Mechanics of bones

wafflecanadianMechanics

Jul 18, 2012 (5 years and 3 months ago)

364 views

1
Mechanics of bones
Philippe GILLET (
Philippe GILLET (
Chirurgie
Chirurgie
de
de
l’appareil
l’appareil
locomoteur
locomoteur
, CHU)
, CHU)
Serge CESCOTTO
Serge CESCOTTO
(FSA, Ulg)
(FSA, Ulg)
Skeletal system
Femur
2
Example of the long bone


2 types
2 types
of
of
materials
materials
:
:


Cortical
Cortical
bone
bone


Cancellous
Cancellous
bone
bone
(
(
trabecular
trabecular
bone
bone
)
)


Orientation
Orientation
of
of
the
the
bone
bone
cells
cells
according
according
to
to
the
the
stresses
stresses
Structure of the cancellous bone
Structure of cortical bone
3
Main characteristics of bone


Composite
Composite
of
of
collagen
collagen
and
and
hydroxyapatite
hydroxyapatite


Collagen
Collagen
has
has
a
a
low
low
E
E
,
,
good
good
tensile
tensile
strength
strength
,
,
poor
poor
compressive
compressive
strength
strength


Calcium
Calcium
appatite
appatite
is
is
a
a
stiff
stiff
,
,
britle
britle
material
material
with
with
good
good
compressive
compressive
strength
strength


=>
=>
anisotropic
anisotropic
material
material
that
that
resists
resists
many
many
forces
forces


Bone
Bone
is
is
strongest
strongest
in compression,
in compression,
weakest
weakest
in
in
shear
shear
,
,
intermediate
intermediate
in tension
in tension


The
The
mineral
mineral
content
content
is
is
the
the
main
main
determinant
determinant
of
of
the
the
E
E
of
of
cortical
cortical
bone
bone


Cancellous
Cancellous
bone
bone
is
is
25% as dense, 10% as
25% as dense, 10% as
stiff
stiff
and
and
500% as ductile as cortical
500% as ductile as cortical
bone
bone


Cortical
Cortical
bone
bone
is
is
excellent in
excellent in
resisting
resisting
torque
torque


Cancellous
Cancellous
bone
bone
is
is
good
good
in
in
resisting
resisting
comression
comression
and
and
shear
shear
Main characteristics of bone


Bone
Bone
is
is
a
a
dynamic
dynamic
material
material


Self
Self
repair
repair


Changes
Changes
with
with
aging
aging
:
:
becomes
becomes
stiffer
stiffer
and
and
less
less
ductile
ductile


Changes
Changes
with
with
immobilisation :
immobilisation :
becomes
becomes
weaker
weaker
Main characteristics of bone
4
Young’s modulus
Anisotropic behaviour of bone


Anisotropic
Anisotropic
behaviour
behaviour
of
of
cortical
cortical
bone
bone
:
:
specimens
specimens
from
from
a
a
femoral
femoral
shaft
shaft
tested
tested
in tension
in tension
in four
in four
directions
directions
Material and
stuctural behavior


A :
A :
cross
cross
-
-
sectional
sectional
area
area


L
L
0
0
: original
: original
length
length
of
of
the
the
cylinder
cylinder


Only
Only
valid
valid
for
for
bone
bone
with
with
the
the
same
same
microstructure
microstructure
and
and
in
in
the
the
same
same
environment
environment
as
as
the
the
test
test
specimen
specimen
5
Cortical bone: elastic behaviour


Poisson’s ratio
Poisson’s ratio
~0.6 for cortical
~0.6 for cortical
bone
bone
!!!!
!!!!
compared
compared
to ~0.3 for
to ~0.3 for
metals
metals


E
E
in
in
the
the
longitudinal
longitudinal
direction ~ 1.5
direction ~ 1.5
E
E
in
in
the
the
transverse direction
transverse direction
σ
ε
Cortical bone: strength (/stress)


In
In
uniaxial
uniaxial
,
,
monotonic
monotonic
tension
tension
and
and
compression
compression
loading
loading
:
:


