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Existence theorems in intrinsic nonlinear elasticity

Abstract : We first show how the displacement-traction problem of nonlinear three-dimensional elasticity can be recast either as a boundary value problem or as a minimization problem over a Banach manifold, where the unknown is the Cauchy–Green strain tensor instead of the deformation as is customary. We then consider the pure displacement problem, and we show that, under appropriate smoothness assumptions on the data, either problem recast in this fashion possesses at least a solution if the applied forces are sufficiently small and the stored energy function satisfies specific hypotheses. In particular, the minimization problem provides an example where the functional is not coercive.
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https://hal.sorbonne-universite.fr/hal-01077302
Contributor : Cristinel Mardare Connect in order to contact the contributor
Submitted on : Friday, October 24, 2014 - 1:34:26 PM
Last modification on : Friday, March 27, 2020 - 3:32:24 AM

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Philippe G. Ciarlet, Cristinel Mardare. Existence theorems in intrinsic nonlinear elasticity. Journal de Mathématiques Pures et Appliquées, Elsevier, 2010, 94, pp.229-243. ⟨10.1016/j.matpur.2010.02.002⟩. ⟨hal-01077302⟩

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