Quasiconvex envelopes in nonlinear elasticity

Abstract : 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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Chapitre d'ouvrage
J. Schröder, P. Neff. Poly-,Quasi- and Rank-one Convexity in Applied Mechanics, Springer, pp.17-51, 2010, CISM Courses and Lectures, vol. 516
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Dernière modification le : mardi 11 octobre 2016 - 12:03:11
Document(s) archivé(s) le : vendredi 12 octobre 2012 - 12:55:22

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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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