STRESS COMPUTATION AND CONSISTENT TANGENT OPERATOR USING NONLINEAR KINEMATIC HARDENING MODELS

One possibility of formulating the finite 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 assumpt ion of a yield surface. The constitutive equations result from the ass umptions of small deformations, Hooke's law for the elastic domain, th e normality rule for the evolution of plastic strains, the von Mises y ield condition and a special kind of kinematic hardening due to Armstr ong and Frederick,1 in which linear kinematic hardening is generalized with a saturation term. We show that it is not generally recommendabl e to propose large load steps. To this end, we investigate the influen ces of the non-linear kinematic hardening model on the stress computat ion and the resulting consistent elastoplastic tangent operator. The m ain topics of this paper are: (1) development of a problem-optimized b ackward Euler method with regard to the kinematic hardening model, (2) study of the influence of the saturation term on the numerical accura cy through isoerror maps and (3) computation of the consistent elastop lastic tangent operator.