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Atomistic to Continuum limits for computational materials science

Published online by Cambridge University Press:  16 June 2007

Xavier Blanc
Affiliation:
Laboratoire J.-L. Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris, France. blanc@ann.jussieu.fr
Claude Le Bris
Affiliation:
CERMICS, École Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, Cité Descartes, 77455 Marne-la-Vallée. MICMAC, Inria Rocquencourt, 78153 Le Chesnay, France. lebris@cermics.enpc.fr
Pierre-Louis Lions
Affiliation:
Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France. CEREMADE, Université Paris Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France. lions@ceremade.dauphine.fr
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Abstract

The present article is an overview of some mathematical results, which provide elements of rigorous basis for some multiscale computations in materials science. The emphasis is laid upon atomistic to continuum limits for crystalline materials. Various mathematical approaches are addressed. The setting is stationary. The relation to existing techniques used in the engineering literature is investigated.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2007

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