Characterizing the Mechanics of Fold-lines in Thin Kapton Membranes

Transcription

1 AIAA SciTech Forum 8 12 January 2018, Kissimmee, Florida 2018 AIAA Spacecraft Structures Conference / Characterizing the Mechanics of Fold-lines in Thin Kapton Membranes Buwaneth Yasara Dharmadasa University of Colorado, Boulder, Colorado, 80309, USA University of Moratuwa, Katubedda, Sri Lanka H.M.Y.C. Mallikarachchi University of Moratuwa, Katubedda, Sri Lanka Francisco López Jiménez University of Colorado, Boulder, Colorado, 80309, USA Novel designs for solar sails and star shades make use of thin films with large surface areas packed into finite volumes by introducing origami-like fold patterns. Predicting the deployed shape, deployment dynamics and mechanical stability of these structures requires an accurate modeling of the mechanical properties of the folds, instead of assuming perfect hinges like in rigid foldable origami. We have performed experiments in thin films with a single crease to investigate the underlying mechanics and characterize the mechanical properties of the fold. A parametric study was conducted on folding a Kapton film, showing that the neutral angle after folding can be rationalized as a function of the parameters in the folding process, but it evolves over time due to viscoelastic effects. Additionally, a framework has been established to quantify the hinge stiffness of a fold by its moment - angle relationship, showing a linear relationship regardless of the neutral angle. Finally an analytic model has been proposed by combining the hinge stiffness along with Elastica theories to predict the deflected shapes of folded thin films. I. Nomenclature A, B = Parameters for relaxation of neutral angle E = Young s modulus E mod = E/[12(1 υ 2 )] F = Pressing force I = Moment of Inertia L = Length of the specimen M = Bending moment P = Applied load R = Bending curvature W = Width of the specimen d = Pressing distance between two rigid plates h = Thickness of the film l h = Distance in x direction between the kinked edge and applied force k = Hinge stiffness t relax = Relaxation time ϕ = Angle of the fold at unstressed state / Neutral angle ϕ 0 = Neutral angle at t relax = t 0 θ = Fold angle under loading υ = Poisson s ratio Graduate Student, Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder. and AIAA Student Member Senior Lecturer, Department of Civil Engineering, University of Moratuwa, Katubedda, Sri Lanka, and AIAA Member. Assistant Professor, Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder, AIAA Member. Copyright 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

2 II. Introduction New designs for space structures such as solar sails and star shades require the packing, deployment and operation of surface areas in the tens to hundreds of meters scale [1, 2]. The main limitation to achieve these large appertures is the capacity of the launch vehicle, and so several architectures are based on the folding and packaging of thin membranes [3, 4]. By leveraging recent advances in origami science, it is possible to design structures in which folded thin membranes deploy following a predetermined and robust path [5 7]. The design of membrane-based deployable structures needs to satisfy many different goals, such as, highest packaging ratio, no damage in the material, ease and predictability of the deployment, and accuracy in achieving the desired deployed geometry [8]. Experimental testing is expensive and time consuming, particularly due to the need to replicate space environmental features such as reduced gravity and vaccuum [9 11], which significantly limits the possibilities of performing an exhaustive exploration of the design space. Numerical simulations have become the preferred alternative to extensive experimental campaigns. Despite the rapid advancement of high performance computers, realistic idealization schemes are crucial in simplifying the model to minimize computational cost while ensuring the required precision. In the case of origami-based thin film designs, most simulations idealize fold-lines as perfect hinges and tend to neglect the complex, localized behavior that takes place in the folds [12]. However, the significance of fold-line behaviour was highlighted by the IKAROS solar sail demonstrator [13], where simulation of the deployment dynamics were greatly affected by the properties used to model the stiffness of the folds [14]. A precise characterization of the mechanical properties of fold-lines is therefore essential to model the efficiency and deployment of solar sails [15]. Fig. 1 Geometric alteration of membrane due to compacting (a) Original state of 200 mm x 200 mm Kapton film, (b) Compacted state: held in place using paper clips, (c) Unstressed state after releasing paper clips, (d) Deployed state, stretched and attached to the cutting board using adhesive tapes. The overall dimensions are reduced due to the curvature of the membrane at the fold lines, as illustrated in the pictures. 2

