A PLANE-STRAIN FORMULATION OF THE ELASTIC-PLASTIC CONSTITUTIVE LAW FOR HARDENING VON MISES MATERIALS

Elastic-plastic (path dependent but time-independent) materials, linear and isotropic in the elastic range and governed by the von Mises yield condition and the relevant associated flow rule, are considered. Both kinematic and isotropic hardening are included. Starting from previous, more general but partial, results and exploiting the purely deviatoric nature of plastic flow, a plane strain version of the constitutive law is formulated in terms of in-plane variables only. The actual plastic strains are replaced by equivalent in-plane measures and the effects of transverse yielding appear as a fictitious, directional kinematic hardening. On this basis, the plane strain elastic-plastic problem can be formulated in a way fully analogous to the equivalent plane stress one: as in the elastic case, differences are confined to the expressions of the constitutive parameters.