Calculus of Variations and Geometric Measure Theory
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R. Alicandro - G. Lazzaroni - M. Palombaro

Derivation of linear elasticity for a general class of atomistic energies

created by lazzaroni on 27 Mar 2020
modified on 03 Apr 2020

[BibTeX]

Preprint

Inserted: 27 mar 2020
Last Updated: 3 apr 2020

Year: 2020

Abstract:

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.


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