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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

8.

PERFORMING

ORGANIZATION

REPORT

NUMBER

9. SPONSORING/MONITORING

AGENCY

NAME(S) AND ADDRESS(ES)

10. SPONSORING/MONITORING

AGENCY REPORT

NUMBER

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 .

NUMBER

OF

PAGES

62

16 .

PRICE CODE

20. LIMITATION OF

ABSTRACT

UL

NSN 7540-01-280-5500

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Form

298 (Rev. 2-89)

Prescribed by

ANSI Std.

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]

10

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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

21

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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,}

24

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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

25

8/18/2019 Ada 370880wd

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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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