Cauchy-Born rule and the stability of crystalline solids: Static problems

doi:10.1007/s00205-006-0031-7

	Cauchy-Born rule and the stability of crystalline solids: Static problems
	Weinan, E.; Ming, Pingbing
	2007-02-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	183 期号:2 页码:241-297
摘要	We study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature. We prove, under certain sharp stability conditions, that the correct nonlinear elasticity model is given by the classical Cauchy-Born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the Cauchy-Born rule. The analysis is carried out for both simple and complex lattices, and for this purpose, we develop the necessary tools for performing asymptotic analysis on such lattices. Our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids.
DOI	10.1007/s00205-006-0031-7
语种	英语
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000244023300003
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4220
专题	计算数学与科学工程计算研究所
通讯作者	Weinan, E.
作者单位	1.Princeton Univ, Dept Math, Princeton, NJ 08544 USA 2.Princeton Univ, PACM, Princeton, NJ 08544 USA 3.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Weinan, E.,Ming, Pingbing. Cauchy-Born rule and the stability of crystalline solids: Static problems[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2007,183(2):241-297.
APA	Weinan, E.,&Ming, Pingbing.(2007).Cauchy-Born rule and the stability of crystalline solids: Static problems.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,183(2),241-297.
MLA	Weinan, E.,et al."Cauchy-Born rule and the stability of crystalline solids: Static problems".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 183.2(2007):241-297.