A return mapping algorithm for cyclic viscoplastic constitutive models

This paper presents a return mapping algorithm for cyclic viscoplastic constitutive models that include material memory effects. The constitutive model is based on multi-component forms of kinematic and isotropic hardening variables in conjunction with von Mises yield criterion. Armstrong–Frederick (A–F) type rules are used to describe the nonlinear evolution of each of the multi-component kinematic hardening variables. A saturation type (exponential) rule is used to describe the nonlinear evolution of each of the isotropic hardening variables. The concept of memory surface is used to describe the strain range dependent material memory effects that are induced by the prior strain histories. In this paper, the above class of cyclic viscoplastic constitutive models is formulated within a consistent thermodynamic framework that encompasses the standard generalized materials framework. Furthermore, a complete algorithmic treatment of the above rate-dependent constitutive model is also presented for any desired stress or strain constrained configuration subspace. A generalized midpoint algorithm is used to integrate the rate constitutive equations. The consistent tangent operator is obtained by linearizing the return mapping algorithm, and is found to be unsymmetric due to the presence of nonlinear evolution rules for the kinematic hardening variables. Several numerical examples representing the cyclic hardening and softening behavior, transient and stabilized hysteresis behavior, and the non-fading memory effects of the material are presented. These examples demonstrate the accuracy and robustness of the present algorithmic framework for modeling the cyclic viscoplastic behavior of the material.