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NAVAL
POSTGRADUATE SC HO O L
M O N T E R E Y,
CALIFORNIA
THESIS
B IO M E C H A N IC A L
M O D E L
O F
TH E H U M A N T H O R A X FO R
IMPACT ANALYSIS
by
Timothy
A. Hughes
September 1999
Thesis Advisor:
Young
W .
Kwon
Approved for public
release;
distribution is unlimited.
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QUALITY
IMSPEc^.
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Master's Thesis
4.
TITLE
AN D
SUBTITLE:
BIOMECHANICAL M ODEL
OF THE H U M A N THORAX FOR IMPACT
ANALYSIS
6.
AUTHOR(S)
Hughes,
Timothy
A.
LT/USN
5.
UNDING NUMBERS
7. PERFORMING ORGANIZATION NAME(S) AN D ADDRESS(ES)
Naval Postgraduate School
Monterey
CA
93943-5000
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REPORT
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11 .
SUPPLEMENTARY
NOTES
The views
expressed
here
are
those
of the
authors and do
not
reflect the official policy
or
position of
the
Department
of
Defense
or the
U.S.
Government.
12a.
DISTRIBUTION/AVAILABILITY STATEMENT
Approved for
public
release;
distribution is unlimited.
12b.
DISTRIBUTION CODE
13. ABSTRACT maximum 200
words)
Th e
Biomechanical
response
of th e
human
thorax
was studied using th e
finite
element
method
by
the
classic
stiffness
method.
Th e
main
focus
was
on
validation
of
the
model.
he
model
was
subjected to
static
an d dynamic
forces
applied
at the sternum. A
plate
was adhered
to
th e
sternum area
an d
th e
model
was subjected to a dynamic
load to
simulate an
impact
load
similar to a projectile
or
bullet impact. he
projectile
characterized a 7.62 NATO M 80 ball
round.
he
bulletproof
vest
was
similar in material properties
to
boron carbon
composite. he
results
included
th e static
analysis an d
transient
analysis
an d
the
subsequent
displacement
du e
to the
external
loading.
tress
was calculated
from
th e
displacements.
he
results
were compared to
earlier research an d
live fire
tests
conducted
on
cadavers.
4 SUBJECT
TERMS
Body
Armor
Biomechanics Thorax
1 7 .
ECURITY
CLASSIFICATION
OF
REPORT
Unclassified
1 8 . ECURITY CLASSIFICATION
OF THISPAGE
Unclassified
1 9 .
ECURITY
CLASSIFICATION
OF
ABSTRACT
Unclassified
15 .
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OF
PAGES
62
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ABSTRACT
UL
NSN 7540-01-280-5500
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Prescribed by
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239-18 298-102
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Approved
for
public release;
distribution is
unlimited.
BIOMECHANICAL
MODEL
OF
THE
HUMAN
THORAX
FOR
IMPACT
ANALYSIS
Timothy A. Hughes
Lieutenant, United States Navy
Bachelor of
Engineering,
University of
Mississippi, 1991
Submitted
in partial fulfillment
of
the
Requirements
for the
degree
of
MASTER OF
SCIENCE IN
MECHANICAL
ENGINEERING
from
the
NAVAL
POSTGRADUATE SCHOOL
September
1999
Author:
Approved
by:
Timothy
A. Hughes
{/ oung
W. Kwon
_
Chairman
Department of Mechanical Engineering
in
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IV
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ABSTRACT
The
Biomechanical
response
of
the
human
thorax
was
studied
using
the
finite
element method
by
the classic stiffness
method. The main focus
was in validation
of
the
model.
The
model
was
subjected
to
static
and
dynamic
forces
applied
at
the
sternum.
A
plate
was
adhered
to
the
sternum
area
and the model
was
subjected
to
a dynamic
load
to
simulate an
impact
load similar
to
a
projectile or bullet impact.
Th e projectile
characterized
a
7.62
NATO M80 ball round.
The bulletproof vest was similar
in
material
properties
to
boron
carbon composite.
The
results
included
the
static
analysis
and
transient
analysis
and
the subsequent
displacement
due
to the external loading. tress
was
calculated
from the displacements.
The results were compared to earlier
research
and
live
fire tests
conducted
on
cadavers.
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V I
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TABLE
OF CONTENTS
I.
INTRODUCTION
II.
BACKGROUND
A.
BIOMECHANICAL
BEHAVIOR
OF
BONE
B.
BIOMECHANICAL BEHAVIOR
OF
CARTILAGE
C.
ANATOMY
OF
TH E
HUMAN
THORAX
3
1 . Spine 4
2. Ribs 6
3.
Sternum 7
D.
LITERATURE
SURVEY .
8
III.
FINITE
ELEMENT
MODEL
1
A.
HUMAN
THORACIC
BODY
MODEL 1
B.
PERSONNEL PROTECTIVE
VEST
2
C.
INTERFACE
ELEMENTS 6
D. PROJECTILE MODEL 6
E.
MODEL
SOLUTION
8
VI.
INJURY
ANALYSIS
9
V.
RESULTS
AND
DISCUSSION 3
A. STATIC
ANALYSIS 3
B.
TRANSIENT
ANALYSIS
2
VI.
CONCLUSIONS AND RECOMMENDATIONS 5
A.
CONCLUSIONS
5
B.
RECOMMENDATIONS 6
LIST OF
REFERENCES 9
INITIAL
DISTRIBUTION
LIST 1
Vll
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ACKNOWLEDGMENTS
I would
like
to express my great appreciation
to
Professor Young
W.
