Constitutive Equation: General Principles

Abstract

In this chapter, we learn that the constitutive equation relates the fluid kinematics to the stresses, and that must be supplied together with the conservation equation plus relevant boundary conditions to define a well-posed problem. Finding a relevant constitutive equation forms the central part of rheology. We learn that there are two alternative to the constitutive modeling: a continuum or a microstructure approach. In the remainder of the chapter, we learn that the continuum approach must satisfy certain principles, including the principles of material objectivity and local action. These limit the types of kinematics variables that can go into the constitutive relation. In addition, we learn how the material symmetry group may place additional constraints on the constitutive equation. We learn how to derive some classic constitutive equation, including the simple fluid, the isotropic elastic material, the order fluid as an approximation to simple fluid at catastrophic memory.