Return-mapping algorithms for associative isotropic hardening plasticity using conic optimization

Abstract

We present a mathematical programming approach for elastoplastic constitutive initial value problems. Consideration of the associative plasticity and a linear isotropic hardening model allowed us to formulate the local discrete constitutive equations as conic programs. Specifically, we demonstrate that implicit return-mapping schemes for well-known yield criteria, such as the Rankine, von Mises, Tresca, Drucker-Prager, and Mohr–Coulomb criteria, can be expressed as second-order and semidefinite conic programs. Additionally, we propose a novel scheme for the numerical evaluation of the consistent elastoplastic tangent operator based on a first-order parameter derivative of the optimal solutions.