9'1 Viscoelasticity

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Chap 9 . Mechanical Properties of Biological
Tissues
9.1 Viscoelasticity

• Linearly elastic material

• Complete recovery after the load is removed.
• Youngs modulus, elastic modulus or stiffness, E
• Stiffer material vs. more compliant material

• Hookes law

• Viscoelastic material

• (Viscous) (Elastic)
• Viscosity measure of resistance to flow (fluid
  property)
• Elasticity solid property
• Loading rate, Deformation rate
• Polymer plastics, most biological materials(soft
  tissue, bone, etc)
• Stress-strain relationship

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9.2 Analogies Based on Springs and Dashpots

• Linear spring

• Elastic solid

k
E
x
E
k
1
1
Hookes law
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9.2 Analogies Based on Springs and Dashpots
(continued)

• Dashpot

• Newtonian fluid (linearly viscous fluid)

Damping force is directly proportional to the
speed.
Shear stress is directly proportional to the
strain rate.
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1
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9.3 Empirical Models of Viscoelasticity

• Vicoelastic material

• A constant applied force (stress) produces a
  constant deformation (strain) in a spring.
• A constant applied force (stress) produces a
  constant rate of deformation (strain rate) in a
  dashpot.
• The deformation in a spring is completely
  recoverable.
• The deformation in a dashpot is permanent.

• Dashpot Viscous fluid

• Spring Elastic solid

E

• Stress relaxation change of stress under a
  const deformation
• Creep change of deformation under a const
  loading

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9.4 Time-Dependent Material Response

• Creep change of deformation under a const
  loading

• Stress relaxation change of stress under a
  const deformation

• Oscillatory response oscillatory loading

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9.5 Comparison of Elasticity and Viscoelasticity

• Elastic material

• Unique relationship

• Viscoelastic material

• time-dependent
• speed as well as magnitude of the stress

increasing
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9.5 Comparison of Elasticity and Viscoelasticity
(continued)

• Elastic material

loading
unloading

• Viscoelastic material

U
R
Y
P
loading
unloading
Hysteresis loop for an elastic-plastic material
Hysteresis loop
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9.6 Common Characteristics of Biological Tissues

• Biological Tissues

• Living tissues are very difficult to determine
  material properties.
• Composite materials
• Nonhomogeneous and anisotropic
• Collagen to withstand axial tension
• Elastin elastic

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2
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9.7 Biomechanics of Bone

• Primary structural element of the human body.

9.7.1 Composition of bone

• Composite material
• Cortical or compact bone
• Cancelleous, trabecular or spongy bone
• Periosteum

9.7.2 Mechanical properties of bone

• Nonhomogeneous because of various cells and
  organic and inorganic substances
• Anisotropic
• Can resist rapidly applied loads better than
  slowly applied loads. (Stiffer and stronger at
  higher strain rates)
• Viscoelastic

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9.7 Biomechanics of Bone (continued)
9.7.2 Mechanical properties of bone (continued)

• Fast loading vs. Slow loading

• Longitudinal loading vs. Transverse loading

Fast loading
Longitudinal loading
slow loading
Transverse loading
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9.7 Biomechanics of Bone (continued)
9.7.3 Structural integrity of bone

• Wet vs. Dry

• Aging effect
• Density
• Strength and stiffness

Dry bone
Wet bone
9.7.4 Bone fractures

• Tensile fractures cancellous bones
• Compressive fractures vertebrae of the elderly,
  oblique fracture pattern
• Torsional fractures spiral oblique pattern
• Bending fractures butterfly fragments
• Fatigue fractures repeated mechanical stress

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9.8 Biomechanics of Tendons and Ligaments

• Tendons connection between muscle and bone
• Ligaments join bones and provide stability to
  the joints
• Tendons and ligaments are passive.
• (Muscle are active to produce mechanical force.)
• Tendons stiffer, higher tensile strength
• Uniaxial tension test

loading
unloading
0
0
0.05
0.1
0.05
0.1
Strain rate dependent ?-? curve for tendon
Hysteresis loop of stretching and relaxing of the
tendon