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- Title
Reference Configurations Versus Optimal Rotations: A Derivation of Linear Elasticity from Finite Elasticity for all Traction Forces.
- Authors
Maor, Cy; Mora, Maria Giovanna
- 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.
- Publication
Journal of Nonlinear Science, 2021, Vol 31, Issue 3, p1
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-021-09716-2