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

TL;DR

This paper extends the mathematical understanding of convexity in yield functions to include surfaces with corners, which are common in practical plasticity models, enhancing the theoretical foundation for material behavior analysis.

Contribution

It generalizes the convexity relationship between yield functions and surfaces to nonsmooth cases with corners, broadening the applicability of convexity criteria in material modeling.

Findings

Provides a generalized proposition linking convexity of functions and surfaces with corners.

Extends a theorem on nonsmooth elastic potential functions.

Facilitates analysis of materials with discontinuous or complex yield surfaces.

Abstract

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.