Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures

In this paper we present a model and a fully implicit algorithm for large strain anisotropic elasto-plasticity with mixed hardening in which the elastic anisotropy is taken into account. The formulation is developed using hyperelasticity in terms of logarithmic strains, the multiplicative decomposition of the deformation gradient into an elastic and a plastic part, and the exponential mapping. The novelty in the computational procedure is that it retains the conceptual simplicity of the large strain isotropic elasto-plastic algorithms based on the same ingredients. The plastic correction is performed using a standard small strain procedure in which the stresses are interpreted as generalized Kirchhoff stresses and the strains as logarithmic strains, and the large strain kinematics is reduced to a geometric pre- and post-processor. The procedure is independent of the specified yield function and type of hardening used, and for isotropic elasticity, the algorithm of Eterović and Bathe is automatically recovered as a special case. The results of some illustrative finite element solutions are given in order to demonstrate the capabilities of the algorithm.