Lattice Mechanics of Origami Tessellations

TL;DR

This paper develops a lattice theory for origami tessellations, linking crease pattern topology to mechanical properties, enabling the design of origami-based materials with tunable mechanical behavior.

Contribution

It introduces a general lattice framework to analyze the mechanics of origami tessellations, bridging origami design with solid mechanics principles.

Findings

Provides a method to associate mechanical properties with periodic origami structures.

Connects origami tessellations to conventional materials and mechanical metamaterials.

Enables analysis of long-wavelength behavior of origami-based materials.

Abstract

Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there has been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures, and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design.