Detroit Medical Center - Biomech1
Transcript of Detroit Medical Center - Biomech1
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Concepts in OrthopaedicBiomechanics
Basic Science LecturesDepartment of Orthopaedic Surgery
Detroit Medical Center
Michele J. Grimm, Ph.D.Director of Orthopaedic Biomechanics
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Mechanical Concepts -- Force
Force: A vector quantity that describes the
action of one body on another
Three attributes must be defined
Magnitude
Direction
Point of Action
Forces can either be normal or shear in
nature
Normal forces act perpendicularly
to a surface
Shear forces act tangentially to a
surface
Newton's Second Law:
F = m*a
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Mechanical Concepts --
Compression and Tension
Compression: defined most simply as a "squeeze"
When a force is applied to an object to squeeze it, the
object is deformed (shortened) along the direction of
the compressive force while expanding perpendicular to
the force.
Tension: opposite of compression, or a "pull"
When a force is applied to pull a fixed object, the object
is lengthened along the direction of the tensile force
while being reduced in size in the direction
perpendicular to the force.
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Mechanical Concepts -- Stress
Stress: Force normalized to cross-sectional area to
eliminate the effect of geometry
Units of force/area
Newtons/square meter (N/m2
) or pascals (Pa) Pounds/square inch (psi)
1 TON
Area
1 TON
Area
1 TON
Area
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Mechanical Concepts -- Strain
Strain: The change in length of a material divided by its
original overall length
Strain is dimensionless and is often expressed as
percent strain
Ten percent strain means an object has been deformed
by one tenth of its original length
L D L L D L
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Mechanical Concepts -- Elastic Modulus
Elastic Modulus: Ratio of stress to strain at any point in
the elastic (linear) region of deformation (small strains)
Also known as modulus of elasticity or Young's modulus
Units of stress/strain (Pascals/dimensionless = Pascals) Often (incorrectly) referred to as stiffness
True stiffness is defined as the change in force per
change in length and is given in units of force/length
Stiffness is dependent both on the material’s elasticmodulus and the object’s geometry
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Mechanical Concepts -- Elastic Modulus
Determined as the slope of thelinear portion of the stress-strain
curve
Higher elastic modulus
indicates that more stress isrequired to deform a material
Ex: A compressive load is
applied to functional spinal unit
(a disc and 2 vertebral bodies).The vertebral body has a higher
elastic modulus than the disc.
Therefore, the disc deforms to a
greater extent than the vertebral
bodies.
Strain
Stress
Ds De
E = Ds De
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Question 1
The deformation of a material as a result of an applied load
is referred to as:
(1) Stress
(2) Strain
(3) Plasticity
(4) Elasticity
(5) Viscoelasticity
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Question 1
The deformation of a material as a result of an applied load
is referred to as:
(1) Stress
(2) Strain
(3) Plasticity
(4) Elasticity
(5) Viscoelasticity
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Question 2
The stress produced when a force acts in line with a
surface is:
(1) Shear
(2) Torque
(3) Tension
(4) Elasticity
(5) Compression
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Question 2
The stress produced when a force acts in line with a
surface is:
(1) Shear
(2) Torque
(3) Tension
(4) Elasticity
(5) Compression
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Question 3
In the Figure, which material has the highest modulus of
elasticity?
Stress
Strain
5
4
1
2
3
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Question 3
In the Figure, which material has the highest modulus of
elasticity?
