Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals

Alicandro, Roberto, Dal Maso, Gianni, Lazzaroni, Giuliano and Palombaro, Mariapia (2018) Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals. Archive for Rational Mechanics and Analysis. pp. 1-45. ISSN 0003-9527

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 08 Mar 2018 12:54
Last Modified: 22 May 2018 15:56
URI: http://sro.sussex.ac.uk/id/eprint/74301

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