Chapter 5 - Constitutive Modeling in Mechanics and Thermomechanics

Abstract

The constitutive equations for a particular material, together with the conservation laws of mass, linear momentum, angular momentum, and energy, govern the response of that material. Unlike the conservation laws, however, the constitutive equations vary from material to material. In other words, they depend on the physical behavior of the particular material being modeled. In this chapter, we provide a broad overview of constitutive modeling in mechanics and thermomechanics. We describe how the constitutive equations must satisfy the second law of thermodynamics, conservation of angular momentum, material symmetry requirements, and invariance under superposed rigid body motions. Special attention is devoted to determining how various kinematic, kinetic, and thermodynamic quantities transform under a superposed rigid body motion and, in turn, how these transformations can be used to develop appropriate invariance requirements. We also examine useful thermodynamic concepts in constitutive modeling, such as thermomechanical processes and Legendre transformations.