Linearisation of multiwell energies

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dc.contributor.areaMathematicsen_US
dc.contributor.authorAlicandro, Roberto
dc.contributor.authorDal Maso, Gianni
dc.contributor.authorLazzaroni, Giuliano
dc.contributor.authorPalombaro, Mariapia
dc.date.accessioned2017-06-22T09:07:10Z
dc.date.available2017-06-22T09:07:10Z
dc.date.issued2017-06
dc.description.abstractLinear 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.identifier.sissaPreprint31/2017/MATE
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35288
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;31/2017/MATE
dc.relation.lastpage35en_US
dc.subjectNonlinear elasticityen_US
dc.subjectLinearised elasticityen_US
dc.subjectDiscrete to continuumen_US
dc.subjectGamma-convergenceen_US
dc.titleLinearisation of multiwell energiesen_US
dc.typePreprinten_US
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