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A Notion of Capacity Related to Elasticity: Applications to Homogenization

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Abstract

We study a notion of capacity related to elasticity which proves convenient for analyzing the concentrations of strain energy caused by rigid displacements of some infinitesimal parts of an elastic body in two or three dimensions. By way of application, we investigate the behavior of solutions to initial boundary value problems describing vibrations of periodic elastic composites with rapidly varying elastic properties. More specifically, we analyze a two-phase medium whereby a set of heavy stiff tiny particles is embedded in a softer matrix. This task is set in the context of linearized elasticity.

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Authors and Affiliations

  1. LMGC, UMR-CNRS 5508, Université Montpellier II, Case courier 048, Place Eugène Bataillon, 34095, Montpellier Cedex 5, France

    Michel Bellieud

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  1. Michel Bellieud
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Correspondence to Michel Bellieud.

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Communicated by G. Dal Maso

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Bellieud, M. A Notion of Capacity Related to Elasticity: Applications to Homogenization. Arch Rational Mech Anal 203, 137–187 (2012). https://doi.org/10.1007/s00205-011-0448-5

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