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

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 full $$\Gamma $$ Γ -convergence result. The analysis relies identifying correct reference configuration to linearize about, studying its relation rotations preferred by forces ( optimal ). -limit is standard model, plus term that penalizes for fluctuations configurations from rotations. However, minimizers this additional zero reduces