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On the derivation of linear elasticity from atomistic models. (English) Zbl 1183.74020
Summary: 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 A. Braides, M. Solci and E. Vitali [Netw. Heterog. Media 2, No. 3, 551–567 (2007; Zbl 1183.74017)]. 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.

MSC:
74B05 Classical linear elasticity
74B20 Nonlinear elasticity
49J45 Methods involving semicontinuity and convergence; relaxation
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