Stress
Strain
5
4
1
2
3
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Mechanical Concepts -- Mechanical Models
Behavior of materials fits into a combination of three
categories
Elasticity is characterized by
Full recovery of deformation when a load is removed
Instantaneous reaction to a force application
Linear relationship between force and deformation
Time
0
ForceOn
ForceOff
Deformation
Time
Force
0
Deformation
Force
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Mechanical Models
Plasticity is characterized by
Resistance of a body to deformation after a critical
(yield) stress is reached
After deformation begins, it continues to occur withoutincreased stress
Plastic deformation is not recoverable
Time
0
Force
On
Force
Off Deformation Force
0
Critical Force
Time
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Mechanical Concepts -- Mechanical Models
Viscosity is characterized by
Time/rate dependence of stress-strain
response
Higher rate of force application
requires higher stress to give desired
deformation Conversely, a given deformation at a
higher strain rate results in an
increased force
Response to stress is not instantaneous
A constant load applied to a viscous
element will cause continuous
deformation until the load is
removed
Deformation is not recoverable
Force
Rate of Deformation
Force
Time
Deformation
F1 F2
F3 F1>F2>F3
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Question 4 The Figure represents the behavior of a material
characterized as
(1) linearly elastic
(2) linearly elastic, linearly plastic
(3) linearly elastic, perfectly plastic
(4) rigid, linearly plastic
(5) rigid, perfectly plastic s
e
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Question 4 The Figure represents the behavior of a material
characterized as
(1) linearly elastic
(2) linearly elastic, linearly plastic
(3) linearly elastic, perfectly plastic
(4) rigid, linearly plastic
(5) rigid, perfectly plastic s
e
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Mechanical Concepts -- Strength and Failure
Ultimate Strength: Maximum stress amaterial supports before failure
NOTE: The elastic modulus and
ultimate strength of a material are not
necessarily related
Yield Strength: The stress at the pointwhere the stress-strain curve undergoes a
transition from linear to non-linear behavior
Typically the transition between elastic
and plastic behavior or the start of plastic deformation in a purely plastic
material
Rupture: Point at which failure occurs and
stress subsequently goes to zero
Rupture
su
sy X
e
s
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Question 5
The Figure shows the stress-strain relationship for a
material loaded in uniaxial tension. The ultimate tensile
strength of this material is defined by which point?
s
e
X
• • •
•
A B
C D E
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Question 5
The Figure shows the stress-strain relationship for a
material loaded in uniaxial tension. The ultimate tensile
strength of this material is defined by which point?
s
e
X
• • •
•
A B
C D E
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Mechanical Concepts - Ductility
Ductility: Total strain to failure
A ductile material will undergo considerable plastic
deformation resulting in greater strains before rupture
occurs
A brittle material (low ductility) will fail soon after the
elastic limit is reached
X X
s
e
Brittle
Ductile
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Mechanical Concepts -- Energy Absorption
Energy Absorption: The area under a load-deformation
curve indicates the amount of strain energy absorbed by
the material during deformation
A portion of the energy may be stored in the material and
is recoverable once the stress is removed
For a purely elastic material, all of the stored strain energy
is recovered
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Mechanical Concepts -- Energy Absorption
Most materials have a viscous component to their behavior, sosome of the absorbed energy is lost, through conversion to heat,
on removal of the stress
Lost energy is indicated by the area between the loading and
unloading curves on a stress-strain plot
This loss of a portion of energy for elastic deformation is
termed hysteresis
The greater the amount of viscous behavior in a material, the
greater the amount of energy lost
s
e
s
e
s
e
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Mechanical Concepts -- Energy Absorption
Energy absorbed during plastic deformation is unrecoverable
If plastic deformation proceeds to fracture, the total area under the
load-deformation curve is the energy absorbed
If the load is removed, the material may return partially to its
original state, with recovery of the elastic deformation. However,the plastic deformation will not be recovered and the energy lost
will be greater than for only elastic deformation
F
L
F
L
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Question 6
The energy absorbed by a specimen during a load-to-
failure test is determined by calculating the
(1) slope of the load-deformation curve
(2) hysteresis of the stress-strain curve
(3) load at failure multiplied by strain at failure
(4) area under the load-elongation curve
(5) slope of the stress-strain curve
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Question 6
The energy absorbed by a specimen during a load-to-
failure test is determined by calculating the
(1) slope of the load-deformation curve
(2) hysteresis of the stress-strain curve
(3) load at failure multiplied by strain at failure
(4) area under the load-elongation curve
(5) slope of the stress-strain curve
