Atomistic to Continuum limits for computational materials science

Xavier Blanc; Claude Le Bris; Pierre-Louis Lions

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 2, page 391-426
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Blanc, Xavier, Le Bris, Claude, and Lions, Pierre-Louis. "Atomistic to Continuum limits for computational materials science ." ESAIM: Mathematical Modelling and Numerical Analysis 41.2 (2007): 391-426. <http://eudml.org/doc/250083>.

@article{Blanc2007,
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. },
author = {Blanc, Xavier, Le Bris, Claude, Lions, Pierre-Louis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Problems of mechanics; variational problems; discrete to continuum limit; multiscale models; homogenization theory; Γ-limit; quasiconvexity; gradient flows; quasicontinuum method; adaptivity.; multiscale computation},
language = {eng},
month = {6},
number = {2},
pages = {391-426},
publisher = {EDP Sciences},
title = {Atomistic to Continuum limits for computational materials science },
url = {http://eudml.org/doc/250083},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Blanc, Xavier
AU - Le Bris, Claude
AU - Lions, Pierre-Louis
TI - Atomistic to Continuum limits for computational materials science
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/6//
PB - EDP Sciences
VL - 41
IS - 2
SP - 391
EP - 426
AB - 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.
LA - eng
KW - Problems of mechanics; variational problems; discrete to continuum limit; multiscale models; homogenization theory; Γ-limit; quasiconvexity; gradient flows; quasicontinuum method; adaptivity.; multiscale computation
UR - http://eudml.org/doc/250083
ER -

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