Mechanical Properties of Biological Materials

Chapter 14

KINE 3301Biomechanics of Human Movement

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 (), strain () and Young’s modulus ().

𝜎=𝐹𝐴𝜎=

3000𝑁.000358𝑚2

8,379,888 Pa or 8.38 MPa

𝜀=∆ 𝐿𝐿𝑜

𝜀=.0005𝑚.42𝑚

.00119 or .119% or 1,190 microstrain

𝛾=𝜎𝜀 𝛾=

8,379,888𝑃𝑎.00119

7.04 x 109 Pa

Effects of Shear Forces on Deformable Bodies

Shear ForceA 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

𝑆𝑡𝑟𝑎𝑖𝑛=∆ 𝐿𝐿𝑜

• is the change in length (amount of deformation).• 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 (), strain () and Young’s modulus ().

𝜏=𝐹𝐴

𝜏=600𝑁

.000358𝑚2

𝜀=∆ 𝐿𝐿𝑜

𝜀=.0005𝑚.42𝑚

𝛾=𝜎𝜀

𝜏=1,675,977𝑃𝑎 .00119

𝛾=1,675,977𝑃𝑎.00119

𝛾=1.4 𝑥109𝑃𝑎

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=−𝑘𝑥The 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

CreepCreep 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.