Self-Folding Metasheets: The Optimal Pattern of Strain of Miura-Ori Folded State

TL;DR

This paper identifies the optimal strain pattern on collinear quadrilateral metasheets that enables stable self-folding into the Miura-Ori configuration, enhancing the design of self-folding origami structures.

Contribution

It introduces the concept of the optimal pattern of strain (OPS) for self-folding metasheets and demonstrates how to determine it using local initial state information.

Findings

OPS minimizes the number of functional creases needed for folding.

Energy analysis shows Miura-Ori pathway is energetically favored initially.

Projected force insights aid in determining OPS from local initial conditions.

Abstract

Self-folding origami has emerged as a tool to make functional objects in material science. The common idea is to pattern a sheet with creases and activate them to have the object fold spontaneously into a desired configuration. This article shows that collinear quadrilateral metasheets are able to fold into the Miura-Ori configuration, if we only impose strain on part of their creases. In this study, we define and determine the optimal pattern of strain (OPS) on a collinear quadrilateral metasheet, that is the pattern of minimum "functional" creases with which the self-folding metasheet can fold into Miura-Ori state stably. By comparing the energy evolution along the folding pathway of each possible folded state under OPS, we conclude that the energy predominance of the desired Miura-Ori pathway during the initial period of time accounts for why the OPS works. Furthermore, we measure the projected force of the OPS on the intial flat metasheet and give insights on how to determine the OPS using only local information of the initial flat state.