Plastic spin associated with a corner theory of plasticity
The paper deals with a corner theory in the framework of finite elasto-plasticity with small elastic deformations. The author proposes two models for plastic spin with a clear loading-unloading criterion. The first model extends the \(J_2\) Gotoh corner theory to include the kinematic hardening. An expression for the plastic spin is derived from Wang's representation theorem for skew-symmetric tensor-valued isotropic function, which depends on the stress, objective stress rate, and back stress. In the second model the plastic spin is represented as a skew-symmetric tensor generator associated with the noncoaxial tensors (the stress and the plastic rate of deformations). Large elasto-plastic deformation analysis is carried out in simple shear according to the proposed models. The author emphasizes that for isotropic hardening the models are identical, while for kinematic hardening an acceptable physically reasonable behaviour is obtained only when the plastic spin is prescribed by the second model. The finite element formulation is used in the rate-type principle of virtual work to analyse the shear band formation when the plastic spin is predicted by the second model. The numerical results show a principal predictive feature of the plastic spin developed in the paper.
skew-symmetric tensor-valued isotropic function
scientific article; zbMATH DE number 834223