Structured Deformations in Linearized Elasticity

TL;DR

This paper extends structured deformation theory to linearized elasticity, deriving an integral energy representation with bulk and surface terms through relaxation methods and nonlinear elastic approximations.

Contribution

It introduces a new integral representation for energies in linearized elasticity using structured deformations, combining direct relaxation and nonlinear approximation techniques.

Findings

Derived an integral energy representation with bulk and surface contributions.

Connected nonlinear elastic energies of nonsimple materials to linearized structured deformations.

Provided a unified approach for relaxation in the context of linearized elasticity.

Abstract

We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a direct approach by means of a global method for relaxation in BD and via an approximation from nonlinear elastic energies associated to {nonsimple} materials.