Shape programming lines of concentrated Gaussian curvature
Shape programming lines of concentrated Gaussian curvature
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DOI：
10.1063/5.0044158
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发表时间：
2021-06-14
影响因子：
3.2
通讯作者：
Warner, M.
中科院分区：
文献类型：
--
作者：
Duffy, D.;Cmok, L.;Warner, M.
液晶弹性体(LCE)在受热或光照时，可沿其向列型指向矢发生大的可逆收缩。因此，平面LCE薄片内的空间图案导向器编码了加热时的收缩模式，这可以将薄片变形为曲线壳，类似于生长模式如何塑造发育中的有机体。在这里，我们从理论上、数值上和实验上考虑由径向和圆形指向矢区域构成的图案，这些区域孤立地形成圆锥和反圆锥。生成的曲面包含具有尖锐V形横截面的曲线脊，与图案中区域之间的边界相关联。这样的脊线可以用正曲线和负曲线的变体来创建，因为它们具有高斯曲率(在这里通过GaussBonnet定理量化)，如果没有能量上令人望而却步的拉伸，它们就不可能被展平。我们的实验和数值计算强调，虽然这种脊线不能等距展平，但它们可以通过交换V角的(奇异)曲率和脊线的(有限)曲率来等距变形。此外，在有限厚度的薄板中，锐脊不可避免地被非等距钝化以减轻弯曲，导致编码的奇异高斯曲率的适度涂抹。最后，我们将讨论诸如驱动线性特征等特征的使用，例如探头、舌头和夹爪。我们推测这些形状变化的模式与在几个生物系统的形态发生过程中发现的那些相似之处。由AIP出版公司独家授权出版。
Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet, thus, encodes a pattern of contraction on heating, which can morph the sheet into a curved shell, akin to how a pattern of growth sculpts a developing organism. Here, we consider theoretically, numerically, and experimentally patterns constructed from regions of radial and circular director, which, in isolation, would form cones and anticones. The resultant surfaces contain curved ridges with sharp V-shaped cross sections, associated with the boundaries between regions in the patterns. Such ridges may be created in positively and negatively curved variants and, since they bear Gauss curvature (quantified here via the GaussBonnet theorem), they cannot be flattened without energetically prohibitive stretch. Our experiments and numerics highlight that, although such ridges cannot be flattened isometrically, they can deform isometrically by trading the (singular) curvature of the V angle against the (finite) curvature of the ridge line. Furthermore, in finite thickness sheets, the sharp ridges are inevitably non-isometrically blunted to relieve bend, resulting in a modest smearing out of the encoded singular Gauss curvature. We close by discussing the use of such features as actuating linear features, such as probes, tongues, and grippers. We speculate on similarities between these patterns of shape change and those found during the morphogenesis of several biological systems. Published under an exclusive license by AIP Publishing.