| Issue |
ESAIM: M2AN
Volume 41, Number 2, March-April 2007
Special issue on Molecular Modelling
|
|
|---|---|---|
| Page(s) | 391 - 426 | |
| DOI | https://doi.org/10.1051/m2an:2007018 | |
| Published online | 16 June 2007 | |
Atomistic to Continuum limits for computational materials science
1
Laboratoire J.-L. Lions, Université
Pierre et Marie Curie, Boîte courrier 187, 75252 Paris, France. blanc@ann.jussieu.fr
2
CERMICS, École Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, Cité Descartes,
77455 Marne-la-Vallée.
3
MICMAC, Inria Rocquencourt, 78153 Le Chesnay, France.
lebris@cermics.enpc.fr
4
Collège de France, 11 place
Marcelin Berthelot, 75231 Paris Cedex 05, France.
5
CEREMADE, Université Paris Dauphine, place du Maréchal de Lattre de
Tassigny, 75775 Paris Cedex 16, France. lions@ceremade.dauphine.fr
Received:
30
November
2005
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.
Mathematics Subject Classification: 35-xx / 39-xx / 41-xx / 49-xx / 65-xx / 68-04 / 73-xx
Key words: Problems of mechanics / variational problems / discrete to continuum limit / multiscale models / homogenization theory / Γ-limit / quasiconvexity / gradient flows / quasicontinuum method / adaptivity.
© EDP Sciences, SMAI, 2007
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