Modified Integration Method for Elasto-plastic Constitutive Relations in the Stress Space

Abstract

An analysis of accuracy of proposed algorithms for the integration of elasto-plastic constitutive relations is carried out in this paper. The well-known Backward-Euler return method is known to be unconditionally stable, but it is first-order accurate. And this can not consider the convective stress rates on the yield surface during the plastic deformation and can be a limitation in many cases of practical interest. The proposed algorithm is integrated analytically using integration by part and chain rule and then is applied to the 2-stage Lobatto IIIA with second-order accuracy. It has advantage that is able to consider the convective stress rates on the yield surface in the stress space. Finally, the presented isoerror maps demonstrate the better accurate properties of the proposed algorithm than those of the Backward-Euler return method irrespective of given strain increments.