How Curved Creases Enhance the Stiffness and Enable Shape Morphing of Thin-Sheet Structures

Abstract

When a thin sheet is folded about curved creases, the resulting shape resists loads in some directions and deforms into compact states in other directions. These curved-crease, origami-inspired structures display a number of functional behaviors advantageous to a design, such as tunable stiffness and shape morphing. This dissertation develops an understanding of how these behaviors are related to the crease pattern and how engineers can exploit these traits in their designs through mechanics.

The dissertation introduces a method for simulating the structural properties of curved-crease origami using a simplified numerical method called the bar-and-hinge model. Based on the geometry and material of the sheet, stiffness expressions were derived for three deformation behaviors, including stretching of the sheet, bending of the sheet, and folding along the creases. The model is capable of capturing the folding behavior, and the simulated deformed shapes are sufficiently accurate when compared to experiments and to theoretical approximations. This model is used to explore the mechanical characteristics of curved-crease structures throughout the dissertation.

Next, the dissertation explores the bending stiffness of curved-crease corrugations that are made by folding thin sheets about curves and without linerboard covers (i.e., flat sheets adhered to the corrugation to give the structure a more isotropic bending stiffness behavior). Curved-creases break symmetry in the corrugation, which allows for a unique property that redistributes stiffness to resist bending deformations in multiple directions. Two formulations for predicting the bending stiffness of any planar-midsurface corrugation were developed and experimentally validated with three-point bending tests.

Then, the dissertations explores a unique behavior seen in creased sheets where localized changes in the folding (i.e., pinching of the structure) result in global bending and twisting deformations. It was found that the increase in curvature and torsion of the crease due to pinching are proportional to the curvature of the crease before folding. Physical prototypes and numerical simulation were used to explore how geometry and the number of creases on a sheet change the global bending and twisting. These relations were used to create a framework for choosing a crease pattern that generates a desired deformation upon pinching.

Continuing the investigation on how pinches cause global deformations, an inverse-design scheme was created that solves three problems related to shape-fitting origami. The first problem aims to find a crease pattern that folds to a desired planar curve. The second problem aims to find a crease pattern and actuation scheme that maximizes the deflection at the end of the crease during pinching. The last problem aims to find a design whose end will reach a target point in three-dimensional space upon folding and pinching. A forward-process to describe the deformation of a single crease composed of several circular arc segments was developed. Using analytical equations and data from the bar-and-hinge method, the deformation values were calculated and were then used in an optimization process. These analyses are a first step towards practical shape fitting of curved-crease origami.

This dissertation sets a foundation for practical application of curved-crease origami in structural engineering by developing appropriate simulation methods and an understanding of how these crease patterns offer unique stiffness properties and shape-morphing capabilities.