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Determination of the Closure of the Set of Elasticity Functionals

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Abstract

We determine the closure for Mosco-convergence in L 2(Ω,ℝ3) of the set of elasticity functionals. We prove that this closure coincides with the set of all non-negative lower-semicontinuous quadratic functionals which are objective, i.e., which vanish for rigid motions. The result is still valid if we consider only the set of isotropic elasticity functionals which have a prescribed Poisson coefficient. This shows that a very large family of materials can be reached when homogenizing a composite material with highly contrasted rigidity coefficients.

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  1. Laboratoire d’Analyse Non Linéaire Appliquée et Modélisation, Université de Toulon et du Var, BP 132 - 83957, La Garde Cedex, France

    M. Camar-Eddine & P. Seppecher

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  1. M. Camar-Eddine
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  2. P. Seppecher
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Correspondence to M. Camar-Eddine.

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Communicated by G. Milton

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Camar-Eddine, M., Seppecher, P. Determination of the Closure of the Set of Elasticity Functionals. Arch. Rational Mech. Anal. 170, 211–245 (2003). https://doi.org/10.1007/s00205-003-0272-7

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