00906nas a2200121 4500008004100000245009600041210006900137520045600206100002300662700002400685700002400709856005100733 2017 en d00aDerivation of a rod theory from lattice systems with interactions beyond nearest neighbours0 aDerivation of a rod theory from lattice systems with interaction3 aWe study continuum limits of discrete models for (possibly heterogeneous)
nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour
interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown
heterostructured nanowires.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526901090nas a2200121 4500008004100000245009000041210006900131520064600200100002300846700002400869700002400893856005100917 2017 en d00aOn the effect of interactions beyond nearest neighbours on non-convex lattice systems0 aeffect of interactions beyond nearest neighbours on nonconvex la3 aWe 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.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526801406nas a2200133 4500008004100000245004000041210004000081520101100121100002301132700002101155700002401176700002401200856004801224 2017 en d00aLinearisation of multiwell energies0 aLinearisation of multiwell energies3 aLinear elasticity can be rigorously derived from finite elasticity under the
assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete
model is provided, showing that the role of the singular perturbation term is played in
this setting by interactions beyond nearest neighbours.1 aAlicandro, Roberto1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://preprints.sissa.it/handle/1963/35288