Kwon for
his
support
throughout this
research.
His
dedicated
guidance
has
significantly
enhanced
my
education
at
the
Naval
Postgraduate
School.
I would
also
wish
to
thank
Dave
Marco
for invaluable time
and guidance
in
overcoming
the
many
hurdles
I encountered in
C
programming skills.
There
is no amount
of
thanks or
acknowledgement
I could
offer my
wife, Mariel,
for he r
love
and
support
during
this entire endeavor.
XX
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I I BACKGROUND
A BIOMECHANICAL BEHAVIOR
OF
BONE
This chapter
describes
the
physical makeup
of human
bone an d cartilage
as well
as the mechanical properties associated
with
compact
and
cortical
bone.
he bone nd
cartilage
simulated
in
the finite
element
model geometrically
and
physically
represent the
spine an d rib
cage. hese
biomechanical
materials
make
up the
vast majority of th e finite
element model that represents the musculoskeletal
structure of the thoracic
lumbar spine
including the
rib
cage.
In the study of engineering
materials
such
as steel an d
alloys
it is imperative to
understand he mechanical roperties of the material se d n tructure.
echanical
properties include but are not limited
to ultimate strength, yield
point, Young's Modulus
(modulus
f
lasticity)
nd
oisson's
atio. ll f hich
re
mportant
esign
considerations
fo r
the
engineer.
he mechanical
behavior of a structure
or member varies
based
n
geometry,
xternal
orces,
oading
rate, nd
frequency
of
application
of
load.
The
engineer must interpret
the
perceived
environment
to
enable
him to
select
the correct
material an d optimize the mechanical structure.
The
iomechanical
r
issue
ngineer
oes
ot
av e
he
uxury
f
material
selection n th e modeling
of
bone issue.
he
iomechanical material roperties nd
behavior
are
just as
important
in
understanding
living
tissue, mechanisms
of
failure, and
modeling
of human tissue.
he engineer must couple
the
knowledge
of
the
human tissue
with he perceived nvironment. he ngineer
an
hen elect
he
most ppropriate
material
for
the
(PPE)
an d
optimize
the
structure.
When examined under the microscope bone
is considered
a composite as shown
b y
Hamm's
1969
adaptation
of
the
bone
as
seen
in
Figure
1.
he
basic
unit
of
the
bone
is
called
the Haversian
system or
osteon.
ac h osteon
ha s a vein in the
center.
he blood
vessels are connected
by
transverse channels
called Volkmann's canals.
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Fibrou* layer of p«wo»*«*-n.
Osteogeuic layer of pcrio*teu.m.
Ou.ter
iT-ciiTTtfer'ervtia.l
lamellae
Lacunae
containins otteocyte*
Can.a.Ucu.lv
lerstitia-l
lamellae
ferervtial
Blood,
vessel
and
etvAoiteai
lining
of
—
tvavePSian canal
Blood
vessel»
Into
marrow
Eudoateum.
Figure
1.
Huma n
Bone
[Ref.
1]
Biomechanically one may e onsidered wo-phase bi-phasic) omposite
material. inerals are on e
phase and collagen
an d ground substance
make
up
the
second
phase, which is similar to fiberglass.
one ha s
similar characteristics to other
composites
in
that strong brittle fibers re mbedded
in
weaker
more uctile material or matrix.
The most mportant roperties of bone
re
ts trength nd tiffness. oad versus
deformation
urves
imilar
o
tress
s.
train
urves
llow
or
he
issue property
determination
uc h
s ltimate ensile
tress,
ield
oint,
nd
train
nergy.
his
technique s imilar to he trength of materials pproach.
on e s considered a non-
homogeneous
anisotropic
composite
material.
here
are
tw o
types
of
bones,
cortical
and
cancelleous or
rabecular
one.
Material nd he material properties
of
bone iffer
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depending
on
the
loading
orientation.
he mechanical properties
of
bone
differ in the
two
ypes
f
one. ortical
one
s
tiffer
han
ancelleous
one.
ortex
one
withstands reater stress but
less
train than
cancelleous
bone when
loaded
to ailure.
Cancelleous
bone
in vitro
(out of body) does
not
fracture
until
strain exceeds
75 %
but
cortical bone fractures at strain levels
as
low
as
2
%
Ref.
4] .
The
cancelleous porous
bone structure
has a
greater
capacity for energy storage.
A
qualitative
review
ofbone
and
other
engineering
material
are
shown
in
Figure
2.
The
stress
strain
curve
shows
bone
exhibits
a
non-linear
behavior
and
both
ductile
and
brittle behavior.
Since
the
structure of bone is different in the
longitudinal
and transverse direction it
is
expected
to exhibit different
material
properties
depending
on the
loading
direction.
STRAIN
Figure
2.
Stress
Strain
Curve
for
Bone
Ref.
2]
The
metal
and glass
have
a
distinct
linear
elastic
region where bone
exhibits
some
plastic
behavior
even in the
typical
metals
elastic
regions.
on e
also deforms less
than
metals
fter
ielding.
icroscopic nvestigation eveals
he
ifference n
biomechanical
materials
and
metals
that precedes failure in the
two
materials.
onsider a
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metal pecimen
in tension,
yielding
is
produced by plastic flow and formation
of
slip
planes
in certain crystallographic
directions
that can
be
predicted
based
on
the metal
such
as
BCC, FCC, and
HCP.
ielding
is a
result
of
dislocations
of
molecules
in
the
lattice
structure. one pecimens,
ested
n
tension,
ields
s
result
of
de-bonding
of
the
osteons
at
cement
line
[Ref.
