On the Cauchy-Born approximation at finite temperature

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)21-28
Number of pages8
JournalComputational Materials Science
StatePublished - 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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