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Mechanical Concepts -- Fatigue
Fatigue Fracture: Results from repetitive loading cyclesthat produce stresses at lower levels than the ultimate stress
Dependent both on level of stress and number of cycles
Begins with a set of microscopic cracks that propagate and
cause failure under repeated loading A material is defined by an endurance limit, a stress up to
which it can withstand an infinite number of cycles of
loading
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Mechanical Concepts -- Fatigue
Above the endurance limit, material behavior can beassessed by an S-n curve relating stress to number of
cycles
Based on experimental evidence
Fatigue can be exacerbated by processes such as corrosionand therefore cannot be expected to be the same for a
material in a physiological environment as it was in a
bench test
"S-n curve"
S t r e s s ( p s i )
125000
100 10 1 0.1 0.01
Endurance Limit
Number of Cycles (millions)
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Behavior of Materials
Bone can fracture as a result of a single, high stress (traumaticfracture)
Bone is also exposed in vivo to repetitive stresses of various
levels
Repeated loading of daily activities can result in microdamageMicro-cracks in both the cortical and trabecular bone
If microdamage accumulates faster than it can be repaired by
physiological processes, the cracks may propagate and result
in fracture of the bone This is fatigue fracture
This is the proposed mechanism behind stress fractures and
atraumatic fractures, such as occur in the vertebrae
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Behavior of Materials -- Viscoelasticity
Actual materials often exhibit viscoelastic behavior
A combination of purely elastic and viscous behavior discussed
above
Bone, cartilage, ligaments, and muscle are all viscoelastic to
varying extents
Ex. Bone or ligament is more likely to rupture or fracture if a
load is applied quickly, such as in an impact situation. The
deformation may be the same for other loading conditions;
however, the high strain-rate results in a higher stress being
required to produce the deformation and the stress may then be greater than the ultimate strength of the structure.
Stress is partially dependent on strain-rate and the strain itself
can change with time for a constant stress
Viscoelastic behavior can be described with two basic models
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Behavior of Materials -- Viscoelasticity Model 1: Maxwell Body
Creep: Slow, continuingdeformation with time
under a constant stress
Ex: The loss of spinal
height over the courseof a day is a result of
creep behavior in the
spine, primarily in the
intervertebral discs Stress Relaxation:
Reduction in measured
stress with time for a
constant strain
D e f o
r m a t i o n
Time
Force
On
Force
Off
ElasticRecovery
Force
Time
Force
On
Force
Off
D e f o r m a t i o n
Time
Structure Deformed
Time
Force
Structure Deformed
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Behavior of Materials -- Viscoelasticity Model 2: Kelvin Body or Voigt Element
No instantaneous response to stress due todash-pot effect
Deformation characterized by initial creep behavior
which is limited by the extension limit of the spring
for that loadRecovery after removal of the load is gradual but
complete due to the tendency of the spring to return to
its original length
Deformation
Time
ForceOn
ForceOff
0
Force
Time
ForceOn
ForceOff
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Question 7
Strain of a material beyond its elastic limit is defined as
(1) Fatigue
(2) Relaxation
(3) Plastic deformation
(4) Creep
(5) Stretching
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Question 7
Strain of a material beyond its elastic limit is defined as
(1) Fatigue
(2) Relaxation
(3) Plastic deformation
(4) Creep
(5) Stretching
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Question 8
A material is subjected to a constant load and is found to
deform with time. The deformation-time curve for this
material approaches a steady state with time. The behavior
of this material is termed
(1) Elastic deformation
(2) Plastic deformation
(3) Creep
(4) Anisotropic deformation
(5) Ductility
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Question 8
A material is subjected to a constant load and is found to
deform with time. The deformation-time curve for this
material approaches a steady state with time. The behavior
of this material is termed
(1) Elastic deformation
(2) Plastic deformation
(3) Creep
(4) Anisotropic deformation
(5) Ductility
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Question 9
The deformation of a material with respect to its original
shape as a result of an applied load is referred to as:
(1) Stress
(2) Strain
(3) Elasticity
(4) Plasticity
(5) Viscoelasticity
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Question 9
The deformation of a material with respect to its original
shape as a result of an applied load is referred to as:
(1) Stress
(2) Strain
(3) Elasticity
(4) Plasticity
(5) Viscoelasticity
(3, 4, 5) related to the modulus
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Question 10
The resistance of a material to deformation from an applied
load is called:
(1) Tolerance
(2) Stiffness
(3) Elasticity
(4) Viscoelasticity
(5) Plasticity
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Question 10
The resistance of a material to deformation from an applied
load is called:
(1) Tolerance
(2) Stiffness
(3) Elasticity
(4) Viscoelasticity
(5) Plasticity