2] .
echanical
properties,
geometry,
loading modes,
load
rate,
nd
requency
of
applied
oad
ffect
the ehavior
of
bone
ubjected to xternal
forces. one
in vivo (in the body)
is
subjected to
all types
of loading
including
tension
compression,
bending, shear,
and torsion. This
study
investigates
the
reaction of
bone
to
applied oads. t
s
herefore mportant to stablish n nderstanding
of
the racture
modes
that
may be seen.
Tension oading n
one
roduces
aximum ensile tress
n
he lane
perpendicular
to
the
applied
load.
t
the
microscopic
level,
the
failure
mechanism
for
bone
tissue
loaded
in
tension
is
a result of
de-bonding
at
the cement
line
and
pulling
out
of
the
osteons
similar to fiber
pullout
as seen in Figure 3
[Ref.
2] .
V
m' *tfii i
Figure 3 . Human
Bone
Loaded
to Failure
[Ref.
2]
Generally
tension
fractures are seen
in
cancelleous bone.
ompressive
loading
results in
bone structure shortening
and
widening.
t
the
microscopic level the fracture
mechanism
or
one
oaded n ompression
s
oblique
cracking
of
he
steons.
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Compressive ractures
re
typically
een
n
the
ertebrae
n
mature one.
n joints
compressive
failure
is usually a result
of
abnormally
strong
contraction
of
the muscles
surrounding he
joint
uch
s een n atients ndergoing lectroconvulsive shock
therapy.
hear is
load applied parallel to the
surface
with
deformation
being
internal
angular shift
of
right
angles.
hese
right angles
become obtuse
or acute due
to
the shear
loading.
hear fractures are
typically seen
in
cancelleous bone
[Ref.
2] .
Bending
is
typically three point
bending
or
four
point
bending.
ince
bone
s
asymmetric,
tensile
and
compressive
stresses
may not be
equal.
he three
point
bending
phenomenon
is seen in
boot
top
fractures
where
four point
bending
can exist between the
hip and knee.
Bone
loaded in
torsion
results in shear stresses
distributed
over
the
entire bone.
The
magnitude
f
the tress ncreases
as
the istance rom
the
neutral xis ncreases.
Maximum shear
stresses
act on a plane
parallel
to the neutral axis.
aximum
tensile and
compressive
stresses act
on
planes
diagonal
to
the neutral
axis.
n
Figure
4
a
torsional
fracture of
a
canine femur
is epicted
where
the hort crack at the initiation ite
that
extends parallel to the
neutral axis represents shear failure. he crack extends
at
an angle
of 30
degrees to the neutral
axis and this
is the plane of
maximum
tensile
stress.
Figure
4 . Torsional
Fracture of
Canine
Femur
[Ref.
2]
Bone
unlike metals
exhibit
both
brittle
and ductile
behavior depending on
age.
Mature
one
s
rittle
n comparison
to rowing one. imilar relation
of
ductile
versus brittle
behavior
can
be
seen
as
a
result
of
loading rate. An
interesting
result of
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several studies
shows
that
bone properties
and
behavior
such
as strength and stiffness
is
greatest
if the
orientation
is
the
same as
the
loading orientation
and
direction
exhibited in
the
body
[Ref. ].
uman
tissue,
particularly
bone, has perfected
the design
optimization
theories uch s maximum tress nd rajectory heory n hat, one material rows
preferentially with maximum material in
line with maximum
force [Ref.
].
B. BIOMECHANICAL
BEHAVIOR
OF
CARTILAGE
COSTACARTILAGE OF
THE
RIB
CAGE
The cartilage that attaches the bony ribs to
the
sternum is in the shape similar to
the
bony ribs an d is called hyaline cartilage. artilage in the rib cage is responsible fo r
the
everyday ease at
which
the thorax
moves
to support respiratory functions. yaline
cartilage is
similar in both costacartilage an d articular cartilage.
ARTICULAR CARTILAGE
The
ib
airs rticulate ith he ertabrae ia he
ostasternal
oint
nd
communicate with
the sternum
via
cartilage.
he costacartilage is articular cartilage
and
forms
a joint referred to
as
costal
articular facet. his
joint
allows
a place fo r the head of
the rib
to
articulate
with
the
vertebrae
as
depicted
in
Figure
5.
The
joints that
make
up
the
costavertabral
joints
ystem
re
ostal
acet
of
transverse
rocess,
he
nferior
ostal
articular acet, uperior ostal
rticular
acet,
nd radiate igament
lso
epicted n
Figure 5.
The
human body
has
three
types of joints.
ibrous
joints are composed
of fibers
as
the name
implies.
artilaginous joints are joints
where
bones
are
united
by
cartilage
allowing nly light lexible movement. he ostovertebral joints re hese ype of
joints. he articulating bone ends are covered
by a thin
(l-5mm) dense white connective
tissue
alled
hyaline
rticular
cartilage
a
type
of
elastic
artilage
that
grossly
appears
smooth an d semitransparent
with a
blueish-white tint.
he articular cartilage is typically
void
of
blood essels, ymph hannels,
nd
erves.
The rimary unction of
articular
cartilage is to distribute the load over a
wide
area and to allow
relative movement of
the
opposing joint surfaces with minimal friction an d wear. The
iber
bundles
orm a
root
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system
that
anchors the cartilage to
the
underlying
bone.
hese fiber bundles
are
made
up
of
collagen.
he
most mportant
mechanical roperty
f
collagen s
heir
tensile
stiffness and strength. he size
of
a single
collagen fiber
prohibits
individual
testing
to
determine
trength
ut
his
may e nferred y
esting
materials with arge ollagen
content such
as
tendons Ref. ]. endons
have tensile tiffness
of
10
3
MPa
and
a
tensile
strength
of 50 M Pa [Ref.
