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 $$n\rightarrow \infty $$ 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.

中文翻译：

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（非线性）平面弹性理论中的精确构造：从弹性晶体到向列弹性体

在本文中，我们推导出几何非线性、平面 n 井问题中存在“Conti 型”、高度对称、完全无应力结构的充分必要条件，概括了 Conti 等人的结果。(Proc R Soc A 473(2203):20170235, 2017)。传递到极限 $$n\rightarrow \infty $$ n → ∞ ，这允许我们同时处理固体晶体和向列弹性体微分夹杂物。特别是，我们恢复并概括了在 Kitano 和 Kifune（超显微镜 39（1-4）：279-286，1991）、Manolikas 和 Amelinckx（Physica Status Solidi（A ) 60(2):607–617, 1980; Physica Status Solidi (A) 61(1):179–188, 1980)。此外，我们讨论了相应的几何线性化问题。