A projected Newton algorithm for the dual convex program of elastoplasticity

In 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.