Phenomenological evolution equations for the backstress and spin tensors

Summary A formulation of a constitutive model involving a new kinematic hardening rule is presented in the Eulerian reference system. The corotational stress and backstress rates involving spin tensors are discussed and incorporated in the evolution equations. The backstress evolution model is compared with other models and is found to be decomposable into a model that consists of two backstresses whose evolution is independent of each other.The elasto-plastic stiffness tensor is derived for all the models considered. It is shown in the proposed backstress evolution model we obtain an implicit system of differential equation in the stress and backstress rates. The theory is applied to two yield functions: one of the von-Mises type and the other of the anisotropic type. It is shown that for both these yield criteria the stress evolution is independent of the stress rate. As an example, the torsion of a cylindrical bar with fixed ends is investigated.