3 Figure 1 illustrates compaction and deployment of a square membrane by introducing seven parallel uni-directional folds and subsequently unfolding the membrane. The stress-free geometry of the membrane has shifted from a flat plane to a modified geometry with a series of V shaped vertices known as residual creases. Despite the application of a non-zero axial force during unfolding, the length of the membrane is reduced by L as a result of localized bending at the creases. The reason is that the force required to unfold a membrane, as well as the final geometry, results from a combination of the bending rigidity of the membrane and the hinge rigidity at the crease [16]. Figure 2 illustrates three different scenarios. If the bending stiffness of the panels is much higher than the rotational stiffness of the crease, the deformations are similar to that of rigid origami. The other limit case is that of a very thin membrane in which the fold has very high hinge stiffness, and so the deformation corresponds exclusively to bending of the membrane. In practice, the stiffness of panel and hinge are comparable, and so the unfolding deformation corresponds to both opening of the fold and bending of the panels. To accurately predict the mechanical behavior and deployment dynamics of folded thin films, it is important to realistically model the behavior of the folds. Fig. 2 Different deformation geometries based on hinge-panel interaction. The two limit cases assume the fold to be either a perfectly compliant hinge or a perfectly rigid connection with constant angle. A realistic model will consider the balance between bending rigidity of the film and the hinge-stiffness of the fold. This paper focuses on two different aspects of the mechanical response of folds. Section III presents an experimental and numerical analysis of the formation of folds, particularly the dependence of their neutral angle on the folding process. Section IV presents additional experiments characterizing the rotational stiffness of folds. Finally, Section V presents strategies to realistically model the behavior of the folds. III. Characteristics of Neutral Angle (ϕ) The goal of this section is to explore the parameters that determine the neutral angle of a fold, ϕ, as a function of the folding process, the applied loading, and the properties of the membrane. 3

4 A. Experimental Setup The membranes were folded by being compressed between two compression platens in a Universal Testing System (Instron-5965 with 5kN load cell), which allowed to track the force (F) applied during folding. Samples of Kapton films with thicknesses 50 µm and 125 µm were used with dimensions of mm x 25.4 mm. The width of the sample was chosen so that the specimens were contained within the compression plate. The samples were first bent parallel to their short edges and made into a loop using adhesive tape as shown in Fig. 3(b), and then placed symmetrically between the compression platens. Loading was applied at a rate of 5 millimeters per minute until reaching a the target force, after which the samples were pressed for a duration of 1 minute before being released, unloading at the same rate. A microscope was positioned to view the sample deformation during pressing and the gauge distance, d, for each specimen was recorded. The distance between the compression platens was calibrated previously to each test by finding the position d = 0 corresponding to initial contact between the platens. Once the samples were unloaded, the adhesive tape was cut out and the samples were let to self-open. Neutral angles were measured by using digital images captured with a 25.3 MegaPixel camera (Nikon D660) which were then processed in MATLAB. Straight lines were fit to portions on either side of the fold, and the angle between them was calculated (Fig. 3(f)). The time evolution of neutral angle was measured by taking snapshots after different relax times (Tr elax ) after the test was completed. Fig. 3 Experimental method of creating a fold (a) Kapton Specimen, (b) Bend the sample parallel to shorter edge, (c) After pressing the tape is removed by cutting along the marked edge, (d) Specimen between the compression platens of Universal Testing Machine (e) View from the microscope during formation of crease (f) Measuring neutral angle by fitting curves using Matlab image processing tool. 4

