A continuum geometric approach for inverse design of origami structures

TL;DR

This paper introduces a continuum geometric framework for the inverse design of generalized Miura-Ori origami structures, enabling the creation of complex curved folding patterns through analytical relations.

Contribution

It develops a novel continuum differential geometry approach for inverse origami design, linking geometrical properties to perturbations in the pattern.

Findings

Derived invertible relations between geometry and perturbation fields.

Enabled design of complex curved origami configurations.

Bridged continuum theories and origami metamaterials.

Abstract

Miura-Ori, a celebrated origami pattern that facilitates functionality in matter, has found multiple applications in the field of mechanical metamaterials. Modifications of Miura-Ori pattern can produce curved configurations during folding, thereby enhancing its potential functionalities. Thus, a key challenge in designing generalized Miura-Ori structures is to tailor their folding patterns to achieve desired geometries. In this work, we address this inverse-design problem by developing a new continuum framework for the differential geometry of generalized Miura-Ori. By assuming that the perturbation to the classical Miura-Ori is slowly varying in space, we derive analytical relations between geometrical properties and the perturbation field. These relationships are shown to be invertible, allowing us to design complex curved geometries. Our framework enables porting knowledge, methods and tools from continuum theories of matter and differential geometry to the field of origami metamaterials.