Exact Constructions in the (Non-linear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers
In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results of Conti et al. (Proc R Soc A 73(2203):20170235, 2017). Passing to the limi...
| Autores: | , , , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1103 |
| Acesso em linha: | http://hdl.handle.net/20.500.11824/1103 |
| Access Level: | acceso abierto |
| Palavra-chave: | convex integration, elasticity, nematic elastomers |
| Resumo: | In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results of Conti et al. (Proc R Soc A 73(2203):20170235, 2017). Passing to the limit $n\rightarrow\infty$, this allows us to treat solid crystals and nematic elastomer differential inclusions simultaneously. In particular, we recover and generalise (non-linear) planar tripole star type deformations which were experimentally observed in Kitano and Kifune (Ultramicroscopy 39(1–4):279–286, 1991), Manolikas and Amelinckx (Physica Status Solidi (A) 60(2):607–617, 1980; Physica Status Solidi (A) 61(1):179–188, 1980). Furthermore, we discuss the corresponding geometrically linearised problem. |
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