# Reference configurations vs. optimal rotations: a derivation of linear elasticity from finite elasticity for all traction forces

created by mora on 28 Aug 2020
modified on 17 May 2021

[BibTeX]

Accepted Paper

Inserted: 28 aug 2020
Last Updated: 17 may 2021

Journal: Journal of Nonlinear Science
Year: 2021
We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full $\Gamma$-convergence result. The analysis relies on identifying the correct reference configuration to linearize about, and studying its relation to the rotations preferred by the forces (optimal rotations). The $\Gamma$-limit is the standard linear elasticity model, plus a term that penalizes for fluctuations of the reference configurations from the optimal rotations. However, on minimizers this additional term is zero and the limit energy reduces to standard linear elasticity.