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Linearisation of multiwell energies

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dc.contributor.author Alicandro, Roberto
dc.contributor.author Dal Maso, Gianni
dc.contributor.author Lazzaroni, Giuliano
dc.contributor.author Palombaro, Mariapia
dc.date.accessioned 2017-06-22T09:07:10Z
dc.date.available 2017-06-22T09:07:10Z
dc.date.issued 2017-06
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/35288
dc.description.abstract Linear 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. en_US
dc.language.iso en en_US
dc.relation.ispartofseries SISSA;31/2017/MATE
dc.subject Nonlinear elasticity en_US
dc.subject Linearised elasticity en_US
dc.subject Discrete to continuum en_US
dc.subject Gamma-convergence en_US
dc.title Linearisation of multiwell energies en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.identifier.sissaPreprint 31/2017/MATE
dc.relation.firstpage 1 en_US
dc.relation.lastpage 35 en_US


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