Multi-valued inverse design: multiple surface geometries from one flat sheet

TL;DR

This paper introduces an analytical method to design flat sheets capable of deforming into multiple 3D shapes through anisotropic deformation, enabling versatile applications like soft robots and micromachines.

Contribution

It presents the first analytical approach for multi-valued inverse design of deformable sheets that can achieve multiple target shapes from a single flat sheet.

Findings

Developed an analytical method for multi-shape inverse design.

Demonstrated a multi-shape swimmer capable of movement in fluid.

Enabled cyclic shape transitions for complex tasks.

Abstract

Designing flat sheets that can be made to deform into 3D shapes is an area of intense research with applications in micromachines, soft robotics, and medical implants. Thus far, such sheets were designed to adopt a single target shape. Here, we show that through anisotropic deformation applied inhomogenously throughout a sheet, it is possible to design a single sheet that can deform into multiple surface geometries upon different actuations. The key to our approach is development of an analytical method for solving this multi-valued inverse problem. Such sheets open the door to fabricating machines that can perform complex tasks through cyclic transitions between multiple shapes. As a proof of concept we design a simple swimmer capable of moving through a fluid at low Reynolds numbers.