Orthotropic model for metallic sheets in finite elasto-plasticity

In this paper we develop a model, with internal variables, small elastic strains, large elastic rotations and plastic deformations, within the constitutive framework of finite (multiplicative) elasto-plasticity, in Eulerian description. The orthotropic initial anisotropy for sheets and evolving anisotropy are involved in the model. We pay attention to the full description of the model, not only on the anisotropic yield criteria. The boundary value problems, which describe at every time t the metal forming processes for sheets, lead to solve an appropriate variational inequality, for the velocity field and the plastic multiplier considered to be unknowns of the quasi-static problem.