Low energy fold paths in multistable origami structures

Abstract

Origami design concepts are finding pervasive utility in engineering applications due to their ability to map complex shape transformations into a series of folding actions. The interplay between stretching, folding, and facet bending modes in origami structures also generates a complex energy landscape of multistable states to leverage for engineering applications. However, identifying rigid and deformable folding paths in this high-dimensional and non-convex energy landscape remains a challenge. To help address this challenge, we first introduce a global, constraint-based approach to modeling origami that uses a redundant kinematic description of the facets and nodes, and treats the kinematic compatibility between these redundant descriptors as a constraint. This approach allows for complex facet shapes without increasing the dimensionality of the system, as would be necessary in truss-based and other node-based formulations in order to stiffen the facet. Secondly, we adopt the nudged elastic band method, that is widely used in computational chemistry, to identify minimum energy folding paths. This strategy addresses, from a global perspective, the difficulty of piecing together sequences of local folding steps in order to connect two different points in configuration space. We implement this path finding approach on both the kinematic constraint formulation and a truss-based model, and compare their behaviors on a series of folding and multistable origami examples.