5 Table 1 Material properties of Kapton HN polymide Property Value Density (kg/m 3 ) 1420 Ultimate tensile strength (MPa) 231 Young s modulus (GPa) 2.5 Poisson s ratio 0.34 Yield point stress (MPa) 69 B. Finite Element Model A finite element simulation of the folding process will be useful to understand the mechanics at the microscale, and in particular illustrate how plastic deformation in the film determines the neutral angle. With that goal, we attempted to replicate the above experiment of folding a thin film using finite element software package ABAQUS. A plane strain static analysis was executed with nonlinear material and geometric properties. Material properties for Kapton polyimide were defined according to Table 1 obtained from manufacturer data sheet[18]. Plastic properties were extracted from nominal stress-strain data at 23 o C, and converted to true stresses and true plastic strains in-order to be defined in tabular form. The thickness of the film is h = 125 µm. The film was modeled using deformable plane strain (CPER4) elements and the two compression platens were modeled as rigid bodies. Surface-surface contact between the two rigid plates and the surface of the membrane was defined using hard, friction-less contact properties. Self contact was defined at the inner surface of Kapton strip as indicated in Fig. 4. Mesh size was refined near the center with a maximum of 25 elements spread through membrane thickness totaling up to 58,044 elements. In order to accurately model the experiment, the simulation requires several steps. First the membrane was bent by fixing the translations of the bottom corner and pulling down the top corner using displacement boundary conditions, see Fig. 4(b). Next, the horizontal restraints were relaxed and the membrane was allowed to contact the rigid plates, which were subsequently moved toward each other pressing the Kapton strip. Gauge distance (d f em ) between the plates was controlled, see Fig. 4(c), and reaction forces (F f em ) from the two plates were extracted. Achieving high compaction (d f em < 400µm ) created numeric instabilities in the model. The proposed explanation is a combination of excessive deformation at the fold and unrealistic modeling of the plastic behavior of the Kapton film. After compression of the film, the plates were moved back in opposite directions, allowing the fold to relax while holding one of its corner nodes to avoid rigid body motions, see Fig. 4(d). The angle after relaxation (θ f em ) was calculated by extracting the slopes of straight portions. Numerical stabilization with a specific damping factor of was used during the simulation. Fig. 4 Finite element model for folding of membranes: (a)initial configuration of the membrane and two rigid planes, (b) Membrane bend by applying displacement boundary conditions, (c) Pressing of the membrane by surface contacts and plastic stresses over the membrane,(d) Final geometry after relaxation. Color in the sample corresponds to the logarithmic plastic strain. 5

6 C. Results Figure 5 plots the results of the experiment along with the prediction from the finite element model. The first graph shows the variation of the force per unit width as a function of the distance between the two plates, for two values of the film thickness, h. The results show a sharp increase in force when d < 2h, corresponding to the point where the membrane is folded back to back. Results from the finite element simulations agree well with the experimental data. Fig. 5 Variation of folding parameters. (a) Variation of force per unit width against the distance between two plates. Numerical results are also plotted. (b) Normalized force plotted against d/h ratio. The solid line represent a slope of two. (c) Variation of ϕ against d/t. Hollow data points were taken 1 minute after folding and solid data point were taken 10 days after folding Figure 5(b) presents the same data by non-dimensionalizing F and d. In the graph E mod represent E/12(1 υ 2 ) and W is the width of the sample. Remarkably, the data for both values of the thickness collapse into a single curve with an almost constant slope for d/h > 2. The slope is close to 2, which can be rationalized by analyzing the folding of the membrane using Euler Bernulli beam theory. Assuming the membrane is bending with a maximum curvature 1/R due to a force F transferred at a single point at x distance from the crease, as in Fig. 5(d), the bending moment can be expressed as: M = Fx = EI 1 R (1) 6

7 Assuming that the shape of the folded membrane is self-similar, and so x, R d ; Fd EW h3 d 2 F h EW h d (2) (3) The deviation from this quadratic exponent that is observed in the experimental data is attributed to the fact that the geometry is not completely self similar during the folding process, particularly for small values of the distance between the platens, d. Next we move on to investigate the neutral angle in the crease after the folding process, ϕ. Figure 5(c) presents the results, with two main findings. First, there is a clear dependance between ϕ and the normalized distance between the plates, d/h, for distances d/h > 2. In the case of d/h < 2, corresponding to complete self-contact in the folded membrane, the evolution is less clear. Second, the neutral angle increases over the relaxation time after the test, trelax. Once the pressing force is released, specimens instantaneously opens up to a given ϕ0 at trelax = t0, and slowly increase due to viscoelastic effects. Figure 5(c) shows values of ϕ for trelax = 1 minute and 10 days. The neutral angles obtained from our finite element simulations were lower than the experimental, which is attributed to an unrealistic modeling of the Kapton film. For example, we have not experimentally verified the plastic properties, and they have been assumed to be the same in tension and compression. In addition, we have not included viscous behavior. We further explore the viscoelastic effects in the relaxation of the folds by tracking the neutral angle ϕ as a function of the relaxation time, tr elax. Figure 6(a) shows images of the same sample, at intervals of 1 minute, 30 minutes, 2 days and 10 days after folding. It should be noted that an increase of 40 deg in neutral angle is observed. Figure 6(b) shows the evolution of 24 different samples over time. We observe a logarithmic law governing the relaxation mechanism, as previously reported in the literature [19]. We fit out results using: Fig. 6 Relaxation of neutral angle over time (a) 50 µ m thick sample (i) after 1 minute, (ii) after 30 minutes, (ii) after 2 days and (iv) after 10 days of relaxing. (b) Relaxation of 24 samples over a span of 10 days. ϕ = A log(trelax /t0 ) + ϕ0 (4) ϕ = A log(trelax ) A log(t0 ) + ϕ0 (5) ϕ = A log(trelax ) + B (6) where A is proportional to relaxing rate and ϕ0 is the initial angle at t0. A values for 50 µm Kapton film was 4.00 and for 125 µm film was 3.53 while their standard deviations were and respectively. 7