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Behavior of Materials Actual materials are based on a
combination of elastic andviscoelastic elements
Biological materials such as
ligament, tendon, or other soft
tissues exhibit the followingdeformation-time response
This behavior can be explained
most simply by the following
model A plastic element should also be
added to the model to account
for plastic deformation at high
stresses
Time
D e f o r m a t i o nForce
On ForceOff
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Behavior of Materials
Mechanical properties of a material can be dependent on the
direction of loading
Behavioral differences are typically related to the structural
organization of the material
Bone, ligaments, and other tissues have obvious fiber or
structural orientations
Properties are different for forces applied parallel and
perpendicular to those structural orientations
This directional dependence is termed anisotropy
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Behavior of Materials
Mechanical properties can also vary depending upon the
mode of loading
Elastic modulus and strength can be different for the
same material when loaded in compression, tension,
and shear
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Question 11
Which of the following is a characteristic property of
viscoelastic materials:
(1) The material is anisotropic
(2) Deformational behavior is independent of time
(3) Deformational behavior is independent of the
applied strain rate
(4) During constant deformation, the internal stress is
gradually increased
(5) During application of a constant load, the material
gradually deforms
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Question 11
Which of the following is a characteristic property of
viscoelastic materials:
(1) The material is anisotropic
(2) Deformational behavior is independent of time
(3) Deformational behavior is independent of the
applied strain rate
(4) During constant deformation, the internal stress is
gradually increased
(5) During application of a constant load, the material
gradually deforms
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Question 12
A material that has the same mechanical properties in all
directions is referred to as:
(1) Plastic
(2) Ductile
(3) Elastic
(4) Isotropic
(5) Viscoelastic
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Question 12
A material that has the same mechanical properties in all
directions is referred to as:
(1) Plastic
(2) Ductile
(3) Elastic
(4) Isotropic
(5) Viscoelastic
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Properties of Bone
Bone is a two-phase, anisotropic and viscoelastic material
which can react to stresses with self-repair and self-
adaptation
Cortical and trabecular bone have different mechanical
properties, based predominantly on the different densitiesof the material
Cortical bone has an apparent density (mass of bone per
total unit volume) of approximately 1.8 g/cm^3
Trabecular bone has an apparent density ranging from0.1 to 1.0 g/cm^3 depending upon the porosity of the
bone, which varies based on anatomic site and between
individuals
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Properties of Bone
Both cortical and trabecular bone have a higher ultimatestrength in compression than in tension
Both cortical and trabecular bone are anisotropic, with
higher ultimate strength and higher elastic modulus in the
direction of predominant structure orientation Changes in bone composition due to disease affect
properties:
A reduction in bone mineralization results in more
ductile, less stiff bones with reduced compressivestrength and elastic modulus
A reduction in bone protein composition results in more
brittle, harder bones with reduced tensile strength and
increased elastic modulus
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Effect of Age on Bone Properties
Changes due to age can affect bone mechanical properties
through both structural changes and changes in material
properties
Aging results in both cortical and trabecular bone becoming
more porous
Strength and elastic modulus are both dependent on the
amount of bone present (increased porosity --> reduced
strength and modulus)
In trabecular bone, strength and elastic modulus are also
dependent on how the trabecular material is lost
An overall thinning of trabeculae will result in different
changes in mechanical properties than if some trabeculae
are lost completely while others maintain their thickness
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Effect of Age on Bone Properties
Aging also results in less ductile bone (more brittle)
The maximum strain to failure is reduced as is the
ability of bone to absorb energy
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Question 13
A long bone is anisotropic because
(1) its material properties are strongest in tension
(2) its material properties have a directional preference
along the long axis
(3) its dimensions are not the same in all directions
(4) it contains an intramedullary canal
(5) it is a porous structure
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Question 13
A long bone is anisotropic because
(1) its material properties are strongest in tension
(2) its material properties have a directional preference
along the long axis
(3) its dimensions are not the same in all directions
(4) it contains an intramedullary canal
(5) it is a porous structure
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Question 14
Which of the following is the best description of the
mechanical properties of wet compact bone in humans?
