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 (Archive for rational mechanics and analysis, 2020)
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 $$n→ ∞ $$, 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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