Convexity studies of two anisotropic yield criteria in principal stress space

Two anisotropic yield criteria, that employ quadratic stress functions and have been extensively used for the elastoplastic analysis of composite materials, are considered. Proposed by Hoffman and by Sun, both these criteria have been formulated using nine parameters. With appropriate choice of parameters they reduce to the well‐known isotropic von Mises criterion and the anisotropic Hill criterion. This paper investigates the convexity, which is an essential condition for any plasticity model, for these criteria in the principal stress space. In each case two orthogonal sections ‐ deviatoric and volumetric ‐ are used to study the shapes of the ensuing curves. Illustrative three‐dimensional plots are included. It is concluded that, while simple interrelationships between the parameters ensure convexity of the Hoffman criterion, conditions for the Sun criterion are quite stringent.