].
lthough
strong in
tension
collagen
is
very
weak
or
irresistant to compression because
of
the high slenderness ratio, which allows for ease
of
buckling
nder
ompressive
oad.
rticular
artilage
s
nistropic
nd
s uch
ts
material
properties
differ with loading
direction.
he
exact
reason
for
the anisotropic
behavior
is unknown.
Proteoglycans
(PG's)
are
large
protein-polysaccharide
molecules
that
exist
either
as
monomers,
simple
molecular
units, or
aggregates.
G
monomers
are
made
p
of
a
core
pproximately
00nm
ong
o
which
about
50
lycosaminglycan
(GAG)
hains
re
ttached.
hese
monomers
make
p everal ifferent types
of
PG
aggregates
epending n
the
onding.
he
PG
ggregates re
ot istributed venly
through he
artilage ut
re
nhomogeneously ispersed
hroughout
he rticular
cartilage.
t is generally
accepted
that the PG aggregation promotes
immobilization
of
the
PG's)
within the
ollagen
etwork dding tructural
igidity
o he xtracellular
matrix.
ater
is
the most abundant
component of
the articular cartilage nd
s
most
concentrated
near
the
surface.
ater
is
found
to
decrease
almost
linearly
with
increasing
depth
nto he
matrix. ater
ontains many
ree
mobile ations
hat
nfluence
he
mechanical behavior of the
cartilage. he
fluid
provides a
transport
medium that permits
diffusion
f
ases,
utrients,
nd
aste
roducts
etween
he hondrocytes
nd
surrounding ynovial
luid.
ost
of
the water n he artilage
s
xtracellular nd
occupies
the intermolecular space in the
collagen
fiber networks. he
water
is free
to
move
when
oad r ressure
radient
s pplied
o
he
issue.
his
movement
s
essential
in
the lubrication
of
the
joint
and
the
mechanical
behavior of
diarthrodial joints.
Articular
cartilage
has
two
distinct
phases, a fluid
phase
which
consists of
ater
with
inorganic
alts
issolved
n
olution nd olid
hase
which
onsists
of
the
rganic
matrix. rticular
cartilage
is considered a
fluid filled,
porous-permeable
medium with
both
solid
and
fluid phases and
each
distinct
constituent of
both
phases
playing
a
role in
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the
functional behavior
of
the
cartilage
Ref.
2].
A human
joint is
exposed
to
varying
degrees
of force
at the surface
from
near
zero
to
several
times
body weight.
Anterior
longitudinal
l igament
Inferior costal
ürlicular
facet
for
head of
rib
Intcrarticular
ligament
Superior costal
articular
facet
for
head
of
rib
Kadiatc
ligament
Costal
facet
of
transverse
process
for
tubercle
of
rib
lateral
costotransverse ligament
Intertransverse
ligament
Superior costotransverse ligament
Superior
coslovertebral
articular
facet
of
rib
head
Interarticular
ligament
Radiate
ligament
Synovial
cavities
Left lateral
view
Superior
costotransverse
l igament (cuf) £?
Superior
costal
articular
facet
for
head
of
rib
Transverse
process
cuf off)
Radiate
l igament
Costotransverse ligament
Lateral
costotransverse ligament
Superior costotransverse ligament
Costotransverse
ligament
Lateral
costotransverse
l igament
Transverse
section:
super ior view
Intertransverse ligament
Right
postero la tera l
v iew
ä
Figure
5.
Costovertebral
Joints
[Ref.
3]
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Under physiologic loading
the
articular
cartilage
is a
highly stressed material.
If
material s
ubjected
o onstant
time
ndependent)
oad
r onstant
deformation
nd
he
esponse
aries
with hese
oads,
he
material
s
aid
o
e
viscoelastic solid. he tw o fundamental responses of
a
viscoelastic solid
are creep an d
stress
relaxation.
reep
occurs du e to
constant
load, where
th e response of
the
material
is
a
rapid
initial
deformation
followed
by
a
slow
progressively
increasing
deformation until
equilibrium is reached. tress relaxation occurs when the
viscoelastic solid is subjected
to
constant
deformation.
he
response is a high
initial
stress
followed
b y
a
slow
(time
dependent) decreasing stress required to maintain th e deformation.
Creep an d
stress relaxation are
caused
by
internal
friction due to motion
of
long
polymer
chains
within
the
stressed
material
as
in
tendons
an d ligaments. he
long-term
viscoelastic
behavior
of
bone
is
du e
to
slip
of
the
lamellae
within
the
osteons
along
with
the flow of interstitial fluids. he compressive viscoelastic behavior of articular cartilage
is
du e
to the
flow of
interstitial
fluid. n
shear
it is primarily
due to th e
motion of the long
polymer
chains
of
collagen
and
PG's.
hese
tw o
components of
viscoelastic behavior in
articular
cartilage
are known
as
biphasic viscoelastic
behavior
and
flow
independent or
intrinsic viscoelastic
behavior.
Biphasic
creep
in articular cartilage
is
caused by exudation of
the
interstitial
fluid.
Exudation
is
at
first
very
rapid
an d
diminishes
gradually
until
flow
ceases.
uring
creep
the
applied
load is
balanced by
th e
compressive
stresses developed
b y
the collagen-PG
matrix nd th e
rag eveloped y the
low of the luid
uring
xudation. n umans
articular
artilage
f m
hick, xperiencing reep eaches
quilibrium
n
approximately 4-16 hrs. artilage of less than
1mm such as seen in rabbits takes about
1
r. o each quilibrium.
enerally
he im e
o
each quilibrium aries
with
he
inverse
of
th e quare
of
the hickness Ref.
].
t
s onsidered elevant o ompare
human
cartilage
to
animals
such as dogs an d
rabbits
because
experimentation has
shown
very similar
results
in
material
properties.
Stress
elaxation
s
esult
of
an
xternally
pplied ompressive
oad. The
compressive load results in a stress rise followed b y s stress relaxation.
tress rise in th e
compressive
phase
is du e
to
exudation
of
the
fluid an d
compaction
of
the solid
material
at
the
surface.
tress relaxation is du e
to
relief
or
rebound of
the
compaction
at the
surface.
1 1
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Under
physiological
loading
conditions excessive
stress levels
are
hard to
maintain since
stress
relaxation quickly attenuates
the stress
[Ref.
1] .
Both tress relaxation and reep
an
be used to etermine permeability
of
the
tissue.
ermeability
is a measure
of
the
ease
at
which a
fluid can flow
through
a
porous
permeable
material.
ermeability
is
inversely proportional
to fluid
drag
exerted by the
flowing fluid.
ompaction
of
the olid matrix reduces porosity and the
verage
hole
diameter
within
the
solid matrix
and
increases frictional
resistance.
he non-linearity
of
permeable
material
suggests
that that
tissue
has a mechanical feedback.
Under high
loads
the increased
frictional
drag against the interstitial fluid
flow
allows the tissue to appear
suffer and thus more
difficult to
allow exudation
of
the
fluid
Ref.
].
Th e
behavior
of
cartilage
as
viscoelastic
solids
allows
the cartilage
to
handle
much larger
loads and
strain
rates than predicted by a pure
solid mechanics
study.
12
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1.
Spine
The pine onsists
of
24 ertebrae, 3
iscs
nd
urrounding igaments. t s
divided ertically nto
hree
major
ections;
ervical,
horacic,
nd umbar
pines s
shown
in
Figure
7.
Th e
upper
seven
vertebrae
are
called
the
cervical
pine,
known
as
neck,
and
give connection between
the
head
and
the
trunk. In
order
to describe
the
unique
location
of
each vertebra, a
naming convention is
used.
The initial
of
each spinal name is
combined
with a number. That is,
the
uppermost cervical
vertebra is
called
'Cl'
and
C2
is
located
right
below
Cl.
Figure
8 shows
how
two
vertebrae are
connected
to each
other.
Each vertebra
varies
in dimensions
depending
on age,
sex, and ethnic
group.
nother
consideration
is
iven to igaments. Ligaments re
uniaxial tructures urrounding the
vertebrae
and they
act
like rubber bands. hey then give resistance under tension but
buckle
when
subjected
to
compression. The main
function
of ligaments
is
to
allow
proper
spinal motion,
without
amaging
he
pinal
ord
nd
tructure, nd o upport
he
vertebrae
and
trunk
with muscle.
The
disc
is the
inter-vertebral material with an anisotropic physical structure
and
viscoelastic
property. It carries the
compressive
loading to the trunk along with
the
facet
joints
under
the
various
forces
and moments
Ref.
4] .
igure
9 shows
a disc
from
the
spinal
olumn.
he
pinal
ord s
linically n mportant
omponent
n
he
pinal
column.
his
pinal
ord
s
nclosed
ithin he
ertebral
anal.
n
echanical
perspective, however, it
is
not
important
and
hence
excluded
in
the spinal
structure
of
this
research.
14
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•
the seven cervical
vertebrae
are
C^Lgv
y Cl
C2
relatively
small,
and
have holes
BÖ£
C3
ervical
(foramna)
in their transverse
t§£\;
C4
processes
B̂ r
C5
C6
C7
Tl
^gj&L
T2
T3
•
the twelve
thoracic
vertebrae jgC&^
T4
articulate with the twelve ^^St r**-
pa i
rs
of
ribs
Zw5r~
I
T7
i
^
3 >
horacic
TO^
11
T1 0
•
the
five
lumbar vertebrae are raäS?
T-)
massive, weight-bearing struc- -CE'W^T
*— A Til
cures
with limted mobility
jjßü^-A
T12
< ^ P
e^fSlfF
•
the sacrum consists offive ^^S
^***
fused,
modified vertebrae,
C3Qf
,
?y7Sj
and arriculares
with the
Sr̂
l
—
lumbar
two iliumbones to com- vSy|*Jj^>
plete
me
pelvic
ring
Ĉ OL**
5
^ /
•
the coccyx or tail- Ŷ Ŝ *̂ /7
bone is a
vestigial
/S'̂ ^̂ Ŝ*j
V
L5
structure
consisting
fĵ &ae.
-V^
or
three
or
tour l|̂ '*»
v
f̂er
fused vertebral U
^^fet-
-̂
f
remnants V̂̂
—
coccyx
Figure 7.
Spinal
Column
[Ref. 5]
Figure 8.
Connectivity
of
Two Vertebrae
[Ref.
6]
1 5
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x -
AP
View
Figure 11.
Structure of
the Sternum[Ref. 10]
D. LITERATURE SURVEY
Reviewing
literature, om e similar
studies
have
been
done
in the
rea
of finite
element
analysis
of
the
human
thorax.
Most
of
the
preceding
research
has been
restricted
to
the tatic
analysis
nd
attempt
at
validation
of
the
inite
lement
model.
