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Chapitre D'ouvrage Année : 2010

Quasiconvex envelopes in nonlinear elasticity

Annie Raoult
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Résumé

We give several examples of modeling in nonlinear elasticity where a quasiconvexification procedure is needed. We first recall that the three-dimensional Saint Venant-Kirchhoff energy fails to be quasiconvex and that its quasiconvex envelope can be obtained by means of careful computations. Second, we turn to the mathematical derivation of slender structure models: an asymptotic procedure using Gamma-convergence tools leads to models whose energy is quasiconvex by construction. Third, we construct an homogenized quasiconvex energy for square lattices.
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Dates et versions

hal-00365910 , version 1 (05-03-2009)

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  • HAL Id : hal-00365910 , version 1

Citer

Annie Raoult. Quasiconvex envelopes in nonlinear elasticity. J. Schröder, P. Neff. Poly-,Quasi- and Rank-one Convexity in Applied Mechanics, Springer, pp.17-51, 2010, CISM Courses and Lectures, vol. 516. ⟨hal-00365910⟩
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