Cauchy-Born Rule and the Stability of Crystalline Solids: Dynamic Problems

Original Papers

DOI: 10.1007/s10255-007-0393

Cite this article as:
Wei-nan*, E. & Ping-bing**, M. Acta Mathematicae Applicatae Sinica, English Series (2007) 23: 529. doi:10.1007/s10255-007-0393

Abstract

We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equations derived from the well-known Cauchy-Born rule.

Keywords

Crystal elasticity Cauchy-Born rule stability of crystals 

2000 MR Subject Classification

35L70 74E15 74J30 

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Department of Mathematics and PACMPrinceton UniversityPrinceton
  2. 2.LSEC, Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingChina