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December  2009, 4(4): 789-812. doi: 10.3934/nhm.2009.4.789

On the derivation of linear elasticity from atomistic models

Bernd Schmidt 1,

1. 

Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching, Germany

Received  July 2008 Revised  July 2009 Published  October 2009

We derive linear elastic energy functionals from atomistic models as a $\Gamma$-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.
Keywords: linear elasticity, Atomistic systems, $\Gamma$-convergence., discrete-to-continuum limits.
Mathematics Subject Classification: 74B05, 74B20, 49J4.
Citation: Bernd Schmidt. On the derivation of linear elasticity from atomistic models. Networks and Heterogeneous Media, 2009, 4 (4) : 789-812. doi: 10.3934/nhm.2009.4.789
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