A duality principle for non-linear elasticity

TL;DR

This paper introduces a duality principle for non-linear elasticity, utilizing convex analysis and Legendre transforms, highlighting the concavity of the dual variational formulation and establishing optimality conditions.

Contribution

It presents a novel dual variational formulation for non-linear elasticity problems, emphasizing its concavity and providing sufficient optimality conditions.

Findings

Dual variational formulation is concave.

Established sufficient optimality conditions.

Applied convex analysis and Legendre transforms.

Abstract

This article develops a duality principle for non-linear elasticity. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation is concave. Moreover, sufficient optimality conditions are also established.