Universal anisotropic yield criterion based on superquadric functional representation: Part 1. Algorithmic issues and accuracy analysis

Abstract

A robust and efficient stress update algorithm for the anisotropic yield criterion represented in the form of superquadric function introduced by Barlat et al. is presented. It relies on a discrete variational formulation of the Lagrangian functional which results from the principle of maximum plastic dissipation. Numerical solution of the discretized equations of evolution is based on the operator split methodology and the Newton-Raphson method. A line search algorithm is implemented to overcome numerical instabilities and to expand the convergence region of the basic Newton-Raphson solution procedure. The consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discrete Kuhn-Tucker condition. Numerical testing of the integration algorithm based on iso-error maps is provided for several variants of the yield function.