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Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals
journal contribution
posted on 2023-06-09, 12:25 authored by Roberto Alicandro, Gianni Dal Maso, Giuliano Lazzaroni, Mariapia PalombaroLinear 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.
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Publication status
- Published
File Version
- Accepted version
Journal
Archive for Rational Mechanics and AnalysisISSN
0003-9527Publisher
Springer VerlagExternal DOI
Issue
1Volume
230Page range
1-45Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-03-08First Open Access (FOA) Date
2019-03-28First Compliant Deposit (FCD) Date
2018-03-07Usage metrics
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