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We rigorously derive linear elasticity as a low energy limit of pure tractionnonlinear elasticity. Unlike previous results, we do not impose any restrictiveassumptions on the forces, and obtain a full $\Gamma$-convergence result. Theanalysis relies on identifying the correct reference configuration to linearizeabout, and studying its relation to the rotations preferred by the forces(optimal rotations). The $\Gamma$-limit is the standard linear elasticitymodel, plus a term that penalizes for fluctuations of the referenceconfigurations from the optimal rotations. However, on minimizers thisadditional term is zero and the limit energy reduces to standard linearelasticity.

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