A uniquely defined multiplicative elasto-plasticity model with orthotropic yield function and plastic spin

Abstract

A rate-independent model for isotropic elastic–orthotropic plastic material behaviour including the plastic spin is presented in this paper. The plastic spin, as introduced by Dafalias, is the spin of the continuum relative to the material substructure. The model is based on a specific multiplicative decomposition of the deformation gradient tensor, which introduces a uniquely defined intermediate configuration as motivated by Casey. We focus our attention on metal sheets in forming processes, in which pre-existing preferred orientations govern the orthotropic plastic behaviour. As a result, we advocate a Hill-type yield criterion enriched by the notion of plastic spin to describe this material behaviour. Our formulation yields three key findings: firstly, the uniquely defined intermediate configuration, namely a plastically stretched intermediate configuration, allows for a neat implementation of the plastic spin; secondly, the algorithmic formulation is straightforward and shows no additional difficulties in the implementation; and thirdly, a good agreement of our numerical model with experimental and numerical results from in-plane sheet forming processes reported in the literature is achieved.