Yield criteria for quasibrittle and frictional materials: a generalization to surfaces with corners

Convexity of a yield function (or phase-transformation function) and its relations to convexity of the corresponding yield surface (or phase-transformation surface) is essential to the invention, definition and comparison with experiments of new yield (or phase-transformation) criteria. This issue was previously addressed only under the hypothesis of smoothness of the surface, but yield surfaces with corners (for instance, the Hill, Tresca or Coulomb-Mohr yield criteria) are known to be of fundamental importance in plasticity theory. The generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase-transformation surfaces is provided in this paper, together with the (necessary to the proof) extension of a theorem on nonsmooth elastic potential functions. While the former of these generalizations is crucial for yield and phase-transformation condition, the latter may find applications for potential energy functions describing phase-transforming materials, or materials with discontinuous locking in tension, or contact of a body with a discrete elastic/frictional support.