Justification of the Cauchy-Born Approximation of Elastodynamics

被引:46
作者
Ortner, C. [1 ]
Theil, F. [1 ]
机构
[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
基金
英国工程与自然科学研究理事会;
关键词
VALIDITY;
D O I
10.1007/s00205-012-0592-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present sharp convergence results for the Cauchy-Born approximation of general classical atomistic interactions, for static problems with small data and for dynamic problems on a macroscopic time interval.
引用
收藏
页码:1025 / 1073
页数:49
相关论文
共 32 条
[1]   A Unified Interpretation of Stress in Molecular Systems [J].
Admal, Nikhil Chandra ;
Tadmor, E. B. .
JOURNAL OF ELASTICITY, 2010, 100 (1-2) :63-143
[2]   Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons [J].
Bartok, Albert P. ;
Payne, Mike C. ;
Kondor, Risi ;
Csanyi, Gabor .
PHYSICAL REVIEW LETTERS, 2010, 104 (13)
[3]   From molecular models to continuum mechanics [J].
Blanc, X ;
Le Bris, C ;
Lions, PL .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (04) :341-381
[4]   FROM THE NEWTON EQUATION TO THE WAVE EQUATION IN SOME SIMPLE CASES [J].
Blanc, Xavier ;
Le Bris, Claude ;
Lions, Pierre-Louis .
NETWORKS AND HETEROGENEOUS MEDIA, 2012, 7 (01) :1-41
[5]  
Ciarlet P.G., 2002, FINITE ELEMENT METHO, V40
[6]  
Conti S, 2006, J EUR MATH SOC, V8, P515
[7]   EMBEDDED-ATOM METHOD - DERIVATION AND APPLICATION TO IMPURITIES, SURFACES, AND OTHER DEFECTS IN METALS [J].
DAW, MS ;
BASKES, MI .
PHYSICAL REVIEW B, 1984, 29 (12) :6443-6453
[8]  
Deny J., 1955, Ann. Inst. Fourier (Grenoble), V5, P305
[9]   Cauchy-Born rule and the stability of crystalline solids: Dynamic problems [J].
E, Wei-nan ;
Ming, Ping-bing .
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2007, 23 (04) :529-550
[10]   Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice [J].
Friesecke, G ;
Theil, F .
JOURNAL OF NONLINEAR SCIENCE, 2002, 12 (05) :445-478