nilakantan gaurav
TRANSCRIPT
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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
List of Figures… continued
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
List of Figures… continued
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
List of Figures… continued
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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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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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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(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