A constitutive model for orthotropic elasto-plasticity at large strains

The paper presents a thermodynamically consistent constitutive model for elasto-plastic analysis of orthotropic materials at large strain. The elastic and plastic anisotropies are assumed to be persistent in the material but the anisotropy axes can undergo a rigid rotation due to large plastic deformations. The orthotropic yield function is formulated in terms of the generally nonsymmetric Mandel stress tensor such that its skew-symmetric part is additionally taken into account. Special attention is focused on the convexity of the yield surface resulting in the nine-dimensional stress space. Of particular interest are new convexity conditions which do not appear in the classical theory of anisotropic plasticity. They impose additional constraints on the material constants governing the plastic spin. The role of the plastic spin is further studied in simple shear accompanied by large elastic and large plastic deformations. If the plastic spin is neglected, the shear stress response is characterized by oscillations with an amplitude strictly dependent on the degree of the plastic anisotropy.