A Hidden Convexity in Continuum Mechanics, with application to classical, continuous-time, rate-(in)dependent plasticity

TL;DR

This paper introduces a novel variational principle framework for PDE models in continuum mechanics, specifically applied to various models of crystal plasticity, enhancing understanding of their mathematical structure.

Contribution

It presents a new variational approach applicable to both rate-independent and rate-dependent plasticity models at finite deformation, expanding the theoretical tools available.

Findings

Unified variational framework for continuum mechanics models

Application to quasi-static and dynamic crystal plasticity

Insights into the mathematical structure of plasticity models

Abstract

A methodology for defining variational principles for a class of PDE models from continuum mechanics is demonstrated, and some of its features explored. The scheme is applied to quasi-static and dynamic models of rate-independent and rate-dependent, single crystal plasticity at finite deformation.