Constitutive Equations

To complete the mechanical model, we still need to define a constitutive law that describes the stress tensor \(\boldsymbol{\sigma }\) . For simplicity, and to expose the fundamental behavior of the system clearly, we consider a class of simple, fundamental, linear models. To set up our multidimensional constitutive equations, we start by describing the standard model variants in one space dimension, and then generalize from there.