ON THE STABILITY OF BRAVAIS LATTICES AND THEIR CAUCHY-BORN APPROXIMATIONS

被引：32

作者：

Hudson, To ^{[1
]}

Ortner, Christoph ^{[1
]}

机构：

[1] Math Inst, Oxford OX1 3LB, England

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2012年 / 46卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Bravais lattice; Cauchy-Born model; stability; CONTINUUM LIMITS;

D O I：

10.1051/m2an/2011014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the stability of Bravais lattices and their Cauchy-Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy-Born continuum limit. We then analyze the atomistic and Cauchy-Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy-Born models respectively. Motivated by recent results in one dimension on the stability of atomistic/continuum coupling methods, we analyze the relationship between atomistic and Cauchy-Born stability regions, and the convergence of atomistic stability regions as the cell size tends to infinity.

引用

页码：81 / 110

页数：30

共 23 条

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