Numerical implementation of a novel accurate stress integration scheme of the von Mises elastoplasticity model with combined linear hardening

Recently, the authors proposed a new integration scheme for the von Mises elastoplasticity model with combined linear isotropic-kinematic hardening. In this paper, the numerical accuracy and the computational efficiency of this method are examined in detail. In addition, the key issues of its numerical implementation are also discussed. The main advantage of the novel approach is that it is based on an exact solution of the governing rate constitutive equations. However, it should be noted that computationally the most expensive part of the novel stress update formulas is the inversion of an incomplete beta function, for which task, an efficient and accurate method was developed, based on nested derivatives. In order to evaluate the computational performance of the new scheme with regards to in finite element (FE) calculations, the method was implemented in the commercial FE software package ABAQUS/Standard via its UMAT material interface. The numerical accuracy and computational speed of the new integration technique were compared to the ABAQUS internal stress integration scheme by solving some FE examples. Based on the results of these numerical experiments one can conclude that the new method is faster than the ABAQUS internal scheme if higher accuracy is required. This advantage shows the usefulness of the new method in elastic–plastic FE calculations.