Exact constructions in the (non-linear) planar theory of elasticity: from elastic crystals to nematic elastomers - Cesana, Pierluigi; Della Porta, Francesco; Rüland, Angkana; Zillinger, Christian; Zwicknagl, Barbara (Arxiv, 2019)
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 $n→ ∞$, 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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