A return mapping algorithm for a class of cyclic plasticity models

A return mapping algorithm for a class of cyclic plasticity models is presented. The constitutive model includes a quadratic yield criterion and multi‐component formulations of non‐linear isotropic and kinematic hardening. Thus, both initially isotropic and anisotropic materials can be described, and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained. The return mapping algorithm employs the closest point projection scheme in combination with a decomposition method, to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is derived in closed form, and is found to be unsymmetric due to the non‐linear evolution of the kinematic hardening terms. The accuracy and robustness of the algorithm are assessed through numerical examples.