(1) Isotropic
(2) Brittle
(3) Fatigue-resistant
(4) Strain-rate dependent
(5) Strongest in tension
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Question 14
Which of the following is the best description of the
mechanical properties of wet compact bone in humans?
(1) Isotropic
(2) Brittle
(3) Fatigue-resistant
(4) Strain-rate dependent
(5) Strongest in tension
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Question 15
What effect does demineralization have on the
biomechanical properties of bone?
(1) Increases toughness
(2) Increases modulus of elasticity
(3) Increases brittleness
(4) Decreases stiffness
(5) Decreases ductility
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Question 15
What effect does demineralization have on the
biomechanical properties of bone?
(1) Increases toughness
(2) Increases modulus of elasticity
(3) Increases brittleness
(4) Decreases stiffness
(5) Decreases ductility
Mechanics of Soft Tissue --
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Mechanics of Soft Tissue --
Ligament and Tendon
Ligaments and Tendons have a defined fiber orientation based on
the arrangement of the collagen fibers
Mechanical behavior is anisotropic with greater strength and
stiffness along the fiber direction
Strength and modulus higher in tension than in compression
Mechanics of Soft Tissue --
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Mechanics of Soft Tissue --
Ligament and Tendon
Deformation of ligaments and tendons has acharacteristic behavior due to the action of
the fibers
Initial "toe" region is a result of the
straightening of crimped collagen fibers
Linear, elastic region is due to theoverall elastic deformation of the
structure
Stiffness begins to decrease in the plastic
region where individual fibers begin tofail
Overall failure occurs when stress
experienced by the remaining fibers
exceeds their ultimate tensile strength
X
Deform.
Force
Mechanics of Soft Tissue --
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Mechanics of Soft Tissue --
Ligament and Tendon
Ligaments and tendons exhibit viscoelastic behavior
Stiffness and strength are dependent on the loading rate,
with increased rates of deformation resulting in
increased stiffness and stress
Comparison of properties:
Ultimate tensile strength:
Tendon = 1/2 Bone
Ligament < Tendon
Elastic modulus
Tendon = 5 - 10 % Bone
Ligament < Tendon
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Question 16
A ligament is subjected to a constant force well below that
required to cause its rupture. The ligament will respond to
these loading conditions by:
(1) Elongating instantly and remaining at that length
(2) Elongating instantly and continuing to do so until a
constant length is reached
(3) Elongating instantly and then shrinking slowly
back to its original length
(4) Elongating indefinitely
(5) Remaining the same length
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Question 16
A ligament is subjected to a constant force well below that
required to cause its rupture. The ligament will respond to
these loading conditions by:
(1) Elongating instantly and remaining at that length
(2) Elongating instantly and continuing to do so until a
constant length is reached
(3) Elongating instantly and then shrinking slowly
back to its original length
(4) Elongating indefinitely
(5) Remaining the same length
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Mechanics of Soft Tissue -- Cartilage
Cartilage is designed to be loaded predominantly in
compression and exhibits substantial anisotropy
Properties are highly dependent on the rate of loading
At high strain rates, collagen behaves almost elastically
At low strain rates, viscoelastic behavior such as creep
is very apparent independent of the direction of loading
Like ligaments and tendons, cartilage exhibits a toe region
in the tension stress-strain curve due to the allignment of
the collagen fibers
Cartilage has an ultimate tensile strength of approximately
5 % that of bone, while the compressive elastic modulus is
about 1 % of bone
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Mechanics of Soft Tissue -- Cartilage
