Shape programming lines of concentrated Gaussian curvature

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 limbs, and highlighting the similarities between these patterns of shape change and those found during the morphogenesis of several biological systems.F.F. and M.W. were supported by the EPSRC [grant number EP/P034616/1]. M.W. is grateful for support from the ELBE Visiting Faculty Program, Dresden. D.D. was supported by the EPSRC Centre for Doctoral Training in Computational Methods for Materials Science [grant no. EP/L015552/1]. J.S.B. was supported by a UKRI “future leaders fellowship” [grant number MR/S017186/1]. This material is partially based upon work supported by the National Science Foundation under Grant DMR 2041671

Frame, metric and geodesic evolution in shape-changing nematic shells

Non-uniform director fields in flat, responsive, glassy nematic sheets lead to the induction of shells with non-trivial topography on the application of light or heat. Contraction along the director causes metric change, with, in general, the induction of Gaussian curvature, that drives the topography change. We describe the metric change, the evolution of the director field, and the transformation of reference state material curves, e.g. spirals into radii, as curvature develops. The non-isometric deformations associated with heat or light change the geodesics of the surface, intriguingly even in regions where no Gaussian curvature results

Shape programming lines of concentrated Gaussian curvature

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.F.F. and M.W. were supported by the EPSRC [grant number EP/P034616/1]. M.W. is grateful for support from the ELBE Visiting Faculty Program, Dresden. D.D. was supported by the EPSRC Centre for Doctoral Training in Computational Methods for Materials Science [grant no. EP/L015552/1]. J.S.B. was supported by a UKRI “future leaders fellowship” [grant number MR/S017186/1]. This material is partially based upon work supported by the National Science Foundation under Grant DMR 2041671

Finite-element analysis of the optical-texture-mediated photoresponse in a nematic strip

In a nematic solid, wherein liquid crystal molecules are incorporated into polymeric chains, the chromophore phase is projected onto the polymer conformation, changing the stress-free configuration metric. Stimulated actuation cannot be separated from the structure itself, since the mesoscopic polymer properties dictate the degree and type of shape change. In this research, we focused on self-deforming device programming, inspired by recent optical techniques, to pattern nontrivial alignment textures and induce exotic strain fields on specimens. A finite-element framework incorporating a light-thermo-order coupled constitutive relation and geometric nonlinearities was utilized to compute mechanical deformations for given external stimuli. The distortion of planar strips into various exotic 3D shapes was simulated, and disclination-defect-like liquid crystal texture topographies with different defect strengths produced various many-poled shapes upon irradiation, as observed experimentally. The effects of the boundary conditions and geometric nonlinearities were also examined, exemplifying the need for a comprehensive finite-element-based framework. The same method was applied to textures naturally emerging due to static distortion, and the effects of the prescribed inhomogeneities on the overall deformations, which is the basis of inverse design, were observed. Furthermore, we analyzed the local Poisson-effect-induced instability resulting from inscribing a hedgehog disclination texture onto a solid; the onset of buckling-like deformations was observed energetically, and the relations between this onset and other physical properties were elucidated to enable microstate design while maintaining structural stability. These results will facilitate the development and comprehension of the mechanisms of remotely light-controlled self-assembly and propulsion systems that may soon be realized