Comptes Rendus
New nonlinear multi-scale models for wrinkled membranes
Comptes Rendus. Mécanique, Volume 341 (2013) no. 8, pp. 616-624.

A new macroscopic approach to the modelling of membrane wrinkling is presented. Most of the studies of the literature about membrane behaviour are macroscopic and phenomenological, the influence of wrinkles being accounted for by nonlinear constitutive laws without compressive stiffness. The present method is multi-scale and it permits to predict the wavelength and the spatial distribution of wrinkling amplitude. It belongs to the family of Landau–Ginzburg bifurcation equations and especially relies on the technique of Fourier series with slowly varying coefficients. The result is a new family of macroscopic membrane models that are deduced from Föppl–von Kármán plate equations. Numerical solutions are presented, giving the size of the wrinkles as a function of the applied compressive and tensile stresses.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2013.06.001
Keywords: Wrinkling, Membrane, Slowly variable Fourier coefficients, Multi-scale

Noureddine Damil 1; Michel Potier-Ferry 2, 3; Heng Hu 4

1 Laboratoire dʼingénierie et matériaux, LIMAT, faculté des sciences Ben MʼSik, université Hassan II Mohammedia Casablanca, Sidi Othman, Casablanca, Morocco
2 Laboratoire dʼétudes des microstructures et de mécanique des matériaux, LEM3, UMR CNRS 7239, université de Lorraine, île du Saulcy, 57045 Metz cedex 01, France
3 Laboratory of Excellence on Design of Alloy Metals for Low-Mass Structures (DAMAS), université de Lorraine, France
4 School of Civil Engineering, Wuhan University, 8 South Road of East Lake, 430072 Wuhan, PR China
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Noureddine Damil; Michel Potier-Ferry; Heng Hu. New nonlinear multi-scale models for wrinkled membranes. Comptes Rendus. Mécanique, Volume 341 (2013) no. 8, pp. 616-624. doi : 10.1016/j.crme.2013.06.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.06.001/

[1] Y.W. Wong; S. Pellegrino Wrinkled membranes—Part 1: Experiments, J. Mech. Mater. Struct., Volume 1 (2006), pp. 3-25

[2] C.G. Wang; X.W. Du; H.F. Tan; X.D. He A new computational method for wrinkling analysis of gossamer space structures, Int. J. Solids Struct., Volume 46 (2009), pp. 1516-1526

[3] Y. Lecieux; R. Bouzidi Experimentation analysis on membrane wrinkling under biaxial load—Comparison with bifurcation analysis, Int. J. Solids Struct., Volume 47 (2010), pp. 2459-2475

[4] Y. Lecieux; R. Bouzidi Numerical wrinkling prediction of thin hyperelastic structures by direct energy minimization, Adv. Eng. Softw., Volume 50 (2012), pp. 57-68

[5] B. Tabarrok; Z. Qin Nonlinear analysis of tension structures, Comput. Struct., Volume 45 (1992), pp. 973-984

[6] J. Rodriguez; G. Rio; J.-M. Cadou; J. Troufflard Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior, Thin-Walled Struct., Volume 49 (2011), pp. 1468-1474

[7] D.G. Roddeman; C.W.J. Oomens; J.D. Janssen; J. Drukker The wrinkling of thin membranes: Part 1—Theory, J. Appl. Mech., Volume 54 (1987), pp. 884-887

[8] K. Lu; M. Accorsi; J. Leonard Finite element analysis of membrane wrinkling, Int. J. Numer. Methods Eng., Volume 50 (2001), pp. 1017-1038

[9] H. Schoop; L. Taenzer; J. Hornig Wrinkling of nonlinear membranes, Comput. Mech., Volume 29 (2002), pp. 68-74

[10] Y. Miyazaki Wrinkle/slack model and finite element dynamics of membrane, Int. J. Numer. Methods Eng., Volume 66 (2006), pp. 1179-1209

[11] T. Akita; T. Nakashino; M.C. Natori; K.C. Park A simple computer implementation of membrane wrinkle behaviour via a projection technique, Int. J. Numer. Methods Eng., Volume 71 (2007), pp. 1231-1259

[12] B. Banerjee; A. Shaw; D. Roy The theory of Cosserat points applied to the analyses of wrinkled and slack membranes, Comput. Mech., Volume 43 (2009), pp. 415-429

[13] N.A. Pimprikar; B. Banerjee; D. Roy; R.M. Vasu; S.R. Reid New computational approaches for wrinkled and slack membranes, Int. J. Solids Struct., Volume 47 (2010), pp. 2476-2486

[14] Cellular Structures in Instabilities (J.E. Wesfreid; S. Zaleski, eds.), Lect. Notes Phys., vol. 210, Springer-Verlag, Heidelberg, 1984

[15] R. Hoyle Pattern Formation, an Introduction to Methods, Cambridge University Press, 2006

[16] N. Damil; M. Potier-Ferry A generalized continuum approach to describe instability pattern formation by a multiple scale analysis, C. R. Mecanique, Volume 334 (2006), pp. 674-678

[17] N. Damil; M. Potier-Ferry Influence of local wrinkling on membrane behaviour: a new approach by the technique of slowly variable Fourier coefficients, J. Mech. Phys. Solids, Volume 58 (2010), pp. 1139-1153

[18] H. Hu; N. Damil; M. Potier-Ferry A bridging technique to analyze the influence of boundary conditions on instability patterns, J. Comput. Phys., Volume 230 (2011), pp. 3753-3764

[19] K. Mhada; B. Braikat; H. Hu; N. Damil; M. Potier-Ferry About macroscopic models of instability pattern formation, Int. J. Solids Struct., Volume 49 (2012), pp. 2978-2989

[20] Y. Liu; K. Yu; H. Hu; S. Belouettar; M. Potier-Ferry A Fourier-related double scale analysis on instability phenomena of sandwich beams, Int. J. Solids Struct., Volume 49 (2012), pp. 3077-3088

[21] E. Cerda; L. Mahadevan Geometry and physics of wrinkling, Phys. Rev. Lett., Volume 90 (2003), p. 074302

[22] E. Cerda; K. Ravi-Chandar; L. Mahadevan Wrinkling of an elastic sheet under tension, Nature, Volume 419 (2000), pp. 579-580

[23] N. Friedl; F.G. Rammerstorfer; F.D. Fisher Buckling of stretched strips, Comput. Struct., Volume 78 (2000), pp. 185-190

[24] N. Jacques; M. Potier-Ferry On mode localisation in tensile plate buckling, C. R. Mecanique, Volume 333 (2005), pp. 804-809

[25] B. Cochelin; N. Damil; M. Potier-Ferry Asymptotic-numerical methods and Padé approximants for nonlinear elastic structures, Int. J. Numer. Methods Eng., Volume 37 (1994), pp. 1187-1213

[26] B. Audoly; A. Boudaoud Buckling of a stiff film bound to a compliant substrate—Part II: A global scenario for the formation of herringbone pattern, J. Mech. Phys. Solids, Volume 56 (2008), pp. 2422-2443

[27] S. Abdelkhalek; P. Montmitonnet; M. Potier-Ferry; H. Zahrouni; N. Legrand; P. Buessler Strip flatness modelling including buckling phenomena during thin strip cold rolling, Ironmak. Steelmak., Volume 37 (2010), pp. 290-297

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