On the Cauchy-Born approximation at finite temperature

Jerry Z. Yang; Chao Mao; Xiantao Li; Chun Liu

doi:10.1016/j.commatsci.2014.11.030

On the Cauchy-Born approximation at finite temperature

Jerry Z. Yang, Chao Mao, Xiantao Li, Chun Liu

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

5 Scopus citations

Abstract

We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first Piola-Kirchhoff stress. For systems under periodic boundary conditions, a derivation is presented, which takes into account the translational invariance and clarifies the removal of the zero phonon modes. Also revealed by the asymptotic approach is the role of the smoothness of the interatomic potential. Several numerical examples are provided to validate this approach.

Original language	English (US)
Pages (from-to)	21-28
Number of pages	8
Journal	Computational Materials Science
Volume	99
DOIs	https://doi.org/10.1016/j.commatsci.2014.11.030
State	Published - Mar 2015

All Science Journal Classification (ASJC) codes

General Computer Science
General Chemistry
General Materials Science
Mechanics of Materials
General Physics and Astronomy
Computational Mathematics

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10.1016/j.commatsci.2014.11.030

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abstract = "We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first Piola-Kirchhoff stress. For systems under periodic boundary conditions, a derivation is presented, which takes into account the translational invariance and clarifies the removal of the zero phonon modes. Also revealed by the asymptotic approach is the role of the smoothness of the interatomic potential. Several numerical examples are provided to validate this approach.",

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AU - Mao, Chao

AU - Li, Xiantao

AU - Liu, Chun

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N2 - We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first Piola-Kirchhoff stress. For systems under periodic boundary conditions, a derivation is presented, which takes into account the translational invariance and clarifies the removal of the zero phonon modes. Also revealed by the asymptotic approach is the role of the smoothness of the interatomic potential. Several numerical examples are provided to validate this approach.

AB - We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first Piola-Kirchhoff stress. For systems under periodic boundary conditions, a derivation is presented, which takes into account the translational invariance and clarifies the removal of the zero phonon modes. Also revealed by the asymptotic approach is the role of the smoothness of the interatomic potential. Several numerical examples are provided to validate this approach.

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VL - 99

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JO - Computational Materials Science

JF - Computational Materials Science

ER -

On the Cauchy-Born approximation at finite temperature

Abstract

All Science Journal Classification (ASJC) codes

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