  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.
