Transcript Mechanical Properties of Biological Materials

KINE 3301
Biomechanics of Human Movement
Mechanical Properties of Biological
Materials
Chapter 14
Strength of Biological Materials
• The strength of biological materials is defined
by the ability of the material to withstand
stress without failure.
• The strength of a material is affected by:
– Microstructure
– Age
– Fluid content
– Type, direction and velocity of loading
Definitions: Stress, Strain, & Young’s Modulus
• Stress (σ or τ) is defined force per unit of area.
Stress quantifies the internal forces acting on the
object as a reaction to the external applied
forces. The units for stress are N/m2 or Pa.
• Strain (ε) is defined as the % change in
deformation of the object.
• Young’s Modulus (ϒ) is the slope of the stress –
strain curve of the material. It describes the
stiffness of the material. The units for Young’s
modulus are N/m2 or Pa.
Effects of Compression Forces on Deformable Bodies
Imagine applying a compression force on a soft deformable object
such as a marshmallow. The object would deform, compress and
the sides would bulge out, directly in proportion to the applied
force. This effect also occurs in rigid objects like a steel rod. The
internal forces acting on the object cause deformation.
Effects of Compression on a Rigid Object
Unlike a soft object, when a compression force is applied to a rigid object
the deformation may not be immediately observable. In the example
above the 20 N force causes deformation which is not visible. An increase
in the force to 40 N will eventually cause visible deformation as bending
occurs.
A runner experiences an impact force of 3000 N that causes the
0.42 m tibia to shorten (compress by 0.5 mm). The tibia has an
area of 0.000358 m2. Compute the axial stress (𝜎), strain (𝜀) and
Young’s modulus (𝛾).
𝐹
3000𝑁
𝜎=
𝜎=
𝐴
2
.000358 𝑚
𝜎 = 8,379,888 Pa or 8.38 MPa
∆𝐿
𝜀=
𝐿𝑜
.0005𝑚
𝜀=
.42𝑚
𝜀 = .00119 or .119% or 1,190 microstrain
𝜎
𝛾=
𝜀
8,379,888 𝑃𝑎
𝛾=
.00119
𝛾 = 7.04 x 109 Pa
Effects of Shear Forces on Deformable Bodies
Shear Force
A shear force is applied sideways to the material and it results in
parallel opposing forces. Examples of shear forces include:
When a pair of scissors cuts a material.
When a material is punched.
When a weight is held perpendicular
to the long axis of a bone.
Material Testing System
Images courtesy of Instron
Effects of Muscle Weakness
Strain is a Normalized Variable
∆𝐿
𝑆𝑡𝑟𝑎𝑖𝑛 =
𝐿𝑜
• ∆𝐿 is the change in length (amount of deformation).
• 𝐿𝑜 is the original length.
• Strain is dimensionless it quantifies the % of deformation
caused by the applied stress.
Young’s Modulus
• Young’s modulus is a measure of the material’s
resistance to deformation.
• Young’s modulus quantifies how much stress is
required to generate a give strain.
• It does not depend upon the size or shape of the
object, but only the material the object is composed of.
• Copper has a modulus of 120 x 109 Pa.
• Steel has a modulus of 200 x 109 Pa.
• Thus, steel is more resistant to deformation then is
copper.
In a takeoff for a long jump a 600 N horizontal force shears the tibia by 0.5 mm.
The tibia has an area of 0.000358 m2. Compute the shear stress (𝜏), strain (𝜀)
and Young’s modulus (𝛾).
𝐹
𝜏=
𝐴
𝜏=
600𝑁
.000358 𝑚2
𝜏 = 1,675,977 𝑃𝑎
∆𝐿
𝐿𝑜
𝛾=
𝜎
𝜀
.0005 𝑚
.42 𝑚
𝛾=
1,675,977 𝑃𝑎
.00119
𝜀=
𝜀=
𝜀 = .00119
𝛾 = 1.4 𝑥 109 𝑃𝑎
Effects of Muscle Weakness
Viscoelasticity
• When an elastic material
containing fluid is deformed the
return of the material to it’s
original shape is time delayed.
• Viscoelastic materials exhibit
both an elastic response and
viscous damping.
• Bones, tendons, ligaments,
cartilage, muscle, and skin are
all viscoelastic.
• Viscoelastic materials display
both a time dependent and rate
dependent response.
Stress – Strain for an Elastic Material
𝐹 = −𝑘𝑥
The force required to deform an elastic spring is
described by Hooke’s law, where x is deformation
and k is the spring stiffness.
Properties of a Viscoelastic Material
• The mechanical response of a viscoelastic
material are time and velocity dependent.
• Viscoelastic materials exhibit:
–
–
–
–
a hysteresis
a creep response
a force relaxation response
Are time dependent, if the force is held for a longer
time they exhibit greater hysteresis.
– A velocity dependent, stiffness of the material
increases with increasing velocity of loading.
Stress – Strain for a Viscoelastic Material
Creep
Creep is a time dependent
response of viscoelastic
tissues. The muscle-tendon
complex is loaded with a
weight. When the load is
initially applied the muscle
undergoes deformation.
Following this initial
deformation the muscle
continues to deform at a
much lower rate, this later
deformation is creep.
Force Relaxation
Force relaxation is a time
dependent response of
viscoelastic tissues. When
the muscle is stretched
the force (resistance to
stretch) rises rapidly. Then
when the stretch is held
the force (resistance to
stretch) slowly declines
over time, this is force
relaxation.