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Atomistic to Continuum limits for computational materials science

Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis (2007), Atomistic to Continuum limits for computational materials science, Modélisation mathématique et analyse numérique, 41, 2, p. 391-426. http://dx.doi.org/10.1051/m2an:2007018

Type
Article accepté pour publication ou publié
Date
2007
Journal name
Modélisation mathématique et analyse numérique
Volume
41
Number
2
Publisher
EDP Sciences
Pages
391-426
Publication identifier
Metadata
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Author(s)
Blanc, Xavier cc
Le Bris, Claude
Lions, Pierre-Louis
Abstract (EN)
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.
Subjects / Keywords
Γ-limit; homogenization theory; multiscale models; discrete to continuum limit; variational problems; Problems of mechanics; quasiconvexity; gradient flows; quasicontinuum method; adaptivity