Numerical model of finite deformation non-isotropic elasto-plastic materials with evolving structural tensors

The paper deals with a constitutive model for finite deformation anisotropic elasto-plasticity and a numerical integration procedure used for its implementation in a FE code. The model is developed within the framework of the multiplicative decomposition of the deformation gradient and of the theory of the structural tensors. One of the main goal of the paper is to analyze the extension of finite deformation plasticity to the case that material directions can evolve. It is shown that the driving force for the evolution of the anelastic deformation is not the classic stress, rather a thermodynamic force where the stress is corrected for a term caused by the transformation of the material directions due to plastic deformations. Two scenarios can arise, one in which the material directions do not evolve, and the other in which the material directions can evolve due to anelastic phenomena. With reference to fiber materials, we examine, in particular, a model characterised by the same structural tensors for both the elastic and the plastic potentials, focusing on the irreversible evolution of the structural tensors; some simple examples show how the model can be applied to fiber materials. The numerical model is thermodynamically consistent and is based on a Full Tensorial Algorithm for the integration of the local constitutive equation. Infact the usual exponential algorithms adopted in plasticity cannot be applied when the principla directions of stress and deformation do not coincide.