Literature
involving
the
dynamic analysis of thoracic
impact is
not
readily
available in
the literature.
This
study
requires
background
information
on the
biomechanics
of
the
human
body,
the
characteristics
of
the
human
injury,
and
modeling
technique,
such as the finite element
method. The
literature survey was conducted
in this
regard.
18
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model of the
human
body
which
extended
the
model King
Ref. 12]
eveloped of
the
human
head
and
cervical
spine.
20
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III.
FINITE ELEMENT
MODEL
A. H U M A N THORACIC BODY
MODEL
The
objective
of
this research
was
to evaluate th e
biomechanical response of the
human thorax
du e to
impact
loading.
Therefore, the
FEM
modeling
of
the
human thorax
was
critical
for this in this
research. However,
it
was
very difficult to model the details
of
the
human body because of
its complex geometry, material property,
an d
wide variation
of
the
geometry and material properties from person to person an d
ag e
distribution. he
finite element
model
developed fo r
this study
is
depicted in
Figure
12 .
Figure
12 .
FE M
Model
of
a
Hu man Skeletal
Thorax
Linear
elastic
behavior is
assumed
fo r all materials. aterial properties
in
earlier
studies
an d
finite
element
approaches
to
the
biomechanical
behavior
of
the
human
thorax
relied heavily
on
data obtained b y
crude
measurement techniques an d approximations.
n
order
to develop a
more
a
refined
an d
more accurate finite model element
the
requirement
to btain
more
ccurate
iomechanical roperties
s
eeded.
ogananda
Ref.
3]
determined
the
biomechanical properties
of
the
seventh and
eighth ribs
by
classical
solid
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deformation
of
the modeled thorax. late bending and shear deformation
are
a
result
of
the indlin/Reissner late
heory
hich ncludes he
effect
f
ransverse
shear
deformation.
Unlike lassical
Kirchoff
plate heory, plane ormal o he midplane
before deformation does not remain normal
to
the mid-plane after
deformation
[Ref.
14].
Figure
1 3 is a free
body diagram
of
the
plate element.
Figure
13.
Free Body Diagram
of
a Plate Element [Ref. 14]
Th e
basic equations for
classical plate theory
are
dM,
dM
y
a=o
dx
dy
dM„
8M
V
+
-ß=0
dx
dy
*
y
dQ*
d
Qy
dx
dy
23
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including the
transverse
shear forces. he
element
stiffness matrix
for
shear
deformable
plate bending
is expressed as
\K-]-£l\B
t
f\p
i
lB
i
]
n+nl
t
\
B.f[D,lB.}n
in
order to
derive
the
element stiffness matrix [K
e
] hown above we
must
express
the
strains in terms of nodal variables. The in-plane
displacements
are given
by
u =
-z@
x
(
x,y)
v = -z®
y
(x,y)
the
transverse displacement is
For the shear deformable
plate
w
=
w x,y).
_ dw
0 =
OX
dw
where s
he
ngle
aused
y
he
ransverse hear
eformation. The
ransverse
deflection or displacement,
w,
and
slope
,0,
are
independent, therefore
shape functions
are
used
to
interpolate
them.
Th e transverse and slope are interpolated as
1=1
7=1
i=i
where
s
he
umber
of
odes nd
he
hape unctions
sed o nterpolate he
displacements
are
the
same
as those used
to
interpolate
the
slope.
ending
and
shear
strains are computed from
the
displacements as follows
{
£
,}
=
-z[Bjrf,}
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where,
M
dH
x
dx
0
0
8H\
dy
M L M L o
dy
dy
0
dH
>
dx
0
0
0
dH
2
dy
dH
2
dH
2
dy
dy
0
0
0
dH
3
dx
0
dH,
0 0
dH
3
dy
dH,
dy dy
dH
4
0
dx
o
dH
A
dy
dH
4
dH
4
dy
dy
is
matrix
representing
the
interpolation of
the
bending
strains
and
W=
0
-H,
»•
-H,
0
- ,
0
^
3x
0
ft
^
S^3
etc
-H
0
Ö K
0
-H
3
^
a
4
dx
H
£
y
is matrix
of
hape
functions
representing the
interpolation of the shear
strains.
The
constitutive
equations
are
given b y
[A]
=
l-v
z
V
0
1 0
0
1-v
2
.
[D,]
=
G
0
0 G
E:
Elastic
modulus
v:
Poisson's
Ratio
G:
Shear
mod
ulus
[D
b
]
an d
D
S
] are
th e
constitutive
equation
for
bending and shear
an d th e
displacements
are
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R}=K)l (Ö,)l
W
l
(®x)
2
(ö,)
2
*2
(0,)
3
®,)3
W
3
(®,)
4
(®„>4
f̂
C.
NTERFACE ELEMENTS
To rovide
n
nterface
etween
he
ib s
nd pine,
ero
ength r
iscrete
elements
were utilized. his same type
of approach was
also
used
in the connection of
the plate nd
thorax model
ubassemblies
to
omplete the
ystem.
he
inite lement
code
defines the discrete beam element for simulating the
effects
of a linear elastic zero
length
eam y
sing ix
prings ach
cting
bout
ne
of the ix ocal
egrees
of
freedom. ac h
spring
constant was adjusted depending
on
its allowable movement based
on
expected
biomechanical
behavior.
D.
PROJECTILE MODEL
For
this research a
N A T O 7.62 m m
Ball
M 80
was
utilized
in
the
simulation of the
projectile.
