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

E. Wei-Nan; Ming Ping-Bing

doi:10.1007/s10255-007-0393

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

E. Wei-Nan, Ming Ping-Bing

Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

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.

Original language	English (US)
Pages (from-to)	529-550
Number of pages	22
Journal	Acta Mathematicae Applicatae Sinica
Volume	23
Issue number	4
DOIs	https://doi.org/10.1007/s10255-007-0393
State	Published - Oct 2007

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

Cauchy-Born rule
Crystal elasticity
Stability of crystals

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10.1007/s10255-007-0393

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title = "Cauchy-Born rule and the stability of crystalline solids: Dynamic problems",

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 = "Cauchy-Born rule, Crystal elasticity, Stability of crystals",

author = "E. Wei-Nan and Ming Ping-Bing",

note = "Funding Information: Manuscript received November 7, 2006. 1Supported 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 2Supported by the National Basic Research Program (No.2005CB321704) and the National Natural Science Foundation of China (No.10571172).",

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T1 - Cauchy-Born rule and the stability of crystalline solids

T2 - Dynamic problems

AU - Wei-Nan, E.

AU - Ping-Bing, Ming

N1 - Funding Information: Manuscript received November 7, 2006. 1Supported 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 2Supported by the National Basic Research Program (No.2005CB321704) and the National Natural Science Foundation of China (No.10571172).

PY - 2007/10

Y1 - 2007/10

N2 - 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.

AB - 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.

KW - Cauchy-Born rule

KW - Crystal elasticity

KW - Stability of crystals

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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