Inserted: 27 mar 2020
Last Updated: 3 apr 2020
The purpose of this paper is the derivation, in the framework of Gamma-convergence, of linear elastic continuum theories from a general class of atomistic models, in the regime of small deformations. We extend existing results in two directions: first, to the case of interactions of finite but arbitrarily long range; second, to the case of multi-well potentials, i.e., when the discrete energy density is minimised on the union of a finite number of disjoint wells. The extension to this setting requires a novel idea for the proof of the Gamma-convergence which is interesting in its own right and potentially relevant in other applications.