Anisotropic Scalar Constitutive Equations and Corresponding Models of Viscoplastic Flow

Abstract

The tensor linear anisotropic constitutive relations of incompressible viscoplastic flow connecting the stress deviator and strain rates and the following scalar relation connecting the quadratic stress invariant and the hardening function are considered. In the case of a perfect plastic material, the latter relation is an anisotropic Mises–Hencky quadratic criterion of plasticity. The mutual dependence of the fourth-rank tensors involved in tensor and scalar constitutive relations is established. As an illustration, the results are given for an orthotropic material.