Cauchy-Born rule and the stability of crystalline solids: Static problems
文献类型：期刊论文
| 作者 | Weinan, E.; Ming, Pingbing
|
| 刊名 | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
 |
| 出版日期 | 2007-02-01 |
| 卷号 | 183期号:2页码:241-297 |
| ISSN号 | 0003-9527 |
| DOI | 10.1007/s00205-006-0031-7 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics ; Mechanics |
| 语种 | 英语 |
| WOS记录号 | WOS:000244023300003 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/4219]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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