Publications
Refereed journal articles
Woodruff, S. R. and Filipov, E. T. (2022). Bending and twisting with a pinch: Shape morphing of creased sheets. Extreme Mechanics Letters, 52, 101656. https://doi.org/10.1016/j.eml.2022.101656. Free version here.
Abstract: In this letter, we introduce a unique behavior seen in creased sheets where localized changes in the folding (i.e., a pinch) result in global bending and twisting deformations. Using isometric deformation theory, we identify the connections between pinching, crease curvature, and crease torsion that begin to explain the shape-morphing behavior. Given the limitations of isometric deformations, we expand our understanding of the behavior using a mechanics-based bar and hinge model of creased sheets, where the sheet is allowed to stretch. With this tool, we found that the increase in crease curvature and torsion due to pinching are proportional to the curvature of the crease before folding and that curved creases facilitate the bending and twisting. Additionally, we explored the bending and twisting of sheets with more than one crease. We found that sheets with an odd number of creases generate less intense twisting than those with an even number of creases, even when the creases are straight. The number of creases had little effect on the pinch-induced bending of the origami. The stiffness of the sheets had little effect on the amount of bending and twisting, but greater spacing between the creases resulted in more bending with little effect on the twisting. Based on these results, we created a framework to design crease patterns to have desirable bending and twisting that can be coupled or not, and demonstrated this programmability with simulations and by pinching physical prototypes. Our findings enable shape morphing of creased sheets with a low-complexity input and a versatile output.
Woodruff, S. R. and Filipov, E. T. (2020). A bar and hinge model formulation for structural analysis of curved-crease origami. International Journal of Solids and Structures, 204-205, 114-127. https://doi.org/10.1016/j.ijsolstr.2020.08.010. Free version here.
Abstract: In this paper, we present a method for simulating the structural properties of curved-crease origami through the use of a simplified numerical method called the bar and hinge model. We derive stiffness expressions for three deformation behaviors including stretching of the sheet, bending of the sheet, and folding along the creases. The stiffness expressions are based on system parameters that a user knows before analysis, such as the material properties of the sheet and the geometry of the flat fold pattern. We show that the model is capable of capturing folding behavior of curved-crease origami structures accurately by comparing deformed shapes to other theoretical and experimental approximations of the deformations. The model is used to study the structural behavior of a creased annulus sector and an origami fan. These studies demonstrate the versatile capability of the bar and hinge model for exploring the unique mechanical characteristics of curved-crease origami. The simulation codes for curved-crease origami are provided with this paper.
Woodruff, S. R. and Filipov, E. T. (2020). Curved creases redistribute global bending stiffness in corrugations: theory and experimentation. Meccanica, 56(6), 1613-1634. https://doi.org/10.1007/s11012-020-01200-7. Free version here.
Abstract: Corrugations offer a convenient way to make thin, lightweight sheets into stiff structures. However, traditional, straight-crease corrugations result in highly anisotropic stiffness which leads to undesirable flexibility in some directions of loading. In this paper, we explore the bending stiffness of curved-crease corrugations – developable corrugations made by folding thin sheets about curves and without lineboard covers on the top or bottom. The curved-crease corrugations break symmetry in the pattern and can redistribute stiffness to resist bending deformations in multiple directions. We formulate a framework for predicting the bending stiffness of any general corrugation from its multiple geometric features at different scales. We use the framework to create two predictive methods that provide valuable insight to the global stiffness of corrugations without a detailed analysis. Results from these methods match well with experimental, three-point bending tests of five corrugation geometries made from polyester film. We found that corrugations with elliptical or parabolic curved-creases that intersect with one edge of the pattern are best at redistributing stiffness in multiple directions. While a straight-crease pattern has a stiffness of about 4 [N/mm] in one direction and about 0 [N/mm] in the other, a parabolic crease pattern has a stiffness of about 2.5 [N/mm] in both directions. These curved-crease corrugations can enable the self-assembly and fabrication of practical, stiff structures from simple, developable sheets.
Conference proceedings
Woodruff, S. R. and Filipov, E. T. (2018). Structural Analysis of Curved Folded Deployables. 16th Biennial International Conference on Engineering, Science, Construction, and Operations in Challenging Environments, pages 793-803, Cleveland, OH. ASCE. https://doi.org/10.1061/9780784481899.075
Abstract: Origami inspired structures are particularly useful for space exploration because they can be compactly stowed during launch and can be deployed to create functional and reconfigurable systems at their final destination. This work presents a finite element implementation for analyzing thin sheets that are folded into curve creased origami. The computational model uses shell elements to capture deformations of the sheet and rotational hinges to simulate the crease line. Different methods for folding, or actuating, the crease are presented and verified with empirical solutions for a curved crease structure. Findings show that the folding method can lead to different energy distributions in the thin sheet while resulting in essentially the same deployed shape. The computational framework is then applied to more complex curved crease structures which can be used to store potential energy for deployment and offer a unique final geometry.
Conference posters
Woodruff, S. R. and Filipov, E. T. (2021, October). Twisting flat surfaces using curved creases and local pinching [Conference poster]. Society of Engineering Science Annual Conference (online). Poster here. Video overview here.
Folding thin sheets along curved creases can result in structures with complex, three-dimensional geometries and a non-uniform distribution of stiffness. After folding, applying local deformations to these structures can result in global motions and complex shape morphing. However, it is still challenging to understand the relationships between the crease pattern, the folded geometry, the local deformation, and the global shape change. In this poster, we explore global twisting of curved-crease origami due to pinching the structure at a single location (i.e., folding the crease(s) locally to a dihedral angle approaching zero). We identify the relationship between crease curvature, local changes in crease dihedral angle, and crease torsion using developable surface theory and verify this relationship using a mechanics-based bar and hinge model. From this study, we see that peak crease torsion is linearly related to the curvature of the crease before folding, which allows for global twisting from the local pinching deformation. Our work further shows that global twisting can be controlled by considering the folding sign of each crease (mountain or valley) and the arrangement of multiple creases on a sheet. We apply this unique property of curved-crease origami to develop crease patterns with multiple creases that can twist in a programmable fashion due to the local pinching. This work shows that curved creases offer a simple approach to create deployable structures where local actuation can lead to complex twisting deformations. These properties are suitable for designs that need simplicity in fabrication but advanced shape morphing, such as dynamic façades, shape-morphing wings, or biomedical exoskeletons.