# American Institute of Mathematical Sciences

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

## On the derivation of linear elasticity from atomistic models

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