A Useful Theorem for Constructing Convex Yield Functions

Abstract

Known yield functions have been constructed in the three-dimensional space of principal stresses. Their convexity in the six-dimensional space of the stress components is only conjectured. Mathematical theorems of convexity are known for functions of Hermitian matrices but have not been applied to yield functions. In this paper, Drucker’s hypothesis is properly restated, leading to convexity requirement for yield functions of elastoplastic materials. Then a special version of a known convexity theorem is presented. The theorem can be applied to construct yield functions for isotropic materials. Examples of such applications are extended to some known yield functions and other theoretically acceptable new ones.