Internal variable formulation for perfectly plastic and linear hardening relations in plasticity

In this paper we consider a simple internal variable model of plasticity, with particular emphasis on the case of isotropic hardening. We show that, for this case, the formulation involving sign constrained internal variables appropriate for uniaxial behaviour and piecewise linear yield surfaces can be modified by a simple transformation to provide a formulation which is applicable to continuously differentiable yield surfaces and which is in accord with the conventional formulation. The utility of the internal variable formulation is demonstrated by its application to incremental relations; the incremental relations are given explicityly for a J2 yield surface.