is representative of the maximum dynamic compression of the vertebral

column and is calculated by describing the human body in terms of an

analogous, lumped-mass parameter, mechanical model consisting of a mass,

spring and damper. The DRI model assesses the response of the human body

to transient acceleration-time profiles. DRI has been effective in predicting

spinal injury potential for + Gz acceleration environments in ejection seats. DRI is

acceptable for evaluation of crash resistant seat performance relative to spinal

injury, if used in conjunction with other injury criteria including Eiband and

Lumbar Load thresholds. [14]


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8

d) Lumbar Load Criterion

The maximum compressive load shall not exceed 1500 pounds (6672 N)

measured between the pelvis and lumbar spine of a 50th-percentile test

dummy for a crash pulse in which the predominant impact vector is parallel to

the vertical axis of the spinal column. This is one of the most widely used

criterions in vertical crash and impact testing. If the spinal cord is severely

compressed or severed, it can lead to either instant paralysis or fatality. [1, 9, 13-

16]

e) Head Injury Criterion (HIC)

HIC was proposed by the National Highway Traffic Safety Administration (NHTSA)

in 1972 and is an alternative interpretation to the Wayne State Tolerance Curve

(WSTC).[14, 15] It is used to assess forehead impact against unyielding surfaces.

Basically, the acceleration-time response is experimentally measured and the

data is related to skull fractures. Gadd [17] had suggested a weighted-impulse

criterion (GADD Severity Index, GSI) as an evaluator of injury potential defined as:

(1.1)

where

SI = GADD Severity Index

a = acceleration as a function of time

n = weighting factor greater than 1

t = time

Gadd plotted the WSTC data in log paper and an approximate straight line

function was developed for the weighted impulse criterion that eventually

became known as GSI. The Head Injury Criteria is given by

n

t SI a dt = ∫


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9

(1.2)

where

a(t) = acceleration as a function of time of the head center

of gravity

t1,t2 = time limits of integration that maximize HIC

FMVSS 208 (Federal Motor Vehicle Safety and Standards) originally set a

maximum value of 1000 for the HIC and specified a time interval not exceeding

36 milliseconds. HIC equal to 1000 represents a 16% probability of a life

threatening brain injury. HIC suggests that a higher acceleration for a shorter

period is less injurious than a lower level of acceleration for a higher period of

time. As of 2000, the NHTSA final rule specified the maximum time limit for

calculating the HIC as 15 milliseconds. [4, 9, 17-23] Table 1.3 shows the HIC for

various dummy sizes.

Dummy

Type

Large size

Male

Mid size

Male

Small size

Female

6 year old

child

3 year old

child

1 year old

infantHIC15 Limit 700 700 700 700 570 390

Table 1.3 HIC for various dummy sizes [15]

f) Head Impact Power (HIP)

A recent report included the proposal of a new HIC entitled Head Impact Power

(HIP) It considers not only kinematics of the head (rigid body motion of the skull)

but also the change in kinetic energy of the skull which may result in

deformation of and injury to the non-rigid brain matter. The Head Impact Power

(HIP) is based on the general rate of change of the translational and rotational

kinetic energy. The HIP is an extension of previously suggested “Viscous Criterion”

1

2

2.5

2 1( ) ( )

t

t

HIC t t a t dt ⎡ ⎤

= − ⎢ ⎥⎢ ⎥⎣ ⎦∫


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first proposed by Lau and Viano in 1986, which states that a certain level or

probability of injury will occur to a viscous organ if the product of its compression

‘C’ and the rate of compression ‘V’ exceeds some limiting value [14].

g) Injury Assessment Reference Values (IARS)

This rule adopts new requirements for specifications, instrumentation, test

procedures and calibration for the Hybrid III test dummy. [14]. The regulation’s

preamble has a detailed discussion of the injury mechanisms and the relevant

automotive mishap data for each of the injury criteria associated with the Hybrid

III ATD. Military test plans should implement these criteria.

h) Neck Injury Criterion (NIC)

The NIC considers relative acceleration between the C1 and T1 vertebra and is

given by [24]:

(1.3)

with

(1.4)

NIC must not exceed 15 m2 /s2. [25]Another criteria NIC50 refers to NIC at 50mm

of C1-T1 (cervical-thoracic) retraction. Newly proposed N ij criteria by NHTSA

combines effects of forces and moments measured at occipital condyles and

is a better predictor of cranio-cervical injuries. Nij takes into account NTE (tension-

extension), NTF (tension-flexion), NCE (compression-extension), NCF (compression-

flexion). FMVSS specification No.208 requires that none of the four Nij values

exceed 1.4 at any point. The generalized NIC is given by [26]:

2( ) 0.2 ( ) [ ( )]rel rel NIC t xa t V t = +

1

1

( ) ( ) ( )

( ) ( ) ( )

T Head

rel x x

T Head

rel x x

a t a t a t

v t a t a t

= −

= −∫ ∫


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(1.5)

where

Fz = Upper Neck Axial Force (N),

M y = Moment about Occipital Condyle

Fzn = Axial Force Critical Value (N), and

M yn = Moment Critical Value (N-m).

In FMVSS 208 (2000) final rule a neck injury criterion, designated Nij , is used. This

criterion is based on the belief that the occipital condoyle-head junction can

be approximated by a prismatic bar and that the failure for the neck is related

to the stress in the ligament tissue spanning the area between the neck and the

head. Nij must not exceed 1.0. [16, 22, 24, 26] Table 1.4 displays the critical

values for various dummies used in the calculation of Nij [15].

Dummy

Type

Fzc (N)

Flexion

Fzc (N)

Extension

M yc (Nm)

Flexion

M yc (Nm)

Extension

Comments

3 year olddummy 2120 2120 68 27

Peak tension force < 1130 NPeak compression force < 1380 N

50thpercentile 6806 6160 310 135

Peak tension (Fz) < 4170 NPeak extension (Fz) < 4000 N

Table 1.4 Critical values for various dummies used in the calculation of NIC [15]

i) Chest Criteria

Peak resultant acceleration will not exceed 60 G’s for more than 3 milliseconds

(Mertz, 1971) as measured by a Tri-axial accelerometer in upper thorax. Also, the

chest compression will be less than 3 inches for the Hybrid III dummy as

measured by a chest potentiometer behind the sternum [14, 15].

Z Y ij

ZC YC

F M N

F M ⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠


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j) Viscous Criterion

Viscous Criterion (V*C) – defined as the chest compression velocity (derived by

differentiating the measured chest compression) multiplied by the chest

compression and divided by the chest depth. This criterion has been mentioned

for the sake of completeness of information; however it is not widely used [14].

k) Femur Force Criterion

This criterion states that the compressive force transmitted axially through each

upper leg should not exceed 2,250 pounds or 10,000 N. Impulse loads that

exceed this limit can cause complete fracture of the femoral bone as well as

sever major arteries that can cause excessive bleeding. In numerical dummies,

discrete spring elements of known stiffness are included within the leg model,

from which the femur axial compressive force is easily extracted. In actual

dummies, load cells are placed on the dummy’s leg, which are calibrated to

provide the compressive force at the femur. [12, 13, 14, 27].

l) Thoracic Trauma Index (TTI)

The Thoracic Trauma Index is given by:

(1.6)

GR is the greater of the peak accelerations of either the upper or lower rib,

expressed in G’s. GLS is the lower spine peak acceleration, expressed in G’s. The

pelvic acceleration must not exceed 130 G’s [14].


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m) Mine Blast Injury Criteria

U.S. Army’s Aberdeen Test Center has established injury criteria for mine blast

testing of high mobility wheeled vehicles. The injury criteria can also provide

guidance in standard crash impact testing orientations. These criteria are

comprehensive and provide a good assessment of injury that takes into

account the entire occupant’s body subject to any combination of external

stimuli associated with a mine blast. A few criteria are listed in Table 1.5 [14].

HYBRID III Simulant

Response Parameter

Symbol (units) Assessment Reference Values

Head Injury Criteria HIC 750 ~5% risk of brain injury

Lumbar spine axial compression force Fz (N) 3800 N (30ms)

Femur or Tibia axial compression force Fz (N) 7562 N (10ms)

Seat (Pelvis) vertical DRI DRI – Z(G) 15, 18, 23 G (low, med, high risk)

Tibia axial compressive force combined with Tibia bending moment

F (N)M (N-m)

F/Fc – M/Mc < 1 where Fc=35,584N and Mc=225N-m

Table 1.5 Recommended injury criteria for landmine testing [14]

1.2.4 Dynamic Axial Crushing of Circular Tubes

The axial crushing of circular tubes by progressive plastic buckling has been the

subject of an extensive study over the years [28-47]. Perhaps one of the most

widely referred to technical paper in this field is that of Abramowicz and Jones

[29]. Gupta et al. [46, 47] studied the axisymmetric folding of tubes under axial

compression and incorporated both the change in tube thickness and yield

stress values of tension and compression into their model. Karagiozova et al.

[37, 38] studied the inertia effects, and dynamic effects on the buckling andenergy absorption of cylindrical shells under axial impact.

Galib and Limam [35] investigated the static and dynamic crushing of circular

aluminum tubes both experimentally and numerically using the commercial

software RADIOSS©. Bardi et al. [33] compared experimental results of tubes

under axial compression to nuemerical studies using the commercial software


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ABAQUS©. Numerical analyses sometimes contain inaccuracies due to the high

mesh-sensitivity of the impact simulation. There is a difference in shell response

when simulating impact as a moving mass striking the stationery shell as

commonly observed in laboratory conditions, and as a the moving shell striking

a stationery rigid wall. Also, inappropriately filtering the data can lead to

significant under estimation of results such as crushing load [38]. Alghamdi [48]

reviewed common shapes of collapsible energy absorbers and different modes

of deformation of the most common ones. Nilakantan [49] presented a

numerical formulation to study the dynamic axial crushing of circular tubes

based on an energy balance approach. Figure 1.9 displays an axially crushed

aluminum tube, modeled in LSDYNA© [49, 50].

