A projected Newton algorithm for the dual convex program of elastoplasticity

Abstract

SUMMARYIn this paper, we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems. The mathematical programming approach stems from energy‐based descriptions of constitutive models. We describe a projected Newton algorithm to solve the dual optimization problem. This algorithm requires solution of an unconstrained optimization problem at the integration point level, rather than a constrained one as carried out by classical return‐mapping schemes. Especially, implementation of multi‐surface plasticity models is no more involved than that of single‐surface models. We explore characteristics and performance of the projected Newton algorithm through numerical examples. Insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non‐convex problems such as non‐associated flow models. Copyright © 2014 John Wiley & Sons, Ltd.