Quasiconvex elastodynamics: weak-strong uniqueness for measure-valued solutions

TL;DR

This paper establishes a weak-strong uniqueness principle for measure-valued solutions in elastodynamics with strongly quasiconvex stored-energy functions, using advanced calculus of variations and relative entropy methods.

Contribution

It introduces a novel approach to handle quasiconvex stored-energy functions in elastodynamics, extending the relative entropy method to this context.

Findings

Proves weak-strong uniqueness for measure-valued solutions

Develops convexity bounds for quasiconvex functions

Adapts the relative entropy method to quasiconvex elastodynamics

Abstract

A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the material is assumed strongly quasiconvex. The proof employs tools from the calculus of variations to establish general convexity-type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics.