One-Dimensional Constitutive Theory

Abstract

In this chapter, the concept of a thermomechanical constitutive model is introduced. Such a model is used to relate the kinematic variables to the kinetic variables in a solid subjected to thermomechanical loading. Because the constitutive behavior of real materials can be quite complicated, a series of constitutive models has been developed historically, and these models increase in mathematical complexity as more physically intricate behavior of materials is encompassed within the models. Because this mathematical complexity is quite challenging, the models to be developed in succeeding chapters in three dimensions are presented in this chapter in one-dimensional form as a means of introducing this subject in as mathematically and physically simple a form as possible. Accordingly, one-dimensional models are introduced for elastic, viscous, elasto-plastic, viscoelastic, and viscoplastic media. In addition, the effects of moisture and temperature on one-dimensional constitutive behavior are discussed. Finally, experimental techniques for obtaining material properties necessary for characterizing one-dimensional constitutive equations are detailed in this chapter.