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 [CKZ17]. Passing to the limit $n\rightarrow \infty$, this allows...
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| Main Authors: | , , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
18 Apr 2019
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| In: |
Arxiv
Year: 2019, Pages: 1-49 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1904.08820
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| Author Notes: | Pierluigi Cesana, Francesco Della Porta, Angkana Rüland, Christian Zillinger, and Barbara Zwicknagl |
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| 245 | 1 | 0 | |a Exact constructions in the (non-linear) planar theory of elasticity |b from elastic crystals to nematic elastomers |c Pierluigi Cesana, Francesco Della Porta, Angkana Rüland, Christian Zillinger, and Barbara Zwicknagl |
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| 520 | |a 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. | ||
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