8 IV. Moment-Angle Response at the Crease A. Experimental Setup After exploring the parameters involved in the determination of the neutral angle (ϕ) our next goal is to investigate the mechanical properties of the fold. We conducted a test in which we vary the angle of the hinge, θ while tracking the applied force. The experiments were performed using 40 mm long and 20 mm wide Kapton strips, of thicknesses 25 µm, 50 µm and 75 µm. The length of the specimen was limited to reduce the origami length scale [16], so that variation in fold angle is more pronounced and easier to identify. Each Kapton sample was first carefully bent at the center and then pressed using a roller with a uniform pressure intensity to produce a fold-line. Different neutral angles were obtained by varying the number of roller passes and the applied force. Folded specimens were kept undisturbed for 2 hours for relaxation, at which the neutral angle reported in the experiments was measured. Figure 7 shows a schematic of the experimental setup. The specimens were attached to a supporting frame using a low stiffness adhesive tape. This mechanism was used to align the fold-lines in the horizontal plane and prevent any moment of resistance transferring from the supporting frame. A nylon string was attached at the bottom center edge of the membrane, and light weight beads were hung using a hook, resulting in a total load P. The membrane was initially loaded at 0.2 g intervals, and a photograph of the deformed configuration was taken at each time step. The applied load was enough to open the fold (increase the fold angle θ) but did not introduce any wrinkles in the membrane. Kapton specimen 40 mm L 20 mm 20 mm Load Low-stiffness adhesive tape String Fold-line x θ (a) (b) (c) Fig. 7 Schematic of the experimental setup used to calculate the moment-angle relationship in a fold showing, (a) specimen before folding, (b) front view and (c) side view after attaching to the frame A digital image processing tool (Webplotdigitize) was used the measure fold-angle θ, defined as the angle between the two tangent lines at the fold, and distance from the boundary line to folded edge x (Fig. 8). The moment induced by the load was calculated according to Eq. (7). M applied = Px (7) 8

9 Fig. 8 Image of the experimental setup used to calculate fold angle and distance to applied loading. Table 2 Regression analysis results 100 HN 200 HN 300 HN Membrane thickness (µm) Hinge stiffness, k (N.deg -1 ) R % 96.23% 91.82% B. Results The applied moment per unit width is plotted against the fold angle θ for three thicknesses in Fig. 9(a-c). Solid points represent experimental data and dashed lines indicate the best linear fit for each experimental run. It should be noted that linear fits are almost parallel to each other suggesting the same relationship M (θ ϕ) for all specimens of the same thickness. We carried out a linear regression analysis between the moment, M, and the variation of fold angle, θ ϕ, for all the samples with the same thickness. The values of the fit and their corresponding R 2 are presented in Table 2. Since all three R 2 values are higher than 90%, the results from the linear fit can be used to characterize the behavior of the fold, independently of the angle opening, Eq.( 8) can be used to model the hinge response for each thickness along with coefficient k in Table 2. M = k W (θ ϕ) (8) where applied moment (M) is measured in N/mm, width of the strip (W) in mm and all angles in degrees. Figure 9(d) presents the same experimental data, with the moment normalized by the bending rigidity of the strip (EI), versus the change in fold angle θ - ϕ. It is interesting to observe that the data for all three thicknesses follows a very similar relationship. More experiments are required to confirm if there is an universal relationship and the differences are due to experimental errors, such as the effect of gravity, or if there is a small dependence on the thickness V. Analytic Model Predicting the Membrane Response A. Elastica Theory As discussed in Section IV, a linear relationship exist between hinge moment and fold-angle for thin folded membranes. By applying symmetry boundary conditions, the behavior of a fold can be idealized as a cantilever beam fixed to a rotational spring at an angle θ/2, with initial rest angle ϕ/2, see Fig. 10. Neglecting self-weight of the beam, the deflection profile considering both bending of the strip and change of angle at the hinge can be obtained by solving the Elastica equation[20]. Deformed x, y coordinates of a beam undergoing large deflection can be estimated by integrating the differential Eq. (9) where G(x) is a function of applied force (F), bending rigidity (EI), angle at fixed end (θ/2) and horizontal 9

