Implicit finite element implementation of Chaboche’s plasticity kinematic hardening model

This paper aims to present a comprehensive guideline for the implementation of Chaboche's plasticity kinematic hardening model in the context of finite element analysis. A detailed strategy for the resolution of the elastoplastic problem (return mapping) as well as for the computation of the consistent tangent operator are presented. Both 2D and 3D numerical implementation strategies are addressed. In the end, a few numerical examples are presented.In the context of cyclic plasticity, Chaboche’s kinematic hardening model is well-known once it is capable of properly capturing the Bauschinger effect. In spite of its relative simplicity, Chaboche’s model allows a good description of material nonlinearities for ductile metallic materials. In this setting, this paper aims to present a comprehensive guideline for the implementation of Chaboche's plasticity kinematic hardening model in the context of finite element analysis. A detailed strategy for the resolution of the elastoplastic problem (return mapping) as well as for the computation of the consistent tangent operator are presented. Both 2D and 3D numerical implementation strategies are addressed. In the end, a few numerical examples are presented demonstrating the accuracy and applicability of the methodology presented, where analytical solutions were used for validation. This paper also investigates the influence of the implicit integration strategy employed in the resolution of the elastoplastic equations showing that, for the material and loading conditions here assessed, results from a fully implicit integration scheme are nearly identical to those obtained by a standard trapezoidal rule.