, Volume 23, Issue 4, pp 529-550

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

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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.

*Supported in part by an NSF grant DMS 04-07866, with additional support from the project "Research Team on Complex Systems" of the Chinese Academy of Sciences
**Supported by the National Basic Research Program (No.2005CB321704) and the National Natural Science Foundation of China (No.10571172).