  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.
