A model for finite strain elasto-plasticity based on logarithmic strains: Computational issues

Abstract

In the context of general isothermal processes, issues related to the constitutive modelling and computational treatment of finite deformation elasto-plasticity are examined employing logarithmic stretches as strain measures. A strain-energy function for isotropic elastic materials is proposed, which leads to a linear stress-strain relation and constant and isotropic elastic modulus in material setting. It is assumed that isotropy is maintained in the intermediate configuration which necessitates a representation of the plastic flow based on the scalar internal variables. By exploiting the main features of the present approach, expressed through the simple hyperelastic constitutive model in conjunction with notions of multiplicative decomposition of the deformation gradient and unstressed configuration, a computationally effective framework is formulated. It is pointed out that in this context, an algorithm could be proposed for rate-independent finite strain elasto-plasticity, which is exact for elastic processes and in the limit of non-hardening, deviatoric elasto-plasticity is in accordance with physical observations. Large elasto-plastic deformations at moderate elastic strains are examined within the approximation theory and displacement based finite element formulation of the boundary value problem proposed. Numerical analysis is performed for a realistic example capturing shear band localisation and the results are compared with experimental data.