10 Fig. 9 Moment-fold angle relationships: (a) Kapton 100HN, (b) Kapton 200 HN and (c) Kapton 300HN (d) Modified moment - angle relationship for from all tests. Solid points represent experimental data and dashed lines indicate the best linear fit for each experimental run. distance between support and load (l h ). y (x) = G(x) { 1 [G(x)] 2 } 1/2 (9) G(x) = P 2EI {x2 l 2 h } + sin(θ/2) (10) We solve this equation with a shooting method guessing l h and verifying that the curve length (l c ) obtained by Eq. (11) is equal to original beam length: l c = lh 0 [1 + y ] 1/2 (11) A second shooting method was necessary, this time guessing the current fold angle, θ/2. The equations were integrated in Matlab using the command ode45, which provided the deflected x and y coordinates at every point. 10

11 Fig. 10 Idealized beam section with symmetric boundary conditions (a) at neutral angle (ϕ) and (b) at θ > ϕ after applying load F. B. FEM Model with Rotational Springs Our simple analysis using the Elastica is useful to rationalize the results and perform parametric studies, but it is hard to implement when modeling large membranes with numerous intersecting fold-lines. As an alternative, a similar modeling approach was implemented through the finite element software ABAQUS. The Kapton film used for the experiments in Section IV, with thickness h = 50 µm, was modeled using two shell portions connected by Revolute connectors with rotational elasticity. Discontinuing the membrane at the fold makes the simulation much more efficient as high curvature deformations at the crease are being eliminated. Plane stress (S3R) elements were used with the same elastic material properties in Table 1. Non-linear geometry was used to account for large deflections of the membrane. The mesh was refined around the crease to capture the curved deformations, with a typical size of 0.2 mm, summing up to a total 1398 elements in each portion. The unfolding steps are illustrated in Fig.11. Initial configuration of the membrane was adjusted to fully folded state where the fold-angle is zero. The top edge of the membrane was restrained with a pinned boundary condition allowing the membrane to freely rotate. The membrane was unfolded with a point load applied at the center of bottom edge as shown in Fig. 11. More details on the numerical modeling can be found in reference [21]. Fig. 11 Finite element model for unfolding of a membrane: (a) Mesh of the model, and images of the model at the (b) Initial completely folded configuration, (b) At the neutral angle and (c) Completely unfolded state. In Fig. 12 we compare the prediction of our analytical and numerical solutions against the experimental observations. 11

12 The proposed model is capable of predicting the interaction between panel bending and hinge stiffness. Slight variations are observed for lower loads where the self-weight of the membrane becomes significant. This can be avoided by adding a distributed load along the membrane. Fig. 12 Comparison of analytic model against the experimental observations for different applied loadings. The thickness of the membrane is h = 50µm. VI. Conclusion We have presented an experimental study of the behavior of creases in thin Kapton films. We found that the neutral angle of the fold can be controlled through the parameters of the folding process, such as the applied loading, but it evolves over time due to viscoelastic effects. Once it is formed, each fold behaves as a hinge with constant rotational stiffness, which is independent of the neutral angle, and scales with the bending rigidity of the film. Our results have been incorporated into a simple analytical model based on the Elastica beam theory to predict the deflected shape of membrane taking into consideration panel bending-hinge stiffness interaction. The model was able to predict the deformation with great accuracy. Future work will focus on refining the material modeling of the Kapton, in order to capture the neutral angle in our folding simulations, as well as exploring the time dependence. This includes not only the time after folding, but also the time during which the folding force is applied. We will also expand our results to other materials, such as Mylar or 12

