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 473(2203):20170235, 2017). Passing to the lim...
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| Main Authors: | , , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
08 April 2020
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| In: |
Archive for rational mechanics and analysis
Year: 2020, Volume: 237, Issue: 1, Pages: 383-445 |
| ISSN: | 1432-0673 |
| DOI: | 10.1007/s00205-020-01511-9 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00205-020-01511-9
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| Author Notes: | Pierluigi Cesana, Francesco Della Porta, Angkana Rüland, Christian Zillinger, Barbara Zwicknagl |
| Summary: | 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 473(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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| Item Description: | Gesehen am 12.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1432-0673 |
| DOI: | 10.1007/s00205-020-01511-9 |