Numerical aspects of a non-proportional cyclic plasticity model under plane stress conditions

The objective of this paper is the investigation of the in uence of a material model representing nonproportional loading conditions with respect to cyclic plasticity phenomena on several plane boundary-value problems and the development of the corresponding stress algorithm. This material model, developed by Haupt and Kamlah,1 contains linear isotropic elastic behaviour, a von Mises yield function, an associated ow rule, non-linear kinematic hardening of Armstrong and Frederick type, a modi ed arc-length representation considering cyclic plasticity phenomena and the inclusion of non-proportional hardening e ects. These rate-independent constitutive equations are based on the assumption of small strains. The boundary-value problem will be solved by the nite element method including investigations of a semi-analytical computation of the consistent tangent operator. Concluding examples will show non-proportional hardening e ects as well as inhomogenization phenomena stated by Luhrs and Haupt2 for specimen under uniaxial cyclic loading.