Programming Shapes with Competing Layered Patterns

TL;DR

This paper explores how differential growth in bilayer systems can be programmed to produce complex, biologically inspired shapes by analyzing the effects of growth patterns, aspect ratios, and active layer programming.

Contribution

It introduces a novel approach to shape programming in bilayer systems with incompatible growth, including the effects of growth gradients and active layer manipulation.

Findings

Growth patterns significantly influence final shapes.

Active layer programming enables complex shape control.

Biologically inspired shapes can be achieved through simple deformation gradients.

Abstract

Studying shape changing thick surfaces induced by differential growth helps us understand morphogenesis in biology and offers opportunities for device design. While ideal 2D differential growth maps have been well studied for both isotropic and anisotropic growth, scenarios involving gradients in thickness growth are far less explored. In this paper, we focus on a bilayer system in which the two layers undergo independent but incompatible growth. We examine how the strength of the growth patterns and the aspect ratio of the bilayer influence the resulting shapes. We first investigate the effect of global area difference in the bilayer. Next, we make one of the two layers active and program it with positive or negative, localized or uniform curvature. We then present examples involving competition between two active surfaces with opposite curvature signs or different curvature distributions and understand how the final configurations follow from the principles identified earlier. Finally, we demonstrate the ability to program biologically inspired shapes, such as dental epithelium and the ventral furrow in Drosophila, using a bilayer with simple, distinct deformation gradients.