TABLE OF CONTENTS In this chapter we will develop relationships between stress and strain for several types of material behavior. We begin with a general discussion of material behavior and then proceed to develop stress-strain relationships for elastic materials that are isotropic. This is followed by a discussion of anisotropic materials and the development of stress-strain relationships for several classes of these materials. We then develop some simple stress-strain models for viscoelastic materials and perfectly plastic materials. Next we develop stress-strain relationships for problems in which the temperature is not uniform. Finally we discuss piezoelectric materials and develop their constitutive equations. The reader should be aware that in Sections 4-5 and 4-13-2 use is made of certain results that are obtained in Chapter 5.
In Chapter 2 we derived relationships between the various stresses acting on an element of material by invoking Newton's second law, and in Chapter 3 we introduced the concept of strain and developed relationships between the strains and the displacement components. It is worthwhile pointing out that in deriving the equations of motion and the strain-displacement relations, the only restrictions placed on the quantities involved are that the stresses and displacements be continuous functions of position and that the strains be infinitesimal. Since these equations were developed without the need to consider any specific material or material behavior, they are valid for all materials and material behaviors.
We note, however, that we are still faced with a situation where the number of unknowns in our problem exceeds...
