We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.
|Titolo:||On the effect of interactions beyond nearest neighbours on non-convex lattice systems|
|Autori:||Alicandro, Roberto; Lazzaroni, Giuliano; Palombaro, Mariapia|
|Rivista:||CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||10.1007/s00526-017-1129-5|
|Appare nelle tipologie:||1.1 Journal article|