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Existence of minimizers for the pure displacement problem in nonlinear elasticity

Abstract : We show that the total energy of the pure displacement problem in nonlinear elasticity possesses a unique global minimizer for a large class of hyperelastic materials, including that of Saint Venant - Kirchhoff, pro- vided the density of the applied forces are small in Lp-norm. We also establish a nonlinear Korn inequality with boundary showing that the H1-distance between two deformation fields is bounded, up to a multi- plicative constant, by the L2-distance between their Cauchy-Green strain tensors.
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  • HAL Id : hal-00959067, version 1

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Cristinel Mardare. Existence of minimizers for the pure displacement problem in nonlinear elasticity. "Alexandru Myller'' Mathematical Seminar, 2010, Romania. pp.181-190. ⟨hal-00959067⟩

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