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An Atomistic-to-Continuum Analysis of Crystal Cleavage in a Two-Dimensional Model Problem

Journal of Nonlinear Science volume 24, pages 145–183 (2014)Cite this article

Abstract

A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that, in the discrete-to-continuum limit, the minimal energy of a crystal under uniaxial tension leads to a universal cleavage law and energy minimizers are either homogeneous elastic deformations or configurations that are completely cracked and do not store elastic energy. Beyond critical loading, the specimen generically cleaves along a unique optimal crystallographic hyperplane. For specific symmetric crystal orientations, however, cleavage might fail. In this case a complete characterization of possible limiting crack geometries is obtained.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, 86159, Augsburg, Germany

    Manuel Friedrich & Bernd Schmidt

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  1. Manuel Friedrich
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  2. Bernd Schmidt
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Correspondence to Manuel Friedrich.

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Communicated by Antonio DeSimone.

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Friedrich, M., Schmidt, B. An Atomistic-to-Continuum Analysis of Crystal Cleavage in a Two-Dimensional Model Problem. J Nonlinear Sci 24, 145–183 (2014). https://doi.org/10.1007/s00332-013-9187-0

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  • DOI: https://doi.org/10.1007/s00332-013-9187-0

Keywords

  • Brittle materials
  • Variational fracture
  • Atomistic models
  • Discrete-to-continuum limits
  • Free discontinuity problems

Mathematics Subject Classification

  • 74R10
  • 49J45
  • 70G75