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Networks and Heterogeneous Media

2009, Volume 4, Issue 4: 789-812. doi: 10.3934/nhm.2009.4.789
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On the derivation of linear elasticity from atomistic models

  • 1.
    Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching
  • Received: 01 July 2008 Revised: 01 July 2009

  • 74B05, 74B20, 49J45.

  • We derive linear elastic energy functionals from atomistic models as a Γ-limit when the number of atoms tends to infinity, respectively, when the interatomic distances tend to zero. Our approach generalizes a recent result of Braides, Solci and Vitali [2]. In particular, we study mass spring models with full nearest and next-to-nearest pair interactions. We also consider boundary value problems where a part of the boundary is free.

    Citation: Bernd Schmidt. On the derivation of linear elasticity from atomistic models[J]. Networks and Heterogeneous Media, 2009, 4(4): 789-812. doi: 10.3934/nhm.2009.4.789

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  • We derive linear elastic energy functionals from atomistic models as a Γ-limit when the number of atoms tends to infinity, respectively, when the interatomic distances tend to zero. Our approach generalizes a recent result of Braides, Solci and Vitali [2]. In particular, we study mass spring models with full nearest and next-to-nearest pair interactions. We also consider boundary value problems where a part of the boundary is free.


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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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