Chapter 3 - Joint and Materials Mechanics

1
Chapter 3 - Joint and Materials Mechanics
Artificial hips
Shoe impact tester
2
Joint Motion

• Anatomical Position
• Planes
• Sagittal
• Frontal
• Transverse

3
Mobility and ROM

• ROM joint person specific
• Injuries excessive ROM
• Factors affecting ROM
• Shape and geometry of articulating surfaces
• Joint capsule and ligaments
• Surrounding muscles
• Apposition of body parts
• Joint Stability

4
Lever Systems
R
F

• Rigid rod fixed at point to which two forces are
  applied
• 1st class
• 2nd class
• 3rd class
• Functions
• ? applied force
• ? effective speed

F
R
F
R
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Instantaneous Joint Center

• Caused by asymmetries in the joint motion
• Basic movements
• rotation
• sliding
• rolling

6
Moment of Force Joint Motion

• Moment F d?
• Moment muscular activity, essential for
  controlling joint motion
• Theory actions at joints can be represented by
  the resultant joint force and the resultant joint
  moment

7
Resultant Joint Force vs Bone-on-Bone Forces

• RJF Net force across the joint produced by bone,
  ligaments, muscle etc.
• Bone-on-Bone more complex calculation

8
Material Mechanics

• Rigid body mechanics body segments are
  considered rigid structures (non-deformable)
• fixed center of mass
• homogeneous material
• Used to analyze movements
• Easier to model and provide a reasonable
  approximation

9
Deformable solids

• Segment or tissue analyzed undergoes deformation
• More complicated analysis and difficult to model

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Material Properties

• Basic properties
• Size
• Shape
• Area
• Volume
• Mass
• Derived
• Density
• Centroid

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Stress

• Stress (?) internal resistance to an external
  load
• Axial (compressive or tensile) ?F/A
• Shear ? F/A (parallel or tangential forces)
• Units Pascal (Pa) 1Nm2

Axial
Shear
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Strain

• Change in shape or deformation (?)
• Absolute strain
• Relative strain
• ??L/Lo

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Stress Strain

• Stress-strain ratio stiffness or compliance of
  the material
• E ?/ ?
• Linear material
• Hooke law ? E ?
• Biological material non-linear due to its tissue
  fluid component (viscoelastic properties)

A
?
B
?
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Uniaxial Loading

• Simplest form forces applied along single line
  typically the primary axis
• compressive
• tensile
• shear
• Stress-strain curve
• Linear region (?B)
• elastic limit (?C)
• yield point (?D)
• ultimate stress (?E)
• Rupture (?F)
• Energy stored (area)

?E
?D
?F
?C
?B
?
?
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Poissons effect
Force

• When a body experiences an uniaxial load its
  axial transverse dimensions will change,
• v -(?t/ ?a)

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Multiaxial Loading

• Deformation in all three directions
• Net effect of the strains
• Shear stresses

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Bending

• Long bones beams
• Compressive stress inner portion
• Tensile stress outer portion
• Max stresses near the edges, less near the
  neutral axis

T
C
axis
axis
y
?x(Mby)/I
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Bending Moments

• Shear stresses max at neutral axis and zero at
  the surface
• ? (QV)/(I b)
• Q area moment
• V vertical shear force

Q
y
h
b
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Bending

• Three point bending
• failure at middle
• ski boot fracture
• Four point bending
• failure at the weakest point between two inside
  forces

20
Bending

• Cantilever bending
• Compressive force acting off-center from long axis

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Torsion

• Twisting action applied to a structure
• Resistance about long axis determined by polar
  moment of inertia
• J?(r4o-r4i)/2
• Shear stress along the shaft ?(Tr)/J
• Twist angle ?(Tl)/(GJ)

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Torsion

• Larger radius of the shaft, greater resistance
• Stiffer the material harder to deform
• In addition to shear stress, normal stress
  (tensile compressive) are produced in a helical
  path (spiral fractures)

r
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Viscoelasticity

• Provided by the fluid component in biological
  tissue
• Resistance to flow
• Affects stress-strain
• Increase in strain rate produces-increases
  stiffness of the material

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Viscoelasticity

• Pure elastic material
• strain energy returned
• no energy loss
• Viscoelastic tissues
• lose energy due to heat
• energy is not returned immediately
• Resilient
• Dampened
• Hysteresis area representing energy lost

Elastic
Load
?
Non
unload
?
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Viscoelasticity
creep

• Creep response
• Stress-relaxation response
• Effects of strain-rate on stress relaxation

?
?
Time
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Material Fatigue Failure
Initial cycle effect

• Fatigue repeated loads above a certain threshold
• Continued loading failure
• First cycle effect shift in mechanical response

1
2
3
n
?
?
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Material failure

• Distribution of stresses
• Discontinuity (stress risers)
• fractures sites
• screws
• osteotendinous junctions
• Ductile vs Brittle materials
• Failure theories
• maximal normal stress
• maximal shear stress
• maximal energy distortion

28
Biomechanical Modeling Simulation

• Model representation of one or more of an
  objects or systems characteristics using
  mathematical equations
• Goal
• improve understanding of a system
• Simulationprocess of using validated model

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Biomechanical Modeling Simulation

• Physical model simulates actual conditions,
  crash test dummies
• Mathematical or computer model conditions are
  represented using mathematical equations

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Why use a model?

• Easy to duplicate
• Easy to make change in the system
• Time
• Economic factor

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How to select a model?

• What questions is being posed?
• Type molecular, tissue, organ etc.
• Deformable or rigid
• finite or continuoum
• static, quasi static or dynamic

• Linear or nonlinear
• 2D or 3D
• Determined or stochastic
• kinematics or kinetics
• inverse or direct

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Model Simulations

• Models are simplifications of actual situations
• Model and simulation are as good as the data use
  as input
• Stability of the model (range of values)

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Finite-element modeling

• Structures are represented as simple blocks
  assembled to form complex geometrical structures
• Connected at poinst (nodes) forming a mathetical
  representation of the structure
• Forces are applied at the structure and stress
  and strain are predicted
• Complex and requires a great deal of computing
  power

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Finite modeling
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Rheological Models

• Study of deformation and flow of matter
• Use to model biological tissue
• Interrelate stress, strain, and strain rate
• Three types
• Linear spring
• dashpot
• frictional
• Linear spring
• elastic properties of tissue

?
?
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Rheological Models

• Dashpot
• loading response that is strain rate dependent
• fluid viscosity (newtonian fluid)
• ? ??
• Frictional element
• Combinations of models

?
?
Strain rate
?
?