Longitudinal
Longitudinal
loading
loading


Tensile
Tensile
strength
strength
~130
~130
MPa
MPa


Compressive
Compressive
strength
strength
~190
~190
MPa
MPa


Transverse
Transverse
loading
loading


Tensile
Tensile
strength
strength
~50
~50
MPa
MPa


Compressive
Compressive
strength
strength
~130
~130
MPa
MPa


Cortical
Cortical
bone
bone
has
has
adapted
adapted
to a situation
to a situation
where
where
compression
compression
loading
loading
is
is
greater
greater
than
than
tensile
tensile
loading
loading


Tensile
Tensile
and
and
compressive
compressive
yield
yield
strengths
strengths
are close to
are close to
the
the
respective
respective
ultimate
ultimate
strength
strength


Bone
Bone
loaded
loaded
above
above
its
its
yield
yield
stress
stress
deforms
deforms
by a
by a
relatively
relatively
large
large
amount
amount
compared
compared
to
to
its
its
elastic
elastic
behaviour
behaviour


Prior to fracture, cortical
Prior to fracture, cortical
bone
bone
has
has
undergone
undergone
relatively
relatively
large
large
deformations
deformations
Cortical bone: strain rate sensitivity


The
The
strain
strain
rate in
rate in
daily
daily
activities
activities
increases
increases
as
as
activity
activity
becomes
becomes
more
more
strenuous
strenuous


Slow
Slow
walking
walking
~ 0.001/sec
~ 0.001/sec


Brisk
Brisk
walking
walking
~ 0.01/sec
~ 0.01/sec


For
For
typical
typical
daily
daily
activities
activities
,
,
E
E
changes
changes
only
only
by ~15%
by ~15%


Slow running ~ 0.03/sec
Slow running ~ 0.03/sec


Jump
Jump
from
from
two
two
stairs
stairs
~ slow running
~ slow running


Fall
Fall
from
from
standing
standing
heigth
heigth
~
~
fast
fast
running
running


Cortical
Cortical
bone
bone
is
is
stronger
stronger
and
and
stiffer
stiffer
for more
for more
strenuous
strenuous
activities
activities


At
At
very
very
high
high
strain
strain
rates,
rates,
ultimate
ultimate
strain
strain
decreases
decreases
=> cortical
=> cortical
bone
bone
exhibits
exhibits
a ductile to
a ductile to
brittle
brittle
transition
transition
as
as
the
the
strain
strain
rate
rate
increases
increases
6


Ultimate
Ultimate
tensile
tensile
strength
strength
is
is
slightly
slightly
more sensitive to
more sensitive to
strain
strain
rate
rate
than
than
Young’s
Young’s
modulus
modulus


Bone
Bone
is
is
approximately
approximately
20%
20%
stronger
stronger
for
for
brisk
brisk
walking
walking
than
than
for
for
slow
slow
walking
walking
Cortical bone: strain rate sensitivity
Cortical bone:
creep behaviour


Bone
Bone
will
will
continue to
continue to
deform
deform
if
if
submitted
submitted
to a constant stress for an
to a constant stress for an
extended
extended
period
period
of
of
time
time


Strain
Strain
plotted
plotted
with
with
time
time
for
for
adult
adult
human
human
cortical
cortical
bone
bone
under
under
tension
tension


If cortical
If cortical
bone
bone
is
is
loaded
loaded
at
at
a certain
a certain
level
level
for
for
enough
enough
time
time
,
,
it
it
will
will
break,
break,
although
although
the
the
stress
stress
level
level
is
is
well
well
below
below
yield
yield
and
and
ultimate
ultimate
strengths
strengths


If
If
creep
creep
occurs
occurs
without
without
fracture, a
fracture, a
permanent
permanent
deformation
deformation
results
results
:
:
viscoplastic
viscoplastic
behavior
behavior


The
The
time
time
for
for
creep
creep
fracture
fracture
decreases
decreases
as
as
the
the
stress
stress
increases
increases