The behavior of cartilage under compressive load is
influenced by its porous, fluid-filled structure
Cartilage can be seen as a matrix of collagen and
proteoglycans filled with a large amount of water
During the first phase of compression, water is expelled
from the gel-like structure and deformation occurs easily
resulting in low stiffness and a high level of creep under
constant loading
Once a large amount of water has been expressed, thestructural elements of the matrix support the load, the
material becomes stiffer, and creep occurs at a lower rate
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Mechanics of Biomaterials -- Metals
Commonly used metals for medical implants
Stainless Steel
Cobalt-Chromium Alloy
Titanium Alloy
Elastic moduli of metals are about 1 order of magnitude higher
than cortical bone
Titanium has an elastic modulus of approximately 1/2 that of
stainless steel or cobalt alloys
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Mechanics of Biomaterials -- Metals
Fatigue Fracture of metals is an important consideration
due to the cyclic loading of orthopaedic implants and the
inability of artificial materials to self-repair
The endurance limit of typical implant metals is
between 250 MPa (Stainless steel) and 400 MPa(Titanium Alloy)
Fatigue is quickened due to the effect of corrosion of
the metals
i
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Corrosion
Corrosion is a chemical reaction that occurs to form metallic
ions and hydroxides. It is extremely common for metals placed
in electrolytic solutions, such as the physiological environment.
Implant metals rely on the existence of an inert protective layer
to resist corrosion
Passivation is a reaction that produces a surface coating,
typically a metal oxide, on the metallic material which results in
an equilibrium solution of metal ions
C i
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Corrosion
Implant metals and surface coatings
Stainless steel -- chromium oxide
Titanium alloy -- titanium dioxide
Cobalt-chromium alloy -- none
corrosion resistance due to an immunity mechanism While an oxide layer may be generally inactive in vivo,
changes in pH -- due to variations in location or disease
processes -- may damage the layer and result in corrosion
Oxide layers can also be damaged due to mechanicaltrauma, such as scratching, which can then lead to
corrosion
Most oxide layers are self-repairing in the presence of
oxygen
C i
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Corrosion
Multiple types of corrosion
Uniform attack: requires a bathing solution with considerable
ionic activity (eg. physiological solution)
Galvanic attack: when two different metals are in contact in an
electrolytic solution, one may tend to release ions to the other
anode --> cathode
Cathodic material gains protection against corrosion
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Corrosion
Stress corrosion: caused by rupture of the passive surface
layer as a result of high tensile stresses, allowing local
attack at the exposed site
If conditions favor passivation, repair of the crack will
occur by formation of the oxide layer
Continued cyclic loading or the presence of organic
molecules may interfere with the repair allowing for
continued local attack, resulting in stress concentrations
and possible failure
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Corrosion
Pitting: galvanic attack which occurs between two
adjacent locations on the same metal due to impurities in
the alloy which result in a galvanic reaction
Intergranular attack: similar to pitting, however the
impurities exist in the boundaries between the metalcrystals or grains. Results in grain-boundary cracks.
Crevice corrosion: A linear and local attack, similar to
stress corrosion, which occurs at sites where scratches,
seams, or fatigue cracks form defects in the metal oxidecoating. These areas typically have low oxygen
concentration and so passivation, and coating repair, is
inhibited.
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Question 17
Which of the following will help prevent corrosion of an
implant?
