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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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