Figure 1.5 Axially crushed aluminum tube

1.2.5 Ballistic impact of dry woven fabrics

I) Modeling of the ballistic impact

Over the past few decades, many different techniques have been used to

derive the constitutive relations and model the overall fabric behaviour for use in

ballistic impact applications. Different models include various effects and

phenomena associated with the ballistic impact of fabrics, however there is no


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single comprehensive model that reproduces and represents all phenomena at

the same time. However many simplistic models have been found to yield

results that are realistic.

a) Classification according to underlying theory

Researchers adopt different ways to approach the modeling of ballistic

response of dry woven fabrics. The methodology is discussed in later

paragraphs. This section simply enlists the approaches adopted by various

authors over time.

i) Analytical

Analytical methods make use of general continuum mechanics equations and

laws such as the conservation of energy and momentum. Governing equations

are set up using various parameters involved during the impact process.

Analytical methods are useful to handle simple physical phenomena, but

become increasingly complicated as the phenomena become more complex

and involve many variables.

This includes work by Vinson et al. [51], Taylor et al. [52], Parga-Landa et al.[53],

Chocron-Benloulo et al.[54], Navarro [55], Billon et al. [56], Gu [57], Hetherington

[58], Cox et al. [59], Naik et al. [60], Phoenix and Porwal [61, 62], Walker [63],

and Xue et al. [64].

ii) Semi-Empirical and empirical

Empirical studies rely on the analysis of data obtained through experimental

work in order to examine the fabric response and obtain constitutive relations

and failure criterion. This includes curve fitting, non-linear regression analysis of

experimental data, and the use of statistical distributions. Parametric equations

relate the various parameters studied during the experiment. The method is


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useful when there are small numbers of variables to correlate [65]. Further, the

shortcoming is that the accuracy of the obtained model will depend on the

accuracy and completeness of the collected data. This includes work by

Cunniff [66], Shim et al. [67], and Gu [68].

iii) Numerical

This approach relies on techniques such as finite element and finite difference

methods, and the use of commercial packages such as ABAQUS©, DYNA3D©,

and LSDYNA© to conduct the analysis or simulation. Contact between and

amongst the yarns and projectile is better handled through the use of

commercial software. Further the fabric yarns may be modeled explicitly. This

includes work by Lomov et al. [69], Johnson et al. [70], Billon et al. [56], Lim et al.

[71], Shim et al. [72], Tan et al. [73, 74], Lim et al. [71], Roylance [75, 76], Hearle

[77], Boisse et al.[78], D’Amato et al. [79, 80], Duan et al. [81], Gu et al. [82],

Simons et al. [83], Teng et al. [84], Tarfaoui et al.[85, 86].

iv) Micromechanical

In a micromechanical approach, the fabric geometry is usually represented by

a representative volume cell or RVC, which by repeated translation will yield the

entire fabric structure. This RVC is then analyzed through equilibrium of forces,

variational potential energy methods, et cetera. to compute displacements,

stresses and strains. This includes work by Tabiei et al. [87, 88], Sheng et al. [89],

Dasgupta et al. [90], Tan et al. [91], Vandeurzen et al. [92] and Xue et al. [93].

v) Multi-scale constitutive

Multi-scale approaches make different assumptions of fabric behavior at

different scales. This arises due to the inherent multi-scale nature of fabrics which


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are constructed from micro-scale fibrils. For example, the fabric behaves as a

continuum membrane at the macro scale; and at the micro scale, the

behavior is accounted for by constitutive modeling of the yarns as elastic or

viscoelastic members. This includes work by Nadler et al. [94] and Zohdi and

Powell [95].

vi) Variational

Variational principles include the Reissner variational principle, Galerkin method,

Rayleigh-Ritz method, and principal of minimum potential energy. These yield

governing differential equations which can then be solved using finite element

and finite difference methods. This includes work by Leech et al. [96], Roy et al.

[97], Sheng et al. [89], and Sihn et al. [98].

vii) Experimental

In order to validate the results from theoretical approaches, experimental data

is required. Further, by experimentally studying the ballistic impact of woven

fabrics, many new mechanisms of energy absorption and failure become

apparent, and effect of various parameters on the ballistic response can be

studied. This includes work by Starratt et al. [99], Susich et al. [100], Field et al.

[101], Wilde et al. [102], Prosser [103, 104], Cunniff [105], Shockey et al. , Wang

et al. [106, 107], Shim et al. [108], Lundin [109], Rupert [110], Orphal et al. [111],

and Manchor et al. [112].

b) Research based on number of fabric plies studied

Majority of the literature available today dealing with ballistic impact of fabrics

focuses on experimental and theoretical work of a single fabric layer. Few

literature deals with the ballistic impact of armor composed of multiple identical


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layers of fabric such as Chocron-Benloulo et al.[54], Hearle et al. [77], Parga-

Landa et al. [53], Vinson et al. [51], Taylor et al. [52], Barauskas et al. [113],

Porwal and Phoenix [62], Sheng et al. [89], Vandeurzen et al. [92], Zohdi et al.

