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Research Papers: Design Automation

An Experimental Study and Model Determination of the Mechanical Stiffness of Paper Folds

[+] Author and Article Information
Clémentine Pradier

Department of Mechanical Engineering and
Development (GMD),
INSA-Lyon,
Villeurbanne F-69621, France

Jérôme Cavoret

Université de Lyon,
INSA-Lyon,
CNRS,
LaMCoS UMR5259,
Villeurbanne F-69621, France

David Dureisseix

Professor
Université de Lyon,
INSA-Lyon,
CNRS,
LaMCoS UMR5259,
Villeurbanne F-69621, France
e-mail: David.Dureisseix@insa-lyon.fr

Claire Jean-Mistral

Associate Professor
Université de Lyon,
INSA-Lyon,
CNRS,
LaMCoS UMR5259,
Villeurbanne F-69621, France

Fabrice Ville

Professor
Université de Lyon,
INSA-Lyon,
CNRS,
LaMCoS UMR5259,
Villeurbanne F-69621, France

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 3, 2015; final manuscript received January 24, 2016; published online February 19, 2016. Assoc. Editor: James K. Guest.

J. Mech. Des 138(4), 041401 (Feb 19, 2016) (7 pages) Paper No: MD-15-1269; doi: 10.1115/1.4032629 History: Received April 03, 2015; Revised January 24, 2016

Over the past few decades, folding paper has extended beyond the origami deployable applications to reach the engineering field. Nevertheless, mechanical information about paper behavior is still lacking, especially during folding/unfolding. This article proposes an approach to characterize the paper fold behavior in order to extract the material data that will be needed for the simulation of folding and to go a step further the single kinematics of origami mechanisms. The model developed herein from simple experiments for the fold behavior relies on a macroscopic local hinge with a nonlinear torsional spring. Though validated with only straight folds, the model is still applicable in the case of curved folds thanks to the locality principle of the mechanical behavior. The influence of both the folding angle and the fold length is extracted automatically from a set of experimental values exhibiting a deterministic behavior and a variability due to the folding process. The goal is also to propose a methodology that may extend the simple case of the paper crease, or even the case of thin material sheets, and may be adapted to other identification problems.