The projectile was fired from a distance
of approximately
3
meters
from the
target. he
initial or muzzle
velocity of approximately
3750
f/s (1143m/s)
results
in
an
impact
velocity of 2575 f/s
(784.86
m/s).
he
velocity
loss (V
L
)
is
a result of drag
an d
relative air
velocity
and
behaves as
V,=
XGD
re l
C
where
X = meters to
impact
G
=
Drag
coefficent
D
rel
= air
density
C
=
ballistic
coefficient
There
s o onsistent
esult
n the mpact ehavior of bullet
triking
a target.
Because f
he
mpossibility f ontrolling
ullet
trike
nd
egree
f penetration
statistical pproaches re ecessary nd he military
ervices
av e stablished V
5
o
2 6
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ballistic
limit [Ref.
5] . hi s is
the
minimum
or
maximum
velocity
at
which
a
particular
projectile s
xpected o ompletely enetrate
he
arget or
onsistently
ail o
ully
penetrate the armor given a thickness of
th e armor
an d
material properties
an d
angle of
obliquity. his
V50
allistic imit was se d o pproximate
he orce of the
bullet
t
impact.
The
orce of th e
mpact an
hen
e alculated
y
alculating
he
momentum
based
on
mass
nd
velocity
of
projectile.
he
im e
eriod of
interest
rom mpact to
bullet
coming
to rest
is
pproximately
00
sec. he
orce
pon
impact
is
alculated
based
on
the
momentum and
time.
Momentum = {mass
bulle
,)X {velocity
bullel
)
Momentum = .00805\9kg
693
Aim
Is
Momentum = 6.59kg -m/sec
\{Force)dt
= Momentum
As he
irst pproximation the
orcing
unction
nd
esponse
s
xpected to
e
sinusoidal in
shape.
his
model did
not consider the
penetrating capabilities of the bullet
or hypervelocity
projectile. he preliminary
results of field experimentation
indicate that
the
rojectile
id
not
ully
enetrate
he
bullet-proof
vest.
he
rojectile
id
ause
extensive rauma esulting n omminutation
f
he ternum. he rojectile ully
penetrated
he
eramic
rmor but
was topped
y
he
kevlar
acking
material.
he
expected
forcing
function applied
to
the bulletproof
vest
is depicted Figure
14.
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4
X1 0
Approximate
Force du e to
Projectile
Impact
14
^
12
-
10
f
a >
I 6
o
4 /
\
2
50
10 0
Time(usec)
15 0
2 00
Figure
14 .
External
Force
E.
MODEL
SOLUTION
A n explicit stiffness method was used in
the
solution of the finite element
model.
This
olution
pproach
s ased
n
he
heory nd ractice escribed n The
inite
Element
Method
using Matlab
Ref. 4].
ATLAB
5.2
was
used
to
solve
the
matrix
equations
for
the
static
study.
language was
utilized
to solve the transient analysis due
to time
considerations.
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IV .
NJURY
ANALYSIS
There
are no
universal standard to evaluate
injury
potential of
the human
body
caused
y
xternal
oading,
ecause
veryone
s
ifferent
n
ize,
trength,
nd
ven
response to
the same loading conditions.
ifferences also arise from sex,
age,
and body
posture.
However,
consistent demands
for
evaluating
injuries
and
protecting
the human
being
from
injuries
were motivated
and
resulted
in
some
njury
criteria
and
reference
values,
which
have
been
commonly used in the
aerospace and automobile
industry
for
safety.
hese re
iscussed
here
to provide
om e
nsight
into
the
type
nd
xtent
of
injury that
can
occur
due
to
a
projectile
strike
to
the
protected
area
of
the sternum.
Injury nalysis s omewhat ifficult n
this
ase ecause he mechanism hat
produces the
injury or
the bullet impact is localized
and
non-linear which includes plastic
flow
around
the impact sight
as
the
bullet travels
to
rest.
everal phenomena occur in
and
around the bullet
strike.
ocal pettaling may
occur which
is
plastic deformation
of
a
ductile
material
when
struck by an
impacting projectile
or fragment
causing
the material
to
be
forced
outward in leaflets
or
petal
forms
[Ref.
5] . palling,
the
detachment
or
delamination
of a
layer
material
in
the
area
surrounding the location
of the impact, can
also
occur
due
to bullet
strike.
palling
can
occur
on either
the front
or rear surface
and
may
roduce
njury
ven
hough
ullet
enetration
s
ot
omplete.
his
s
ocal
behavior
and
was neglected because the interest is strictly in the overall displacement
of
the
ternum. he
ocus
of
this esearch
is
trauma
to he
uman
thorax aused
y
deflection
or
loading
rate.
n
other
words
a basic assumption
is
that
the protective
body
armor
will
stop
the
projectile
prior
to
full
penetration
of
the
body
armor.
Rib
fracture and
flail
chest,
excessive
motion
of
the
chest,
occur
due
to
frontal
impact
of
the
chest.
t
is
most probable
that
the
ribs fail due
to bending on the
tensile side
of
the
rib.
ib
fractures
normally
occur
with
chest deflection
of
over
3
nches, but
no
fractures
ccur
t
eflections
of
less
han .3 nches.
he umber f rib
ractures
depends
on
the
magnitude
of the chest
deflection
[Ref. 16].
The
amount of force
depends
on
the
rate
of
loading. herefore
at
a given loading rate force appears
to be related
to
the
number
of
rib fractures due
to
the
viscous
nature
of the
thorax
[Ref.
16].