[114], Lomov et al. [69], Navarro et al. [55], Billon et al. [56], Tan et al. [74], Lim et

al. [74], Cunniff [115-117] and Schweizerhof et al. [118]. There is very limited work

on ballistic impact of fabrics composed of multiple layers of different fiber

material such as Cunniff et al. [119], Hearle [120] and Porwal and Phoenix [62].

c) Commercial finite element software packages used for analysis

With the advent of supercomputing, commercial finite element packages are

gaining popularity, because of the low cost alternative offered to costly

experimentation and destructive testing, as well as the potential testing of

materials not yet developed. Finite element packages also offer the option of

using of user-defined material models in place of the standard material models

and thereby provide a useful platform for the testing of new theories utilizing a

numerical form of solution. Finite element codes also can handle interaction

between the projectile and fabric, penetration, contact and friction between

yarns, and the deformation and failure of the fabric. Thus it is a very useful tool

for the simulation of ballistic impact of woven fabrics.

In the ballistic impact testing of fabrics, the most commonly used commercial

finite element packages are ABAQUS© by ABAQUS Inc. which involves the

ABAQUS/Standard and ABAQUS/Explicit solvers, DYNA3D© which is a part of a set

of public codes developed in the Methods Development Group at Lawrence

Livermore National Laboratory (LLNL) [121], and LS-DYNA© by Livermore Software

Technology Corporation [122, 123].

A few examples of research into ballistic impact of woven fabrics that use

these finite element packages are; ABAQUS© used by Xue et al. [64] and Diehl

et al. [124], DYNA3D© used by Shockey et al. [125, 126] and Lim et al. [71], and

LSDYNA© used by Tabiei et al. [87, 88, 127, 128], Gu et al. [57, 68], Shockey et


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al. [129-131] and Duan et al. [81, 132-134], Shahkarami et al. [135], and

Schweizerhof et al [118].

d) Computer software and codes for solid modeling and computing

properties of textile composites

Brown et al. [136] describes a technique to automatically generate a solid

model of the representative volume element (RVE) of the fabric structure. The

solid model is generated using a program file written in I-deas® Open

Language. Cox et al. [59] lists various codes used in the computation of textile

composites properties, especially macroscopic stiffness, strength and

occasionally damage tolerance. These include μTEX-10 and μTEX-20 by Marrey,

R. V. et al, TEXCAD by Naik, Rajiv A., PW, SAT5, SAT8 by Raju, I. S., SAWC by

Whitcomb, J., CCM-TEX by Pochiraju, K., WEAVE by Cox, B., and BINMOD by

Cox, B. et al.

e) Approaches to modeling, based on author(s)

Vinson and Zukas [51] and Taylor and Vinson [52] modeled the fabric as conical

isotropic shells. The model treated the fabric as isotropic and did not

differentiate between warp and weft directions leading to a conical shaped

transverse deflection of the fabric, which is contrary to experimental findings.

Leech et al. [96] and Hearle et al. [77] modeled the fabric as a net. Prosser

[103] derived a mathematical model for the FSP-nylon system in his study of

ballistic impact of nylon panels by 0.22 caliber FSPs. He stated that for a set of

Vc determinations, plots of Vr (residual) and Vs (striking) can be adequately

represented by parabolas. There are periods in the plots of the squared V 50

velocities and number of layers, where the plot linearity signifies that the

mechanism of penetration is constant. Cunniff [119] examined system effects

that occur during ballistic impact of woven fabrics by developing a conceptual


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framework that relates ballistic impact mechanics of a single yarn to ballistic

impact mechanics of the fabric. Ting J. et al. [137] extended on the work of

Roylance et al. [138] and provided for contact between adjacent plies of a

multi-ply target and introduced slippage at yarn cross over points. Their model

predicted an increase in the ballistic limit when the friction of slippage

increases. Cunniff and Ting [139] developed a numerical model that treated

yarns as elastic rod elements, based on the work of [76]. Walker [63] developed

a constitutive model for an anisotropic fabric sheet based on elastic

deformations of the fibers. The centerline deflection of the fabric sheet was

solved with an approximate analytical solution that yields the final deformed

fabric shape and a simple equation for the force-displacement curve. Ting et

al. [137] and Shim et al. [72] modeled the fabric material as an orthogonal grid

of pin-jointed member elements. Shim et al. [67] used a three-element spring-

dashpot model to represent the viscoelastic behavior of the fibers and capture

its strain-rate sensitivity. The model accounts for yarn crimp. Roylance et al. [75]

modeled the fabric as an orthogonal mesh assembly of nodes interconnected

by flexible fiber members. A finite difference method was applied at the yarn

crossover points to simulate ballistic impact. Artificial buck up springs in the

transverse direction play a significant role in the ballistic limit determination. The

model lacks contact surfaces to interact with the projectile. Johnson et al. [70]

modeled the fabric with both pin-jointed members and thin membrane shells.

The computational model used a constitutive strength and fracture model that

depended on individual fiber characteristics. Bi-linear stress strain relationship is

assumed for the bar members to simulate yarn crimp. Shell elements provide

the contact surface and shear stiffness.

Shockey et al. [125, 126, 129-131] used finite solid elements to explicitly model

individual yarns and combined them in an orthogonal weave to form the fabric.

