Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers
| Autor: | Christian Zillinger, Francesco Della Porta, Pierluigi Cesana, Barbara Zwicknagl, Angkana Rüland |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
convex integration elasticity nematic elastomers Mechanical Engineering 010102 general mathematics Complex system Elastomer 01 natural sciences 010101 applied mathematics Nonlinear system Mathematics (miscellaneous) Planar Mathematics - Analysis of PDEs Differential inclusion Liquid crystal FOS: Mathematics 0101 mathematics Elasticity (economics) Analysis Mathematical physics Analysis of PDEs (math.AP) |
| Zdroj: | BIRD: BCAM's Institutional Repository Data instname |
| Popis: | 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 [CKZ17]. 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 [MA80,MA80a,KK91]. Further we discuss the corresponding geometrically linearised problem. 49 pages, 18 figures |
| Databáze: | OpenAIRE |
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