Does convexity of yield surfaces in plasticity have a physical significance?

Abstract

Convexity of a function or set is an often needed and important mathematical property. In the case of yield functions [Formula: see text] (or elastic ranges) in terms of stresses, almost all empirical and mechanism-based yield functions have this property. However, requiring positive plastic dissipation does not necessarily exclude non-convex yield functions, which is confirmed by the fact that non-convex yield functions are observed experimentally, although this rarely happens. We therefore ask whether this nice mathematical property reflects a physical material property. This is investigated in an elastic–plastic, small strain, 2D setting. It appears that, at least in this setting, no specific material property can be attributed to the convexity of the yield function.