The model was found to be computationally very expensive; and became

unstable as the number of elements used to discretize the yarns crosses a

certain value. However the explicit yarn modeling allowed for observation of


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phenomena such as yarn-yarn interaction and yarn pull-out. Chou et al. [140]

reviewed recent advances in the fabrication and design of three dimensional

textile preforms. Their review detailed advances made towards realizing an

integrated approach in the design and manufacture of three dimensional

textile preforms. Rao et al. [141] experimentally and theoretically studied the

influence of twist on the mechanical properties of high performance fiber yarns

including Kevlar© 29, Kevlar© 49, Kevlar© 149, Vectran© HS, Spectra© 900,

and Technora©. A model based on composite theory was developed to

highlight the decrease in modulus as a function of degree of twist and elastic

constants of the fibers. They concluded the existence of an optimal twist angle

of around 7° where all fibers exhibit their maximum tensile strength. At higher

angles of twist, the fibers get damaged reducing their tensile strength. The study

of Gasser et al. [142] aimed at recalling the specificity of the mechanical

behavior of dry fabrics and to understand the local phenomena that influence

the macroscopic behavior. A 3-d finite element analyses was compared to

biaxial tests on several fabrics. The developed model helped understand the

main aspects that lead to the specific behavior of woven fabrics and also help

design new fabrics by varying mechanical and geometric parameters. Billon et

al. [56] considered the fabric to be a collection of pin jointed members. Both an

analytical method and direct step finite element method were used and their

results were compared to experimental results. The input to the analytical model

includes fabric material properties, a constitutive relation and a failure criterion.

The model then predicts the ballistic limit and residual velocity. Lim et al. [71]

modeled fabric armor composed of Twaron© fibers in the finite element code

DYNA3D, using membrane elements under the continuum assumption of fabric.

A standard isotropic strain-rate dependant elastic-plastic model was used to

incorporate the strain-rate dependency of the Twaron fibers studied in [67].

Since the fabric architecture such as yarn crimp and cross section was not

considered, and the material was treated as isotropic, the deformation of the

fabric was conical when in fact it should have been pyramidal. Cheeseman


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and Bogetti [143] reviewed the factors that influence ballistic performance,

specifically, the material properties of the yarn, fabric structure, projectile

geometry and velocity, far field boundary conditions, multiple plies and friction.

Ivanov and Tabiei [144] considered the fabric to be a grid of pin jointed bar

elements in their micromechanical approach. Tabiei et al.[87, 88, 144-146]

modeled the fabric as thin shells and developed their own material model for

use with the shell elements, that included effects of fiber reorientation and

locking angle, and fabric architecture such as crimp. The trellis mechanism

behavior of the flexible fabric in a free state before the packing of the yarns is

achieved by discounting the shear moduli of the yarn material. The fibers were

treated as viscoelastic members with a strain-rate based failure. The model was

implemented as a user defined subroutine in LSDYNA©. Contact forces at the

fiber cross over points were used to determine the rotational friction that

dissipated a part of the energy during reorientation.

Figure 1.10 Numerical simulation of ballistic impact of fabric in LSDYNA© byTabiei [144]

Gu [68] explicitly modeled individual yarns and combined them to form the

fabric mesh. A bimodal Weibull distribution was used to form the tensile

constitutive equations of the Twaron© yarn at high strain rates. Diehl et al. [124]


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used ABAQUS/Standard and ABAQUS/Explicit to model structural performance of

systems containing woven fabrics. They investigated the limitations and

numerical problems of classical orthotropic lamina models, and introduced an

improved generalized cargo-net approach, models for membrane-only and

general shell behaviors, and experimental measurements utilized to obtain

effective modeling constants and parameters. Termonia [147] formulates the

mechanics of wave propagation in terms of impulse-momentum balance

equations, which are solved at each fiber cross over using a finite difference

technique. The model accounts for projectile characteristics such as shape,

mass and velocity, and also fiber properties such as denier, modulus and tensile

strength. The model also considers yarn slippage through the clamps, which is

often seen in experimental work. Termonia [148] also numerically investigates

the puncture resistance of fibrous structures by driving a needle shaped

projectile through a single fabric ply at a constant velocity of 100 m/s. Termonia

et al. [149] theoretically studied the influence of the molecular weight on the

maximum tensile strength of polymer fibers.

Barauskas and Kuprys [150] developed a model that could handle the collision

between fabric yarns in woven structures, where the longitudinal elastic

properties of each yarn are presented as a system of non-volumetric springs.

Their collision and response algorithm worked in a 3-d space and was based on

tight fitting of the yarns by using oriented bounding boxes, with a separation axis

theorem to handle collision detection between the oriented bounding boxes.

They assumed the yarn cross-sectional area to be constant and elliptical in

shape, with changing lengths of axes. Their system is characterized by a

significant reduction in degrees of freedom while still preserving the volumetric

behavior of the structure, when compared to traditional models that consider

yarns as fully deformable volumetric bodies. Phoenix and Porwal [61] developed

a membrane model based on an analytical approach to study the ballistic

response and V 50 performance of multi-ply fibrous systems. They developed

solution forms for the tensile wave and curved cone wave considering constant


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projectile velocity, and obtained an approximate solution for the membrane

response using matching boundary conditions at the cone wave front. Then

projectile deceleration due to membrane reactive forces was considered to

obtain other results such as cone velocity, displacement, and strain

concentration versus time. A later study by Porwal and Phoenix [62] based on

the above membrane model, studied the system effects in ballistic impact of a

cylindrical projectile into flexible, multi-layered targets with no bonding between

the layers. Each layer was assumed to have in-plane, isotropic, and elastic

mechanical properties.

II) Constitutive modeling of yarn

The fibers used in the ballistic impact resistant fabrics are viscoelastic. During

their constitutive modeling, it is important to account for their strain-rate

sensitivity. Properties such as the elastic modulus are dynamic and vary non-

linearly with strain. If static values are used during the analysis of the ballistic

impact of fabrics, it will lead to inconsistencies between numerical and

experimental results, as was observed in [76].

i) Based on the three element spring-dashpot model

Lim et al. [71] and Ivanov et al. [144] used a three-element spring dashpot

model to represent the viscoelastic behavior of the Twaron fibers. Twaron© fibers

are very similar to Kevlar© fibers as both belong to the Aramid family and have

identical static properties.

The viscoelasticity exists as a property of all materials but it is significant at room

temperature for polymeric materials mainly. The creep and the stress relaxation

are the results of the viscoelastic behavior of materials. For impact simulations,

we do not need the long-term effects of the viscoelasticity, so that the material

behavior can be simply described by a combination of one Maxwell element


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without the dashpot and one Kelvin-Voigt element. The differential equation of

viscoelasticity can be derived from the model equilibrium in the form

(1.7)

where σ , ε , and ε are the stress, strain and strain rate respectively. Constants

K a , K b and μ b can be derived experimentally and vary according to the material.

The principal behind the response of the fibers at different strain rates is as

follows. At low strain rate, below the transition strain rate, the dashpot offers little

resistance as damping is proportional to the velocity. The dashpot and parallel

connected spring are free to move according to spring stiffness K b

. Since K a

>

K b, spring A remains rigid and spring B displaces preferentially. However at higher

strain rates, above the transition strain rate, the dashpot offers a resistance

higher than the stiffness of spring A. Now spring A moves preferentially

compared to the dashpot-spring B assembly, which remains rigid. In reality,

spring A represents the primary or intramolecular covalent bonds of the fiber

microstructure while spring B represents the secondary bonds which are the Van

der Waal forces and hydrogen bonds. The failure associated with these bonds is

discussed in later sections. The transition strain rate for Twaron© CT716 was

experimentally observed by [71] to be 410s-1. Based on their numerical

modeling, Ivanov et al. [144] observed the transition strain rate of 840 denier

Kevlar© 129 to be 100s-1.

ii) Based on Weibull distribution

Gu used a Weibull distribution of yarn strength to describe the stress-strain

response of Twaron fibers, based on [151, 152]. He used a two modal Weibull

distribution using the observation form [153] that aramids have a distinct skin-

core structure and that defects in the skin and core are the two main factors

( )a b b a b b aK K K K K σ μ σ ε μ ε + + = +


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that influence the yarn strength composed of filaments without twist. From this

Gu obtained the following constitutive relation

(1.8)

The scale (m) and shape (σ) parameters were calculated from tensile

experimental data of yarn filaments [57] with the Levenberg-Marquardt

nonlinear least square estimation method [154]. Different constitutive relations

were obtained based on the strain rate. Wang et al. [106, 107] also used a

bimodal Weibull statistical distribution model to describe the strain-rate

dependence of Kevlar© 49 aramid fiber bundles for strain rates varying from

10-4 s-1 to 103 s-1.

1.3 Scope of Work

The stages involved in this research are as follows, but not necessarily in that

order

1) Extensive review of literature

2) Preliminary design of energy absorbing seat

a. Modeling and meshing of structure in HYPERMESH©

b. Setup of simulation inputfile in LS-PREPOST©

3) Validation of design by comparing simulation data with experimental

data of vertical drop testing of energy absorbing seat

4) Conducting numerical simulations of the mine blast on the energy seat

and studying occupant survivability

a. Use of prescribed acceleration pulses simulating a mine blast

b. Extraction of dummy data and comparison with injury criteria

1 2

01 02

exp

m m

E E E ε ε σ ε σ σ

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥= − −⎜ ⎟ ⎜ ⎟

⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦


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5) Final energy absorbing seat design including additional energy absorbing

concepts

a. High density foam / airbag cushion

b. Use of GEBOD and HYBRID III dummy

6) Conducting numerical simulations of the impact of occupant lower leg

by the vehicle floor during IED explosion under an armored vehicle

a. Use of GEBOD and HYBRID III dummy

b. Variation of wall speed – 1, 5, 10, 15, 25, 35 ft/s

c. Seated Straight and Driving position

7) Development of a numerical formulation to study the response of

dynamic axial crushing of circular tubes and to predict occupant

survivability during impact events

a. Program coded in MATLAB©

b. Comparison with experimental data for validation

c. Used in two different configurations

8) Development of a material model to realistically simulate ballistic impact

of loose woven fabric with elastic crimped fibers, and integration of the

material model into LS-DYNA©

a. Utilizes a micromechanical approach

b. Subroutine coded in FORTRAN© and integrated into LS-DYNA© as

a User Defined Material Model.

c. Comparison of axial testing of the elastic fabric model with the

viscoelastic fabric model.

