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 Gauss–Bonnet 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.

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How morphogenetic movements are robustly coordinated in space and time is a fundamental open question in biology. We study this question using the wing ofDrosophila melanogaster, an epithelial tissue that undergoes large-scale tissue flows during pupal stages. We showed previously (Etournay et al 2015) that pupal wing morphogenesis involves both cellular behaviors that allow relaxation of mechanical tissue stress, as well as cellular behaviors that appear to be actively patterned. The core planar cell polarity (PCP) pathway influences morphogenetic cell movements in many other contexts, which suggests that it could globally pattern active cellular behaviors during pupal wing morphogenesis. We show here, however, that this is not the case: there is no significant phenotype on the cellular dynamics underlying pupal morphogenesis in mutants of core PCP. Furthermore, using laser ablation experiments, coupled with a rheological model to describe the dynamics of the response to laser ablation, we conclude that while core PCP mutations affect the fast timescale response to laser ablation, they do not affect overall tissue mechanics. In conclusion, our work shows that cellular dynamics and tissue shape changes duringDrosophilapupal wing morphogenesis are independent of one potential chemical guiding cue, core PCP.