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.

我们严格地将线性弹性作为纯牵引非线性弹性的低能量极限。与以前的结果不同，我们不对力施加任何限制性假设，而是获得完整的\（\ Gamma \）-收敛结果。该分析依赖于识别正确的参考配置以使其线性化，并研究其与受力偏好的旋转（最佳旋转）的关系。的\（\伽玛\） -limit是标准线性弹性模型，加上一个术语，用于从最佳旋转的参考配置的波动惩罚。但是，在最小化器上，此附加项为零，并且极限能量减小为标准线性弹性。