On the convexity of yield and potential surfaces in rotational hardening critical state models

This article shows that a common formulation often used for an anisotropic modified cam clay yield and potential surface with a modified Lode angle dependency may become concave for high values of anisotropy. Concave surfaces are undesirable in plasticity theory and could lead to numerical problems. To remediate this problem the article suggests a formulation for the Lode angle dependency that will not suffer from concavity. The suggested formulation is discussed. The formulation does not introduce any additional parameters for Lode angle dependency than that used to describe Lode angle dependency of an isotropic yield surface. In this paper, a generalized continuous Mohr–Coulomb criterion is used that allows a π-plane cross-section to take the shape of several criteria including Mohr-Coulomb, Matsuoka-Nakai and Lade-Duncan.