Evolving, complex topography from combining centers of Gaussian curvature

Abstract

Liquid crystal elastomers and glasses can have significant shape change determined by their director patterns. Cones deformed from circular director patterns have non-trivial Gaussian curvature localised at tips, curved interfaces, and intersections of interfaces. We employ a generalised metric compatibility condition to characterize two families of interfaces between circular director patterns -- hyperbolic and elliptical interfaces, and find that the deformed interfaces are geometrically compatible. We focus on hyperbolic interfaces to design complex topographies and non-isometric origami, including n-fold intersections, symmetric and irregular tilings. The large design space of three-fold and four-fold tiling is utilized to quantitatively inverse design an array of pixels to display target images. Taken together, our findings provide comprehensive design principles for the design of actuators, displays, and soft robotics in liquid crystal elastomers and glasses.

13 pages, 11 figures

References in corpus (13)

• Geometric Mechanics of Curved Crease Origami
• Disclination-mediated thermo-optical response in nematic glass sheets
• Blueprinting Nematic Glass: Systematically Constructing and Combining Active Points of Curvature for Emergent Morphology
• Orientation of topological defects in 2D nematic liquid crystals
• Encoding Gaussian curvature in glassy and elastomeric liquid crystal polymer networks
• The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
• Curvature generation in nematic surfaces
• Helical Miura Origami
• Curved geometries from planar director fields - Solving the two-dimensional inverse problem
• Nematic director fields and topographies of shells of revolution
• Demonstration and interpretation of "scutoid" cells in a quasi-2D soap froth
• Actuation of thin nematic elastomer sheets with controlled heterogeneity
• Phase transformations and compatibility in helical structures

Cited by in corpus (7)

• Defective nematogenesis: Gauss curvature in programmable shape-responsive sheets with topological defects
• Shape programming lines of concentrated Gaussian curvature
• Origami and materials science
• Multi-valued inverse design: multiple surface geometries from one flat sheet
• Interfacial metric mechanics: stitching patterns of shape change in active sheets
• Metric mechanics with non-trivial topology: actuating irises, cylinders and evertors
• Bistability and equilibria of creased annular sheets and strips