Atomistic to continuum limits for computational materials science
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 2, p. 391-426

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.

DOI : https://doi.org/10.1051/m2an:2007018
Classification:  35-xx,  39-xx,  41-xx,  49-xx,  65-xx,  68-04,  73-xx
Keywords: problems of mechanics, variational problems, discrete to continuum limit, multiscale models, homogenization theory, Γ-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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {2},
     year = {2007},
     pages = {391-426},
     doi = {10.1051/m2an:2007018},
     zbl = {pre05252008},
     mrnumber = {2339634},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2007__41_2_391_0}
}
Blanc, Xavier; Bris, Claude Le; Lions, Pierre-Louis. Atomistic to continuum limits for computational materials science. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 2, pp. 391-426. doi : 10.1051/m2an:2007018. http://www.numdam.org/item/M2AN_2007__41_2_391_0/

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