Dawn Leger

Mechanical Properties of Biological Tissues

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:

Stress and Strain

\sigma =\sigma \left(\epsilon \right).

Introduction to Dynamics

Equation (15.1) 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 E of the material (Fig. 15.1):

Multiaxial Deformations and Stress Analyses

\sigma =E\epsilon .

Basic Biomechanics of the Musculoskeletal System

In Chap. 8, Newton’s second law of motion is presented in the form of “equations of motion.” In Chap. 10, the concepts of work and energy are introduced. Based on the same law, “work-energy” and “conservation of energy” methods are devised to facilitate the solutions of specific problems in kinetics. In this chapter, the concepts of linear momentum and impulse will be defined. Newton’s second law of motion will be reformulated to introduce other methods for kinetic analyses based on the “impulse-momentum theorem” and the principle of “conservation of linear momentum.” These methods will then be applied to analyze the impact and collision of bodies.