A Cross Integration for von-Mises Plasticity Along with Nonlinear Isotropic Hardening and Lemaitre Damage Model

Abstract

What lies at the core of an elastoplastic finite element analysis is updating the stress and its related plastic variables. The process is carried out through integrating an array of elastoplastic fundamental relationships, which are typically called constitutive equations. The complex essence of such relations as well as the usual lack of analytical closed-form solutions to these problems compels the use of numerical solutions. The research considers the von-Mises plasticity model coupled with nonlinear isotropic hardening and Lemaitre damage mechanics. Subsequently, a new algorithm is constructed based on the explicit and implicit Euler schemes to update the stress and the related internal parameters. Finally, a wide range of numerical tests are conducted in order to evaluate the correctness, precision and the performance of the proposed method. The obtained results demonstrate an appreciable precision and efficiency for the derived integration.