Reference Configurations Versus Optimal Rotations: A Derivation of Linear Elasticity from Finite Elasticity for all Traction Forces

Cy Maor, Maria Giovanna Mora*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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 Γ -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 Γ -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.

Original languageAmerican English
Article number62
JournalJournal of Nonlinear Science
Volume31
Issue number3
DOIs
StatePublished - Jun 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).

Keywords

  • Gamma-convergence
  • Linear elasticity
  • Nonlinear elasticity
  • Pure traction

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