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.
Mots-clés : problems of mechanics, variational problems, discrete to continuum limit, multiscale models, homogenization theory, $\Gamma $-limit, quasiconvexity, gradient flows, quasicontinuum method, adaptivity
@article{M2AN_2007__41_2_391_0,
author = {Blanc, Xavier and Bris, Claude Le and Lions, Pierre-Louis},
title = {Atomistic to continuum limits for computational materials science},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {391--426},
publisher = {EDP-Sciences},
volume = {41},
number = {2},
year = {2007},
doi = {10.1051/m2an:2007018},
mrnumber = {2339634},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007018/}
}
TY - JOUR AU - Blanc, Xavier AU - Bris, Claude Le AU - Lions, Pierre-Louis TI - Atomistic to continuum limits for computational materials science JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 391 EP - 426 VL - 41 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007018/ DO - 10.1051/m2an:2007018 LA - en ID - M2AN_2007__41_2_391_0 ER -
%0 Journal Article %A Blanc, Xavier %A Bris, Claude Le %A Lions, Pierre-Louis %T Atomistic to continuum limits for computational materials science %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 391-426 %V 41 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007018/ %R 10.1051/m2an:2007018 %G en %F M2AN_2007__41_2_391_0
Blanc, Xavier; Bris, Claude Le; Lions, Pierre-Louis. Atomistic to continuum limits for computational materials science. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 391-426. doi : 10.1051/m2an:2007018. http://www.numdam.org/articles/10.1051/m2an:2007018/
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