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Tolerance
Level
Injury Level
Force
3.3kN
to
sternum
Minor injury
8.8kN
to chest
and
shoulders
Minor injury
Acceleration
60g's
3ms limit
for
hybrid
II&III
Deflection(mm)
58
No rib
fracture
76
Limit for
Hybrid
III
Compression(%)
20
Onset
of
rib fracture
40
Flail
Chest
32
Tolerance for rib
cage
stability
Table
1.
Frontal
Impact
Injury Tolerances.
[Ref.
16 ]
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V. RESULTS
AND
DISCUSSION
The
human
thorax
model was first
exposed to
a
static
load
applied at the
sternum
in order
to
provide some
insight
into
the validity
of
the model. his
was
accomplished
using
MATLAB
nd
he
esults
were
ompared
o
arlier
tudies.
Earlier
tudies
include experimental information
and
finite
element modeling. he finite element
model
was
then subjected
to
a
transient load
applied
at
the protective
vest
covering
the
sternum
and compared to recent live-fire testing
of
instrumented cadavers. he finite element
model
was
assembled
with the
use
of
ANSI
C
programming language because
of
the
increased speed
of
the
processing
time.
he
MATLAB
5 files
were
translated
to
ANSI
C
language.
he
plate
and thoracic body
stiffness
matrices
were
computed
separately and
then
ssembled
nto
ystem
matrix.
cceleration,
elocity,
nd
isplacement
were
computed
using
numerical integration scheme called the central difference
technique
O f articular
nterest
as he
isplacement
f
he
ternum
nd ubsequent
displacement
of
the
thoracic
body
resulting in
applied
stresses and strains
of
the
internal
organs uch
as the
heart, ungs,
liver, nd
other
soft tissue.
lthough
not
specifically
modeled,
damage
to
internal organs is
readily
apparent
in
the
displacement
field of the
sternum and rib cage
and
laceration
injury may
result
due
to rib fracture sites.
A.
STATIC
ANALYSIS
Literature describing
the static loading
of
the human thorax
provided an
avenue
for he initial model validation
and
was
used in the static phase
of
this
research.
nitially,
a tatic r uasistatic orce was
pplied o rovide
om e
measure
s o he model
usefulness.
Tw o loading cases were considered. A 1001b (444.82 kg.)
load
was
applied
to
the
mid-sternum
line
and
a
501b
(222.41)
point
force
applied
at
rib
two.
he
global system
stiffness matrix was
formed.
oundary
conditions appropriate
for
the
simulation
were
then
applied. n
this
case, the boundary
conditions
simulated
a
cadaver
lying on
a
table.
The
nodes corresponding approximately
to the position
of
the
ribs
that extend
posteriorly
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the
farthest
distance
out
were
pinned.
This
normally
corresponds to a
position
between
the
angle and
tubercle
of
each
rib
pair.
Th e global displacement
were
obtained
and
used
in an
initial validation process of
the model. he
displacement
field
of
the
sternum
was evaluated and
compared
to
the
experimental and numerical studies
of Andricchii
Ref.16],
Nahum
[Ref.16],
and work
done
by
Patrick [Ref.16] with embalmed
cadavers and
fresh cadavers
(males
and
females).
he static
loading results
compared
favorably with
the embalmed
cadavers
s
well
s
the
arlier numerical
models
of Andricchi.
igure
5
rovides
qualitative
omparison between
the
model
eveloped
nd
arlier
models
s
well
s
comparison between
the
developed
model and earlier analysis of
a
static or
quasi-static
force
applied
to fresh
and
embalmed cadavers.
Comparison
of
Load
Deflection
0.4
.6
Deflection of sternum
in inches
Figure
15. Comparison
of Thoracic Load
Deflection
Curves [After Ref.9]
The anterior to
posterior
displacement
of
the
sternum is
shown
in
Figure 16
as a
result of the
1001b load. The
deflection
of
sternum
and
the deflection
of
the
individual
ribs
pairs
though
7
are
shown
in
figures
17
-
23
as a result of 1001b load.
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Displacement of Sternum
0.45
0.4
a
.3 5
E
N
0.3
0.25
..
Y
o o-original
v
v-deformed
V
°
0
V
o
0 V
V
-0.12 0.1
0.08 0.06 0.04 0.02
y.meters
Figure 16. Sternum
Deflection
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R ib
1
Displacement
0.03
0.06
0.04-
0.02
>-
0
-0.02
-
-0.04
-
-0.06
-0.08
Figure
17. R ib 1
Deflection
R ib 2 Displacement
0.08
Figure
18 . ib 2
Deflection
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0.08
0.06
0.04
0.02
Rib 3
Displacement
>
-0.02
-0.04
-0.06
,
A
.,
\\
/
\̂
^̂ -̂
deflected position
^
-0.1
-0.05 0
X
0.05 0.1
Figure
19 .
Rib
.3 Deflection
0.06 r
0.04
0.02
Rib 4 Displacement
-0.02
0.05
. 1
.15
Figure 20. Rib 4
Deflection
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0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
R ib 5
Displacement
-0.08
0. 1
r
J \
\T
1/
^x^—
/
A
-0.05
X
-0.2
0.15
0. 1
Figure
21.
Rib
5 Deflection
0.05
0.1
0.15
R ib
6
Displacement
0.15
Figure
22. Rib 6 Deflection
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0.1
0.08
0.06
0.04
0.02
-0.02
-0.04
-0.06
-0.08
R ib
7
Displacement
\
i —̂
— -^^-ideflected postion
-0.2
0.15
0.1
0.05
.05
.1
.1 5
X
Figure 2 3 .
R ib
7 Deflection
Once he
isplacements re
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