Implementation of cyclic plasticity models based on a general form of kinematic hardening

This paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear, as well as non-linear, evolution of back stress. First, in order to incorporate such a general form of kinematic hardening in finite element methods, successive substitution and its convergence are discussed for implicitly integrating stress; moreover, a new expression of consistent tangent modulus is derived by introducing a set of fourth-rank constitutive parameters into discretized kinematic hardening. Then, the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening; the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation. Numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness. Error maps for implicitly integrating stress under non-proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large, Copyright (C) 2002 John Wiley Sons, Ltd.