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References

Chen, Y. , and You, Z. , 2007, “ Square Deployable Frames for Space Applications. Part 2: Realization,” Proc. Inst. Mech. Eng., Part G, 221(1), pp. 37–45. [CrossRef]
Zirbel, S. A. , Lang, R. J. , Thomson, M. W. , Sigel, D. A. , Walkemeyer, P. E. , Trease, B. P. , Magleby, S. P. , and Howell, L. L. , 2013, “ Accommodating Thickness in Origami-Based Deployable Arrays,” ASME J. Mech. Des., 135(11), p. 111005. [CrossRef]
Buri, H. , and Weinand, Y. , 2008, “ ORIGAMI—Folded Plate Structures, Architecture,” 10th World Conference on Timber Engineering (WCTE), Miyazaki, Japan, June 2–5, pp. 2090–2097.
Gioia, F. , Dureisseix, D. , Motro, R. , and Maurin, B. , 2012, “ Design and Analysis of a Foldable/Unfoldable Corrugated Architectural Curved Envelop,” ASME J. Mech. Des., 134(3), p. 031003. [CrossRef]
You, Z. , and Kuribayashi, K. , 2006, “ Expandable Tubes With Negative Poisson's Ratio and Their Application in Medicine,” Origami4: Fourth International Meeting of Origami Science, Mathematics, and Education, R. Lang , ed., Pasadena, CA, Sept. 8–10, A K Peters/CRC Press, Wellesley, MA, pp. 117–127.
Kuribayashi, K. , Tsuchiya, K. , You, Z. , Tomus, D. , Umemoto, M. , Ito, T. , and Sasaki, M. , 2006, “ Self-Deployable Origami Stent Grafts as a Biomedical Application of Ni-Rich TiNi Shape Memory Alloy Foil,” Mater. Sci. Eng. A, 419(1–2), pp. 131–137. [CrossRef]
Vincent, J. F. V. , 2000, “ Deployable Structures in Nature: Potential for Biomimicking,” Proc. Inst. Mech. Eng., Part C, 214(1), pp. 1–10. [CrossRef]
Kobayashi, H. , Kresling, B. , and Vincent, J. F. , 1998, “ The Geometry of Unfolding Tree Leaves,” Proc. R. Soc. London, Ser. B, 265(1391), pp. 147–154. [CrossRef]
Resch, R. , 1992, “ The Ron Resch Paper and Stick Film (Video), Presentation of His Work Between 1960 and 1966,” Last accessed May 12, 2014, http://vimeo.com/36122966
Gjerde, E. , 2009, Origami Tessellations: Awe-Inspiring Geometric Designs, A K Peters, Wellesley, MA.
Tachi, T. , 2013, “ Designing Freeform Origami Tessellations by Generalizing Resch's Patterns,” ASME J. Mech. Des., 135(11), p. 111006. [CrossRef]
Dureisseix, D. , 2012, “ An Overview of Mechanisms and Patterns With Origami,” Int. J. Space Struct., 27(1), pp. 1–14. [CrossRef]
Lechenault, F. , Thiria, B. , and Adda-Bedia, M. , 2014, “ Mechanical Response of a Creased Sheet,” Phys. Rev. Lett., 112(24), p. 244301. [CrossRef] [PubMed]
Silverberg, J. L. , Na, J.-H. , Evans, A. A. , Liu, B. , Hull, T. C. , Santangelo, C. D. , Lang, R. J. , Hayward, R. C. , and Cohen, I. , 2015, “ Origami Structures With a Critical Transition to Bistability Arising From Hidden Degrees of Freedom,” Nat. Mater., 14(4), pp. 389–393. [CrossRef] [PubMed]
ISO 8791-4, 2007, Paper and Board—Determination of Roughness/Smoothness (Air Leak Methods)—Part 4: Print-Surf Method, 2nd ed., ISO, Geneva, Switzerland.
ISO 5633, 1983, Paper and Board—Determination of Resistance to Water Penetration, 1st ed., ISO, Geneva, Switzerland.
ISO 5626, 1993, Paper—Determination of Folding Endurance, 2nd ed., International Organization for Standardization (ISO), Geneva, Switzerland.
Sampson, W. W. , 2009, “ Materials Properties of Paper as Influenced by Its Fibrous Architecture,” Int. Mater. Rev., 54(3), pp. 134–156. [CrossRef]
Réthoré, J. , Gravouil, A. , Morestin, F. , and Combescure, A. , 2005, “ Estimation of Mixed-Mode Stress Intensity Factors Using Digital Image Correlation and an Interaction Integral,” Int. J. Fracture, 132(1), pp. 65–79. [CrossRef]
Avril, S. , Bonnet, M. , Bretelle, A.-S. , Grédiac, M. , Hild, F. , Ienny, P. , Latourte, F. , Lemosse, D. , Pagano, S. , Pagnacco, E. , and Pierron, F. , 2008, “ Overview of Identification Methods of Mechanical Parameters Based on Full-Field Measurements,” Exp. Mech., 48(4), pp. 381–402. [CrossRef]
Dureisseix, D. , Colmars, J. , Baldit, A. , Morestin, F. , and Maigre, H. , 2011, “ Follow-Up of a Panel Restoration Procedure Through Image Correlation and Finite Element Modeling,” Int. J. Solid Struct., 48(6), pp. 1024–1033. [CrossRef]
