Introduction

The kinematic relations developed in Chapter 3, and the principles of conservation of mass and momenta and thermodynamic principles discussed in Chapter 5, are applicable to any continuum irrespective of its physical constitution. The kinematic variables such as the strains and temperature gradient, and kinetic variables such as the stresses and heat flux were introduced independently of each other. Constitutive equations are those relations that connect the primary field variables (e.g., ρ, T, x, and u or v) to the secondary field variables (e.g., e, q, and σ). In essence, constitutive equations are mathematical models of the behavior of materials that are validated against experimental results. The differences between theoretical predictions and experimental findings are often attributed to inaccurate representation of the constitutive behavior.

A material body is said to be homogeneous if the material properties are the same throughout the body (i.e., independent of position). In a heterogeneous body, the material properties are a function of position. An anisotropic body is one that has different values of a material property in different directions at a point, that is, material properties are direction-dependent.