1.4 Outline of Thesis

Chapter 1 introduces the subject of this research and extensively reviews the

previous literature. The steps followed during the course of this research are

briefly presented.


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Chapter 2 looks at the design of the energy absorbing seat and the setup of the

numerical model. The various components of the design and the input pulses

used are studied. Initial simulation results of vertical drop testing are compared

with experimental results for validation.

Chapter 3 presents the detailed results of all the numerical simulations

conducted with the energy absorbing seat in accordance with the test matrix.

The crushing of aluminum tubes is studied. The final EA seat design is then

presented. A new mechanism using a honeycomb structure is briefly

introduced.

Chapter 4 studies the occupant lower leg impact during a mine blast. The

numerical setup is explained. A series of floor impact simulations are conducted

and numerical results are studied. A parametric study is also introduced.

Chapter 5 presents a numerical formulation using an energy balance approach

to study the dynamic axial crushing of circular tubes. The formulation is

implemented as a program and results are compared to experiments.

Chapter 6 presents a micromechanical model to study the ballistic impact of

loose woven fabrics with elastic crimped fibers. Fabric axial tests at various strain

rates are numerically simulated and results are compared to the viscoelastic

model.

Appendix I lists the source code for the dynamic axial crushing of circular tubes

and Appendix II lists the source code used to derive the incremental stress-strain

relationship for the elastic material model.


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Chapter 2

Energy Absorbing Seat

2.1 Preliminary Design

The crashworthy commuter aircraft seat used in [9] forms the basis for this

design. Figure 2.1 displays the preliminary design of the energy absorbing seat

structure.

Figure 2.1 Preliminary EA seat design

The support structure rigidly holds two cylindrical steel rails inclined at a 20° angle

to the vertical. A set of upper and lower cylindrical brackets which slide along

the rails are attached to the seat. A steel collar is rigidly attached to each rail.

The aluminum crush tubes are coaxial with the steel rails and are positioned


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between the upper bracket and collar. During vertical drop testing, the upper

brackets move downwards causing the crushing of the aluminum tubes against

the collars, which is the primary energy absorption principal used here. During a

mine blast, the entire support structure along with the attached collars move

upwards causing the crushing of the tubes against the upper brackets. For the

initial testing without a numerical dummy, the density of the seat material is

scaled to include the weight of an occupant. Later on, the occupant is

modeled using both a GEBOD dummy and a 5th percentile HYBRID III dummy.

An initial time delay of 50 ms in all simulations allows for gravity settling of the

dummy against the seat to ensure proper contact. In addition to the aluminum

crush tubes, further energy absorbing elements such as high density foam

cushions and airbag cushions are added to the design.

While modeling the structure in LSDYNA, certain simplifications are made to the

model. This facilitates the replacement of detailed structures and designs with

equivalent simplistic representations. The two inclined steel rails are attached to

the support structure by creating a ‘Node Set’ consisting of nodes belonging to

the rail and structure at the joint location and then using this node set in the

*CONSTRAINED_NODAL_RIGID_BODY keyword definition which ensures a rigid

joint between the rail and structure. The seat structure is modeled using shell

elements and a rigid material model. The reason for using rigid material defined

by the *MAT_RIGID keyword is that they are computationally efficient when

representing parts that do not deform or do not need to be monitored during

the study. Rigid elements are bypassed during the element processing in


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LSDYNA. The set of four brackets are also attached to the seat by creating a

node set and then using this node set in a nodal rigid body definition. Figure 2.2

displays the linear dimensions of the rail, brackets, collar and crush tube.

Figure 2.2 Specifications of the rail substructure

Contact definitions are created in LSDYNA to specify contact between the rail,

crush tube, brackets, and collar. *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE

and *CONTACT_AUTOMATIC_GENERAL are used to this effect. By using the

AUTOMATIC specification, the orientation of the shell segment normals is

automatic. The SOFT=2 option can be used to activate a different contact

formulation and causes the contact stiffness to be calculated considering the

global time step and nodal masses. This approach is generally more effective

when creating contact definitions between components of different mesh

densities and material stiffness.

The crush tube has the finest mesh as it deforms the most during the simulation

thus controlling the time step, and constitutes the energy absorbing member. If


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Stress Vs. Strain for *Mat 24 - Aluminum

4400045000

46000

47000

48000

49000

50000

51000

52000

0 0.1 0.2 0.3 0.4 0.5 0.6

Strain (%)

S t r e s s ( M P a )

*Mat 24 - Aluminum

the mesh is too fine, the time step falls to very small values causing the

simulation to run indefinitely. However LSDYNA Material Model 24 which is

*MAT_PIECEWISE_LINEAR_PLASTICITY allows the user to specify a minimum time

step for the material and when the simulation time step falls below this defined

value, the controlling element with this material model is deleted. Thus the

overall minimum time step of the problem can be controlled without using Mass

Scaling which adds mass to the component to prevent the time step from

falling below a certain value. Also, this material model allows an arbitrary stress

versus strain curve as well as arbitrary strain rate dependency to be defined,

which is illustrated by the curve shown in Figure 2.3 below. The yield stress needs

be specified for this model and is given a value of 145 MPa corresponding to

Aluminum 3003.

