On the derivation of linear elasticity from atomistic models

2009, Volume 4, Issue 4: 789-812. doi: 10.3934/nhm.2009.4.789

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1.
Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching

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.
- Atomistic systems,
- linear elasticity,
- discrete-to-continuum limits,
- $\Gamma$-convergence
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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Abstract

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.
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