Resistance
Resistance
to
to
creep
creep
fracture
fracture
is
is
greater
greater
under
under
compression
compression
than
than
tension
tension
Cortical bone:
creep behaviour
7


If
If
the
the
applied
applied
stress
stress
is
is
above
above
a
a
threshold
threshold
level
level
(70
(70
MPa
MPa
or
or
55%
55%
of
of
its
its
ultimate
ultimate
strength
strength
for
for
human
human
cortical
cortical
bone
bone
in
in
tension),
tension),
the
the
rate
rate
at
at
which
which
creep
creep
deformation
deformation
occurs
occurs
and
and
the
the
magnitude
magnitude
of
of
permanent
permanent
deformation
deformation
after
after
unloading
unloading
both
both
increase
increase
sharply
sharply
Cortical bone:
creep behaviour
Cortical bone: age effects


The
The
longitudinal
longitudinal
E
E
and
and
tensile
tensile
yield
yield
strength
strength
of
of
cortical
cortical
bone
bone
decrease
decrease
by ~2%
by ~2%
per
per
decade
decade
after
after
age 20
age 20


The
The
slope
slope
of
of
the
the
stess
stess
-
-
strain
strain
curve
curve
after
after
yielding
yielding
increases
increases
by 8%
by 8%
per
per
decade
decade


There
There
is
is
reduction
reduction
in
in
energy
energy
absorption ~ 7%
absorption ~ 7%
per
per
decade
decade
,
,
mainly
mainly
due to
due to
reduction
reduction
in
in
the
the
ultimate
ultimate
strain
strain


=>
=>
less
less
strong
strong
,
,
less
less
stiff
stiff
, more
, more
brittle
brittle
with
with
aging
aging
Cancellous
bone: Young’s
modulus in
compression


Young’s
Young’s
modulus
modulus
in
in
compression as a
compression as a
function
function
of
of
apparent
apparent
density
density
for
for
trabecular
trabecular
bone
bone
8
great energy absorbtion of trabecular bone
Cancellous
bone: ultimate
strength in
compression


Ultimate
Ultimate
strength
strength
in
in
compression as a
compression as a
function
function
of
of
apparent
apparent
density
density
for
for
trabecular
trabecular
bone
bone
Apparent density/ modulus and strength


The
The
relationships
relationships
between
between
apparent
apparent
density
density
and
and
both
both
modulus
modulus
and
and
strength
strength
have important
have important
clinical
clinical
consequences
consequences
1.
1.
Bone
Bone
can
can
easily
easily
regulate
regulate
its
its
strength
strength
2.
2.
Stiffness
Stiffness
can
can
easilly
easilly
be
be
regulated
regulated
by
by
adjusting
adjusting
apparent
apparent
density
density
9
Comparison tensile and compressive
behaviour of trabecular bone


The
The
tensile
tensile
behavior
behavior
of
of
trabecular
trabecular
bone
bone
is
is
much
much
different
different
from
from
its
its
compressive
compressive
behavior
behavior
after
after
yielding
yielding
:
:
failure
failure
occurs
occurs
by fracture
by fracture
of
of
the
the
individual
individual
trabeculae
trabeculae
=>
=>
the
the
specimen
specimen
can
can
take
take
less
less
and
and
less
less
load
load
until
until
final fracture
final fracture
occurs
occurs
Age and osteoporosis


The
The
loss
loss
of
of
trabeculae
trabeculae
in
in
osteoporosis
osteoporosis
is
is
more
more
damaging
damaging
for
for
the
the
overall
overall
structural
structural
integrity
integrity
and
and
strength
strength
of
of
a
a
trabecular
trabecular
bone
bone
structure
structure
than
than
thinning
thinning
of
of
the
the
trabeculae
trabeculae
because
because
lamellar
lamellar
new
new
bone
bone
can
can
only
only
form
form
on
on
existing
existing
surfaces
surfaces


Decrease
Decrease
in
in
bone
bone
density
density
must
must
be
be
futher
futher
analysed
analysed
as
as
the
the
result
result
of
of
thinning
thinning
or
or
loss
loss
of
of
trabeculae
trabeculae