Formulation of Anisotropic Constitutive Equations

Abstract

This chapter is concerned with the formulation of constitutive expressions of the form

$$$$

(1)

where d_ij = (v_i,j + v_j,i)/2 are the cartesian components of the so called “rate-of-deformation tensor” $$. Other common names are the “rate-of-strain” or “strain-rate-tensor”. Note that d_ij is linear in the velocity components v_i, and that this linearity is exact and no approximation has been made in deriving it. Furthermore, the tensor $$ is not to confuse with the “material time derivative” $$ of the infinitesimal strain tensor ε_ij = (u_i,j + u_j,i)/2, because we have [I]:

$$$$

.