Computational aspects of anisotropic finite strain plasticity based on the multiplicative decomposition

Abstract

The paper is concerned with the computational aspects of two different models for anisotropic multiplicative finite strain plasticity. The first model is based on the idea that Fp, which defines the plastic part of the multiplicative decomposition, is a material tensor. The free energy function is then formulated using the elastic strain measure Ce together with structural tensors defined at the reference con- figuration [1]. In the second formulation, non-symmetric modified structural tensor are utilized together with the strain measure Ce, following [2]. The second formulation prove to be invariant with respect to rigid body rotations superimposed on Fp. In both formulations a Hill-type yield criterion, described by the material non-symmetric stress tensor and further structural tensors, is utilized. However, there is difference in the form of the stress tensor which the help of which, the yield function is defined. While in the first formulation we use Eshelby-like stress tensor, in the second, a modified stress tensor is applied. The integration of evolution equations is performed using the exponential map which preserves plastic incompressibility. However, the multiplicative nature of the formulations makes the numerical procedures quite involved. Nonetheless, consistent linearisations of the formulations are achieved by recognising various implicit dependencies of the variables involved. Corresponding expressions related to the local iteration and the tangent operator are presented. The interrelation of the two different formulations is demonstrated by numerical examples. In details, the formulations differ from those recently reported in the literature ([3], [4], [5]).