Calculus of Variations and Geometric Measure Theory

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 by alicandr on 02 Oct 2021


Published Paper

Inserted: 27 mar 2020
Last Updated: 2 oct 2021

Journal: SIAM J. Math. Anal.
Volume: 53
Number: 5
Pages: 5060-5093
Year: 2021


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. Existing results are available only in the special case of one-well potentials accounting for very short interactions. We consider here the general case of multi-well potentials accounting for interactions of finite but arbitrarily long range. 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.