Figure 2.3 Stress Vs. Strain curve for the aluminum crush tubes

2.2 Dynamic Axial Crushing of the Aluminum Tubes

Axial crushing of cylindrical tubes became a very popular choice of impact

energy absorber because of its energy absorption capacity. It provides a

reasonably constant operating force, has high energy absorption capacity and

stroke length per unit mass. Further a tube subjected to axial crushing can


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ensure that all of its material participates in the absorption of energy by plastic

work. [33, 35]. Classification of axial crushing of cylindrical tubes under quasi

static loading includes sequential concertina mode, sequential diamond

mode, Euler mode, concertina and diamond mode, simultaneous concertina

mode, simultaneous diamond mode, and tilting of tube axis mode. [155] The

D/t ratio of the cylindrical tubes used in the design determines the mode in

which the tubes will crush. Experimental observations of Alghamdi [48] showed

that thick cylinders (small D/t ratio, D/t


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According to Alexander [31], the mean crushing load of a cylindrical tube is

given by the following expression:

(2.1)

where

Pav = Mean crushing load

Y = Yield strength

t = Tube thickness

D = mean tube diameter

It provides a good prediction for D/t


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(acceleration pulse) of the EA seat during impact. The maximum compressive

lumbar load that can be sustained without injury is 6672 N. This must be kept in

careful consideration while selecting the tube material and geometric

properties.

100 MPa 145 MPa 220 MPa 300 MPa

Static crushing load (N) 3316.6 4809.1 7296.5 9949.8

Dynamic crushing load (N) 4151.1 6019.1 9132.5 12453

Number of folds possible 52 52 52 52

Total energy absorbed / fold (J) 24.54 35.58 53.98 73.61

Effective crushing distance (mm) 6.91 6.91 6.91 6.91

TABLE 2.2 Axial crushing parameters of the cylindrical aluminum tubes used

Figure 2.4 displays the static and dynamic axial crushing loads of cylindrical

aluminum tubes with a D/t ratio of 30.7 as a function of yield strength.

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300 350

Yield Stre ngth (MPa)

L o a d ( N )

Static Crushing Load

Dynamic Crushing Load

Figure 2.4 Static and dynamic axial crushing load of cylindrical aluminum tubes

with a D/t ratio of 30.7


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2.2.1 Techniques to reduce the initial crushing load of a tube

It has been observed that while the crushing of the tubes occurs under a

reasonably constant operating force, there always exists an initial peak thatcorresponds to the formation of the first plastic hinge. This peak usually is about

1.5 to 2 times larger than the average crushing load of the tube and will be

dangerous to the occupant’s survivability if not attenuated.

a) Introduction of annular grooves in the crush tube

Research conducted by Daneshi et al. [34] shows that the introduction of

annular grooves in the crush tube will force plastic deformation to occur at

regular intervals along the tube, thereby causing uniform energy absorption and

a uniform deceleration pulse thus resulting in a controllable energy absorption

element, without any spike in the load-deformation plot that is usually

associated with the initial crushing force required for plastic buckling. Thus far,

only quasi static axial crushing tests have been performed, but have yielded

promising results.

Figure 2.5 Annular grooves on a circular crush tube


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b) Weakening the finite element mesh of the crush tube

Simulations showed that by removing periodic shell elements along the

periphery of the crush tube, local buckling (and plastic deformation) can be

induced at a desired location, which will result in a lower initial deceleration

pulse. The energy absorption rate remains unaffected. By reducing the initial

deceleration pulse, we can make sure that at no point in the simulation, the

deceleration reaches the critical value causing injury. In Figure 2.6, red

elements correspond to the rail and blue elements correspond to the crush

tube.

Figure 2.6 Weakening the FE mesh of the crush tube

c) Heat treatment and wasting of the crush tube

Research conducted showed that by first subjecting the crush tube to an

Annealing cycle and then Wasting it by introducing a wrinkle around the tube’s

perimeter via a pipe cutting tool could reduce the crush initiation load and

deceleration pulse by as much as 50% as well as the initial peak in the load-displacement curve. Figure 2.7 displays the heat treatment curve during the

annealing of the aluminum crush tube.


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Figure 2.7 Heat treatment curve used during the annealing process [9]

As can be observed from the Figure 2.8, there is a great difference in both theCrush Initiation Load as well as the Mean Sustainable Crushing Load when the

tube is subjected to different combinations of Annealing and Wasting. The tube

that was annealed and then wasted was found to be most suitable for the

simulations and had the closest desired crush initiation load [9]. When a wrinkle is

created on the tube’s periphery, strain hardening occurs due to plastic

deformation. Annealing helps remove this and restores the softness back to the

material

Figure 2.8 Static performances of plain and wasted tubes [9]


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2.3 Additional energy absorbing elements

In addition to the aluminum crush tubes, additional energy absorbing elements

are added to the design to help further attenuate

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