Variational linearization of pure traction problems in incompressible elasticity

TL;DR

This paper demonstrates that incompressible linearized elasticity can be derived as a variational limit of finite elasticity in pure traction problems, under specific load conditions, providing a theoretical bridge between finite and linearized models.

Contribution

It introduces a variational approach to connect finite elasticity with linearized models in incompressible materials for pure traction scenarios.

Findings

Incompressible linearized elasticity is obtained as a variational limit.

The approach applies under suitable external load conditions.

Provides a theoretical framework linking finite and linearized elasticity.

Abstract

We consider pure traction problems and we show that incompressible linearized elasticity can be obtained as variational limit of incompressible finite elasticity under suitable conditions on external loads.