Atomistic to continuum limits for computational materials science

被引：50

作者：

Blanc, Xavier

Le Bris, Claude

Lions, Pierre-Louis

机构：

[1] Univ Paris 06, Lab JL Lions, F-75252 Paris, France

[2] Ecole Natl Ponts & Chaussees, CERAMICS, F-77455 Marne La Vallee, France

[3] MICMAC, F-78153 Le Chesnay, France

[4] Coll France, F-75231 Paris 05, France

[5] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2007年 / 41卷 / 02期

关键词：

problems of mechanics; variational problems; discrete to continuum limit; multiscale models; homogenization; theory; Gamma-limit; quasiconvexity; gradient flows; quasicontinuum method; adaptivity;

D O I：

10.1051/m2an:2007018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：391 / 426

页数：36

共 142 条

[1] A general integral representation result for continuum limits of discrete energies with superlinear growth [J].