Topological mechanics of origami and kirigami

TL;DR

This paper explores the topological properties of origami and kirigami structures, demonstrating how geometric design can induce localized, boundary-specific folding motions through topological invariants, with implications for mechanical metamaterials.

Contribution

It introduces a topological framework for designing origami and kirigami with localized folding modes, extending concepts from quantum topological states to mechanical structures.

Findings

Localized folding motions are governed by topological invariants.

A simple quasi-1D model demonstrates topological states in origami.

Topological design principles are extended to two dimensions.

Abstract

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.