An optimization-based reformulation of the classical displacement approach for state update of non-linear material models

TL;DR

This paper reformulates the classical displacement approach for updating non-linear material models as a dual optimization problem, providing deeper insights and removing heuristics in incremental state analysis.

Contribution

It introduces an optimization-based reformulation of the displacement method for non-linear material models, unifying various algorithms through a mathematical programming perspective.

Findings

Reformulation as a reduced dual optimization problem

Elimination of heuristics in the classical approach

Enhanced understanding of algorithmic workings

Abstract

In this paper, we build on recent work using a mathematical programming approach for incremental state update in analysis of non-linear mechanics models. In particular, we consider quasi-static analysis of continuum problems in the linearized kinematics regime, with non-linear material models described using convex energy functions. We find in this case that the classical displacement-based nested approach for incremental state update can be reformulated as solving a reduced dual optimization problem. This reformulation provides insights into the working of the algorithm, and eliminates the need for some heuristics. An important purpose of this paper is to further illustrate the unifying nature of the mathematical programming approach. We therefore present relationships with several of these types of algorithms recently presented in the literature for incremental state update.