Mechanical Properties of Biological Tissues

Abstract

The material response discussed in the previous chapters was limited to the response of elastic materials, in particular to linearly elastic materials. Most metals, for example, exhibit linearly elastic behavior when they are subjected to relatively low stresses at room temperature. They undergo plastic deformations at high stress levels. For an elastic material, the relationship between stress and strain can be expressed in the following general form:

$$\sigma = \sigma (\varepsilon )$$

((9.1))

Equation (9.1) states that the normal stress σ is a function of normal strain ε only. The relationship between the shear stress τ and shear strain γ can be expressed in a similar manner. For a linearly elastic material, stress is linearly proportional to strain, and in the case of normal stress and strain, the constant of proportionality is the elastic modulus ε of the material (Figure 9.1):

$$\sigma = E\varepsilon $$

((9.2))

While investigating the response of an elastic material, the concept of time does not enter into the discussions. Elastic materials show time-independent material behavior.