Linear elasticity obtained from finite elasticity by $$\Gamma$$-convergence under weak coerciveness conditions.(English)Zbl 1250.74008

Summary: The energy functional of linear elasticity is obtained as $$\Gamma$$-limit of suitable rescalings of the energies of finite elasticity. The quadratic control from below of the energy density $$W(\nabla v)$$ for large values of the deformation gradient $$\nabla v$$ is replaced here by the weaker condition $$W(\nabla v)\geqslant |\nabla v|^{p}$$, for some $$p>1$$. Energies of this type are commonly used in the study of a large class of compressible rubber-like materials.

MSC:

 74B05 Classical linear elasticity
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References:

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