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),
Villeurbanne F-69621, France

Jérôme Cavoret

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

David Dureisseix

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

Claire Jean-Mistral

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

Fabrice Ville

Université de Lyon,
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.

Copyright © 2016 by ASME
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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. 2

Experimental device for determination of the opening angle under loading

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Fig. 1

Experimental results for the traction to rupture test

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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. 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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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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