13 paper, in order to identify universal relationships that can be used in a general model of folded thing films. Acknowledgments Authors are grateful to Matthew Mccallum for assisting with experimentation work. Furthermore financial assistance provided by the Senate Research Council of University of Moratuwa and National Research Council of Sri Lanka is greatly appreciated. References [1] Sickinger,C., Breitbach,E., Ultralightweight deployable space structures, 4th International conference on thin-walled structures, Loughborough, England, [2] Guest, S., Deployable structures: Concepts and analysis, Doctoral Thesis, University of Cambridge, [3] Jenkins, C.H.M., Gossamer Spacecraft: Membrane and Inflatable Structures Technology for Space Applications, Volume 191 Progress in Astronautics and Aeronautics, AIAA, Virginia, [4] Ruggiero, E.J., Inman,D.J.,"Gossamer Spacecraft: Recent Trends in Design, Analysis, Experimentation, and Control, J.Spacecraft and Rockets, Vol.43, No.1, Jan.-Feb [5] Natori, M., Sakamoto, H., Katsumata, N., Yamakawa, H., Kishimoto, N., Conceptual model study using origami for membrane space structures a perspective of origami-based engineering, Advance Publication by J-STAGE, Mechanical Engineering Reviews, [6] Papa, A., Pellegrino,S., Systematically Creased Thin-Film Membrane Structures,Journal of Spacecraft and Rockets, Vol. 45, No. 1, January February [7] Nojima, N., Modelling of Folding Patterns in Flat Membranes and Cylinders by Origami, JSME International Journal, Series C, Vol 45, No 1, [8] Arya,M., Lee,N., Pellegrino,S.,Wrapping Thick Membranes with Slipping Folds, 2nd AIAA Spacecraft Structures Conference, AIAA SciTech Forum, [9] Lichodziejewski, D., Derbès, B., Slade, K., Mann, T., Vacuum Deployment and Testing of a 4-Quadrant Scalable Inflatable Rigidizable Solar Sail System, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Austin, TX, United States, [10] Sleight, D.W., Michii,Y., Lichodziejewski,D., Derbès, B.,Mann,T.O.,Finite Element Analysis and Test Correlation of a 10-Meter Inflation-Deployed Solar Sail, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Austin, TX, United States, [11] Arya,M., Pellegrino,S., Deployment mechanics of highly compacted thin membrane structures, Spacecraft Structures Conference, AIAA SciTech Forum, [12] Banik, J.A., Murphey, T.W., Synchronous Deployed Solar Sail Subsystem Design Concept, 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii, April [13] Sakamoto, H., Natori, M., Kadonishi, S., Satoua, Y., Shirasawac, Y., Okuizumic, N.,Mori,O., Furuya,H., Okumaa, M., Folding patterns of planar gossamer space structures consisting of membranes and booms, Acta Astronautica, Pages 34 41, [14] Okuizumi, N., Mura, A., Matsunaga, S., Sakamoto, H., Shirasawa, Y., Mori, O., it Small-scale Experiments and Simulations of Centrifugal Membrane Deployment of Solar Sail Craft "IKAROS", 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, Colorado, 4-7 April [15] Lappas, V.,Adeli, N., Visagie, L., Fernandez, J., Theodorou, T.,Steyn, W., Perren, M.,CubeSail: A low cost CubeSat based solar sail demonstration mission, Journal of Advanced Space Research, Volume 48, Issue 11, December [16] Lechenault, F., Thiria, B., Adda-Bedia, M., The mechanical response of a creased sheet, Physical Review Letters, [17] Andrew, A.C., Philip,B.C.,James,J.J., Gregory,R.W., Richard, V.A., Characterization of creases in polymers for adaptive origami structures,asme 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS2014, Newport, Rhode Island,

14 [18] DuPont, DUPONT KAPTON : Summery of Properties, Technical Data Sheet, 2017 [19] Thiria, B., Adda-Bedia, M., Relaxation Mechanisms in the Unfolding of Thin Sheets B., Physical Review Letters, July [20] Fertis, D.G.,Nonlinear Structural Engineering: with Unique Theories and Methods to Solve Effectively Complex Nonlinear Problems, Springer - Verlag, 2006, Chapter 1. [21] Dharmadasa, B.Y., Mallikarachchi, H.M.Y.C., Finite Element Simulation of Thin Folded Membranes, 7th International Conference on Sustainable Built Environment, Kandy, Sri Lanka,