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Archive for Rational Mechanics and Analysis

, Volume 230, Issue 2, pp 735–781 | Cite as

From Atomistic Model to the Peierls–Nabarro Model with \({\gamma}\)-surface for Dislocations

  • Tao Luo
  • Pingbing Ming
  • Yang Xiang
Article
  • 100 Downloads

Abstract

The Peierls–Nabarro (PN) model for dislocations is a hybrid model that incorporates the atomistic information of the dislocation core structure into the continuum theory. In this paper, we study the convergence from a full atomistic model to the PN model with \({\gamma}\)-surface for the dislocation in a bilayer system. We prove that the displacement field and the total energy of the dislocation solution of the PN model are asymptotically close to those of the full atomistic model. Our work can be considered as a generalization of the analysis of the convergence from atomistic model to Cauchy–Born rule for crystals without defects.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe Hong Kong University of Science and TechnologyClear Water Bay, KowloonHong Kong
  2. 2.LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of SciencesBeijingChina
  3. 3.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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