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Variational Convergences of Dual Energy Functionals for Elastic Materials with a ε-Thin Strong Inclusion

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Abstract

We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco-limit of the stored complementary energy functional when the thickness is of order ε and the stiffness of order 1/ε where ε is a positive real adimensional parameter. In order to prove the existence of the displacement associated with the stress we use a suitable weak version of the Saint-Venant compatibility condition also known as Donati’s theorem.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulon, EA-CNRS 2134, Université de Toulon et du Var, Avenue de l’Université, BP 132, 83957, La Garde Cedex, France

    Anne-Laure Bessoud

  2. Laboratoire de Mécanique des Solides, UMR-CNRS 7649, École Polytechnique, 91128, Palaiseau Cedex, France

    Giuseppe Geymonat

  3. I3M, UMR-CNRS 5149, Université Montpellier II, Case courier 051, Place Eugène Bataillon, 34095, Montpellier Cedex 5, France

    Françoise Krasucki & Gérard Michaille

  4. MIPA Université de Nîmes, Case courier 051, Place Eugène Bataillon, 34095, Montpellier Cedex 5, France

    Gérard Michaille

Authors
  1. Anne-Laure Bessoud
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  2. Giuseppe Geymonat
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  3. Françoise Krasucki
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  4. Gérard Michaille
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Corresponding author

Correspondence to Françoise Krasucki.

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Bessoud, AL., Geymonat, G., Krasucki, F. et al. Variational Convergences of Dual Energy Functionals for Elastic Materials with a ε-Thin Strong Inclusion. J Elast 109, 51–65 (2012). https://doi.org/10.1007/s10659-011-9368-8

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  • DOI: https://doi.org/10.1007/s10659-011-9368-8

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