Giampieri, A. , Perego, U. , and Borsari, R. , 2011, “ A Constitutive Model for the Mechanical Response of the Folding of Creased Paperboard,” Int. J. Solid Struct., 48(16–17), pp. 2275–2287. [CrossRef]
Huffman, D. A. , 1976, “ Curvature and Creases: A Primer on Paper,” IEEE Trans. Comput., C-25(10), pp. 1010–1019. [CrossRef]
Demaine, E. D. , Demaine, M. L. , Koschitz, D. , and Tachi, T. , 2011, “ Curved Crease Folding: A Review on Art, Design and Mathematics,” IABSE-IASS Symposium: Taller, Longer, Lighter, London, UK, Sept. 20–23, pp. 20–30.
Dias, M. A. , and Santangelo, C. D. , 2012, “ The Shape and Mechanics of Curved-Fold Origami Structures,” Europhys. Lett., 100(5), p. 54005. [CrossRef]
Golub, G. H. , and Van Loan, C. F. , 2012, Matrix Computations, 4th ed., The Johns Hopkins University Press, Baltimore, MD.
Eckart, C. , and Young, G. , 1936, “ The Approximation of One Matrix by Another of Lower Rank,” Psychometrika, 1(3), pp. 211–218. [CrossRef]
Everson, R. , and Sirovich, L. , 1995, “ The Karhunen–Loeve Procedure for Gappy Data,” J. Opt. Soc. Am. A, 12(8), pp. 1657–1664. [CrossRef]
Lee, K. , and Mavris, D. N. , 2010, “ Unifying Perspective for Gappy Proper Orthogonal Decomposition and Probabilistic Principal Component Analysis,” AIAA J., 48(6), pp. 1117–1129. [CrossRef]
Golub, G. H. , Hansen, P. C. , and O'Leary, D. P. , 1999, “ Tikhonov Regularization and Total Least Squares,” SIAM J. Matrix Anal. Appl., 21(1), pp. 185–194. [CrossRef]
Barbier, C. , Larsson, P.-L. , and Östlund, S. , 2006, “ On the Effect of High Anisotropy at Folding of Coated Papers,” Compos. Struct., 72(3), pp. 330–338. [CrossRef]
Rolland du Roscoat, S. , Decain, M. , Thibault, X. , Geindreau, C. , and Bloch, J.-F. , 2007, “ Estimation of Microstructural Properties From Synchrotron X-Ray Microtomography and Determination of the REV in Paper Materials,” Acta Mater., 55(8), pp. 2841–2850. [CrossRef]
Huang, H. , Hagman, A. , and Nygårds, M. , 2014, “ Quasi Static Analysis of Creasing and Folding for Three Paperboards,” Mech. Mater., 69(1), pp. 11–34. [CrossRef]
Abbott, A. C. , Buskohl, P. R. , Joo, J. J. , Reich, G. W. , and Vaia, R. A. , 2014, “ Characterization of Creases in Polymers for Adaptive Origami Structures,” ASME Paper No. SMASIS2014-7480.
Francis, K. C. , Blanch, J. E. , Magleby, S. P. , and Howell, L. L. , 2013, “ Origami-Like Creases in Sheet Materials for Compliant Mechanism Design,” Mech. Sci., 4(2), pp. 371–380. [CrossRef]

Figures

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Fig. 1

Experimental results for the traction to rupture test

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Fig. 2

Experimental device for determination of the opening angle under loading

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Fig. 3

Experimental results: (a) the experimental curve for one specimen and the convex hull of all the specimens of the same length and orientation; (b) for a single orientation, the convex hulls of the different lengths; and (c) for a single length, the convex hulls of the different orientations

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Fig. 4

Obtained modes for restructured data. Top: functions k(α), bottom: functions f(L), left: for nα = 5, and right: for nα = 31. Fold orientation is transverse.

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Fig. 5

Compared functions k(α) obtained for several discretizations nα: (a) restructured data and (b) raw data. Fold orientation is transverse.

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Fig. 6

Comparison of the raw data (spherical points) and the model (central surface), with levels of confidence (outer surfaces). Top: fold orientation is transverse only; bottom: all orientations.

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Fig. 8

Comparison of the identified function k(α) for nα = 5, for each orientation of the fold separately, and all together

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Fig. 7

CDF obtained by statistical analysis on the sample provided by the experiments: (a) fold orientation is transverse only and (b) all orientations. Thin line is the centered Gaussian CDF with the same standard deviation.

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