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 multiwell 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.

Derivation of linear elasticity for a general class of atomistic energies

Alicandro R.;Palombaro M.
2021

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. 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 multiwell 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.
File in questo prodotto:
File Dimensione Formato  
A-L-P-2021_DiscreteLinear-REVISED.pdf

solo utenti autorizzati

Tipologia: Documento in Pre-print
Licenza: Dominio pubblico
Dimensione 543.38 kB
Formato Adobe PDF
543.38 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/176690
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact