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Analysis of a Prototypical Multiscale Method Coupling Atomistic and Continuum Mechanics: the Convex Case

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Abstract

In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical basis for such a coupling in a one-dimensional setting, in the case of convex energy.

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Authors and Affiliations

  1. Laboratoire J.L.-Lions, Université Pierre et Marie Curie, Boite courrier 187, F-75252, Paris, France

    Xavier Blanc

  2. CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, Cité Descartes, F-77455, Marne-la-Vallée, France

    Claude Le Bris & Frédéric Legoll

  3. MICMAC, Inria Rocquencourt, F-78153, Le Chesnay, France

    Claude Le Bris & Frédéric Legoll

  4. EDF R & D, 1 avenue du Général de Gaulle, F-92140, Clamart, France

    Frédéric Legoll

Authors
  1. Xavier Blanc
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  2. Claude Le Bris
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  3. Frédéric Legoll
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Correspondence to Frédéric Legoll.

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Blanc, X., Le Bris, C. & Legoll, F. Analysis of a Prototypical Multiscale Method Coupling Atomistic and Continuum Mechanics: the Convex Case. Acta Mathematicae Applicatae Sinica, English Series 23, 209–216 (2007). https://doi.org/10.1007/s10255-007-0364-5

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  • DOI: https://doi.org/10.1007/s10255-007-0364-5

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