Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers

Pierluigi Cesana; Francesco Della Porta; Angkana Rüland; Christian Zillinger; Barbara Zwicknagl

doi:10.1007/s00205-020-01511-9

Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers

Analysis of PDEs 2020-03-17 v1

Authors: Pierluigi Cesana , Francesco Della Porta , Angkana Rüland , Christian Zillinger , Barbara Zwicknagl

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Abstract

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.

Keywords

nonlinear elasticity subgraph isomorphism n-well problem stress-free constructions nematic elastomers differential inclusions geometrically linearised problem

Cite

@article{arxiv.1904.08820,
  title  = {Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers},
  author = {Pierluigi Cesana and Francesco Della Porta and Angkana Rüland and Christian Zillinger and Barbara Zwicknagl},
  journal= {arXiv preprint arXiv:1904.08820},
  year   = {2020}
}

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49 pages, 18 figures

Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers

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