A consistent plasticity theory of incompressible and hydrostatic pressure sensitive metals – II

The plasticity theory of incompressible and hydrostatic pressure sensitive metals presented in [Aretz, H., 2007. A consistent plasticity theory of incompressible and hydrostatic pressure sensitive metals. Mechanics Research Communications 34, 344–351] is further elaborated. In the present article the issue of the yield function’s convexity in the presence of a hydrostatic pressure sensitive yield stress is addressed. For the considered class of materials it is proven that even in the presence of pressure sensitivity the yield function must be convex in stress space if the dependence of the yield stress on hydrostatic pressure is linear. Constraints regarding higher-order dependences are provided. Furthermore, the framework is extended with respect to plastic compressibility thereby providing its applicability to a broad class of engineering problems.