Chapter 6 - Constitutive Relations

Abstract

This chapter considers the remaining pieces of information we need in order to examine the thermomechanics of a metamorphic system, namely, the nature of the material that is deformed. This means we need relations between the stress, the heat flow, the deformation gradient and the stretching tensor. These relations are called constitutive relations. They take the same place in mechanics as do equations of state in chemical equilibrium thermodynamics. In general other constitutive relations involving fluid flow and chemical reactions are required but these are left to Section B. We discuss the restrictions that thermodynamics places on the form of constitutive relations in order that they are thermodynamically admissible. These restrictions are expressed as the Coleman-Noll procedure. Examples of the common thermomechanical constitutive laws are given including elasticity, plasticity and viscosity. An important application is the development of anisotropy during crystal plastic deformation where the purely plastic yield surface and the rate-dependent flow surface are considered.