A simple orthotropic finite elasto-plasticity model based on generalized stress-strain measures

Abstract

In this paper we present a formulation of orthotropic elasto-plasticity at finite strains based on generalized stress–strain measures, which reduces for one special case to the so-called Green–Naghdi theory. The main goal is the representation of the governing constitutive equations within the invariant theory. Introducing additional argument tensors, the so-called structural tensors, the anisotropic constitutive equations, especially the free energy function, the yield criterion, the stress-response and the flow rule, are represented by scalar-valued and tensor-valued isotropic tensor functions. The proposed model is formulated in terms of generalized stress–strain measures in order to maintain the simple additive structure of the infinitesimal elasto-plasticity theory. The tensor generators for the stresses and moduli are derived in detail and some representative numerical examples are discussed.