(1) An oxide layer
(2) Repetitive axial loading
(3) Contact of two dissimilar metals
(4) Muscle over the implant
(5) A layer of fibrin
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Question 17
Which of the following will help prevent corrosion of animplant?
(1) An oxide layer
(2) Repetitive axial loading
(3) Contact of two dissimilar metals
(4) Muscle over the implant
(5) A layer of fibrin
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Mechanics of Biomaterials -- Polymers
Polyethylene, polymethyl methacrylate (PMMA), and siliconesare commonly used polymers for orthopaedic applications
Polyethylene
Low friction coefficient reduces wear when used as a
bearing surface for joint replacements
Low strength
Limited resistance to wear which does occur
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Mechanics of Biomaterials -- Polymers
PMMA
Typically used as bone cement
Low viscosity immediately following mixing, allowing
for insertion in the medullary canal
Low tensile strength, higher compressive strength
Silicones (rubber)
Very low strength, poor wear behavior
High energy absorption properties
Used as spacer for small, load-bearing joints
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Mechanics of Biomaterials-- Ceramics
Include aluminum oxide, calcium phosphate, and various"bioglasses"
Investigated due to chemical inertness for use as implant
materials
Very brittle, hard, low tensile strength, high modulus
High resistance to wear, low friction coefficient when
polished, high compressive strength
Possibility exists for development of a bio-reactive ceramic
which induces bone growth
Mechanical Properties --
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p
Biomaterials
Cortical Bone
Cancellous Bone
Stainless Steel
Titanium Alloy
Cobalt-Chrome
Polymethylmethacrlyate
Polyethylene
Aluminum Oxide
ElasticModulus
(GPa)
15
1
200
100
200-230
2
1
350
100
2
>500
900
>450
40
40
175
3
80
20
3500
2%
10%
15-40%
10%
8-10%
500%
5%
minimal
Ultimate
Tensile
Strength
(MPa)
Ultimate
Compressive
Strength
(MPa)
Maximum
Elongation
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Question 18
Which of the following is the best description of acomparison of mechanical properties of titanium and
cortical bone?
(1) Titanium is twice as stiff as bone
(2) Titanium has a higher modulus of elasticity than bone
(3) Bone has a higher modulus of elasticity than
titanium
(4) Titanium and bone have the same stiffness
(5) Titanium and bone have the same modulus of
elasticity
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Question 18
Which of the following is the best description of acomparison of mechanical properties of titanium and
cortical bone?
(1) Titanium is twice as stiff as bone
(2) Titanium has a higher modulus of elasticity than bone
(3) Bone has a higher modulus of elasticity than
titanium
(4) Titanium and bone have the same stiffness
(5) Titanium and bone have the same modulus of
elasticity
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Question 19
Compared to a stainless steel bone plate that is the samesize, the rigidity of a titanium plate is:
(1) Two times greater
(2) The same
(3) Half as great
(4) One-fourth as great
(5) One-eighth as great
Question 19
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Question 19
Compared to a stainless steel bone plate that is the samesize, the rigidity of a titanium plate is:
(1) Two times greater
(2) The same
(3) Half as great
(4) One-fourth as great
(5) One-eighth as great
Question 20
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Question 20
The modulus of elasticity of methylmethacrylate bonecement is:
(1) The same as that of polyethylene
(2) Between the values of cortical bone and cancellous
bone
(3) Between the values for cobalt-chromium alloy and
cortical bone
(4) Less than that of cancellous bone
(5) Less than that of cortical bone but greater than that
of cobalt-chromium alloy
Question 20
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Question 20
The modulus of elasticity of methylmethacrylate bonecement is:
(1) The same as that of polyethylene
(2) Between the values of cortical bone and cancellous
bone
(3) Between the values for cobalt-chromium alloy and
cortical bone
(4) Less than that of cancellous bone
(5) Less than that of cortical bone but greater than that
of cobalt-chromium alloy