Stress computation and consistent tangent operator using non‐linear kinematic hardening models

One possibility of formulating the tinite element method is founded on the principle of virtual displacement, in which we want to include a rate‐independent elastoplastic constitutive model based on the assumption of a yield surface. The constitutive equations result from the assumptions of small deformations, Hooke's law for the elastic domain, the normality rule for the evolution of plastic strains, the von Mises yield condition and a special kind of kinematic hardening due to Armstrong and Frederick,¹ in which linear kinematic hardening is generalized with a saturation term. We show that it is not generally recommendable to propose large load steps. To this end, we investigate the influences of the non‐linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator. The main topics of this paper are: (1) development of a problem‐optimized backward Euler method with regard to the kinematic hardening model, (2) study of the influence of the saturation term on the numerical accuracy through isoerror maps and (3) computation of the consistent elastoplastic tangent operator.