Evolving, complex topography from combining centers of Gaussian curvature

TL;DR

This paper develops a geometric framework for designing complex, curved topographies in liquid crystal elastomers and glasses by analyzing interface compatibility and inverse designing pixel arrays for targeted shapes and images.

Contribution

It introduces a generalized metric compatibility condition for interface design and demonstrates its use in creating complex topographies and displays.

Findings

Compatible hyperbolic interfaces enable complex shape design.

Inverse design of pixel arrays achieves target images.

Framework supports applications in soft robotics and displays.

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.