Membrane wrinkling revisited from a multi-scale point of view

Advanced Modeling and Simulation in Engineering Sciences

Volumn 1, Issue 1, 2014, Pages

  Damil, Noureddine ^a   Potier Ferry, Michel ^b   Hu, Heng ^c  

^a Faculté des Sciences Ben M Sik Av Driss El Harti Sidi Othmane   (Morocco)

^b UNIVERSITÉ DE LORRAINE   (France)

^c WUHAN UNIVERSITY   (China)

Author keywords

Bifurcation; Buckling; Membrane; Multi scale; Slowly variable Fourier coefficients; Wrinkling

Indexed keywords

EID: 84906948964     PISSN: None     EISSN: 22137467     Source Type: Journal    
DOI: 10.1186/2213-7467-1-6     Document Type: Article

References (73)

1. Jenkins CH: Nonlinear dynamic response of membranes: state of the art–update. Applied Mechanics Review 1996, 49: S41-S48. 10.1115/1.3101975
2. Cerda E, Ravi-Chandar K, Mahadevan L: Wrinkling of an elastic sheet under tension. Nature 2000, 419: 579.
3. Cerda E, Mahadevan L: Geometry and physics of wrinkling. Phys Rev Lett 2003, 90: 074302–1-4.
4. Jenkins CHM, Korde UA: Membrane vibration experiments: an historical review and recent results. J Sound Vib 2006, 295: 602–613. 10.1016/j.jsv.2006.01.036
5. Allaoui S, Boisse P, Chatel S, Hamila N, Hivet G, Soulat D, Vidal-Salle E: Experimental and numerical analyses of textile reinforcement forming of a tetrahedral shape. Compos Part A 2011, 42: 612–622. 10.1016/j.compositesa.2011.02.001
6. Li B, Cao YP, Feng XQ, Gao HJ: Mechanics of morphological instabilities and surface wrinkling in soft materials: a review. Soft Matter 2012, 8: 5728–5745. 10.1039/c2sm00011c
7. Wong YW, Pellegrino S: Wrinkled membranes-Part1: experiments. J Mech Mater Struct 2006, 1: 3–25. 10.2140/jomms.2006.1.3
8. Wang CG, Du XW, Tan HF, He XD: A new computational method for wrinkling analysis of gossamer space structures. Int J Solids Struct 2009, 46: 1516–1526. 10.1016/j.ijsolstr.2008.11.018
9. Lecieux Y, Bouzidi R: Experimentation analysis on membrane wrinkling under biaxial load – comparison with bifurcation analysis. Int J Solids Struct 2010, 47: 2459–2475. 10.1016/j.ijsolstr.2010.05.005
10. Lecieux Y, Bouzidi R: Numerical wrinkling prediction of thin hyperelastic structures by direct energy minimization. Adv Eng Softw 2012, 50: 57–68.
11. Healey TJ, Li Q, Cheng RB: Wrinkling behavior of highly stretched rectangular elastic films via parametric global bifurcation. J Nonlinear Sc 2013, 23: 777–805. 10.1007/s00332-013-9168-3
12. Everall PR, Hunt G: Arnold tongue predictions of secondary buckling in thin elastic plates. J Mech Phys Solids 1999, 47: 2187–2206. 10.1016/S0022-5096(99)00008-3
13. Everall PR, Hunt G: Mode jumping in the buckling of struts and plates: a comparative study. Int J Non-Linear Mech 2000, 35: 1067–1079. 10.1016/S0020-7462(99)00080-3
14. Coman CD: Edge-buckling in stretched thin films under in-plane bending. Z Angew Math Phys 2007, 58: 510–525. 10.1007/s00033-006-6036-0
15. Coman CD, Bassom AP: On the wrinkling of a pre-stressed annular thin film in tension. J Mech Phys Solids 2007, 55: 1601–1617. 10.1016/j.jmps.2007.01.006
16. Coman CD, Liu X: Semi-analytical approximations for a class of multi-parameter eigenvalue problems related to tensile buckling. Z Angew Math Phys 2013, 64: 863–883. 10.1007/s00033-012-0237-5
17. Diaby A, Le Van A, Wielgosz C: Buckling and wrinkling of prestressed membranes. Finite Element Analysis and Design 2006, 42: 992–1001. 10.1016/j.finel.2006.03.003
18. Liu XX, Jenkins CH, Schur WW: Large deflection analysis of pneumatic envelopes using a penalty parameter modified material model. Finite Element Analysis and Design 2001, 37: 233–251. 10.1016/S0168-874X(00)00040-8
19. Rossi R, Lazzari M, Vitaliani R, Onate E: Simulation of light-weight membrane structures by wrinkling model. Int J Numer Methods Eng 2005, 62: 2127–2153. 10.1002/nme.1266
20. Tabarrok B, Qin Z: Nonlinear analysis of tension structures. Comput Struct 1992, 45: 973–984. 10.1016/0045-7949(92)90056-6
21. Troufflard J, Cadou JM, Rio G: Recherche de forme des gilets de sauvetage gonflables. Mécanique et Industries 2010, 11: 117–122. 10.1051/meca/2010023
22. Rodriguez J, Rio G, Cadou JM, Troufflard J: 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 2011, 49: 1468–1474. 10.1016/j.tws.2011.07.011
23. Roddeman DG, Oomens CWJ, Janssen JD, Drukker J: The wrinkling of thin membranes. Part 1: theory. J Appl Mech 1987, 54: 884–887. 10.1115/1.3173133
24. Roddeman DG, Oomens CWJ, Janssen JD, Drukker J: The wrinkling of thin membranes. Part 2: numerical analysis. J Appl Mech 1987, 54: 888–892. 10.1115/1.3173134
25. Lu K, Accorsi M, Leonard J: Finite element analysis of membrane wrinkling. Int J Numer Methods Eng 2001, 50: 1017–1038. 10.1002/1097-0207(20010220)50:5<1017::AID-NME47>3.0.CO;2-2
26. Schoop H, Taenzer L, Hornig J: Wrinkling of nonlinear membranes. Comput Mech 2002, 29: 68–74. 10.1007/s00466-002-0326-y
27. Miyazaki Y: Wrinkle/slack model and finite element dynamics of membrane. Int J Numer Methods Eng 2006, 66: 1179–1209. 10.1002/nme.1588
28. Akita T, Nakashino T, Natori MC, Park KC: A simple computer implementation of membrane wrinkle behaviour via a projection technique. Int J Numer Methods Eng 2007, 71: 1231–1259. 10.1002/nme.1990
29. Banerjee B, Shaw A, Roy D: The theory of Cosserat points applied to the analyses of wrinkled and slack membranes. Comput Mech 2009, 43: 415–429. 10.1007/s00466-008-0314-y
30. Pimprikar NA, Banerjee B, Roy D, Vasu RM, Reid SR: New computational approaches for wrinkled and slack membranes. Int J Solids Struct 2010, 47: 2476–2486. 10.1016/j.ijsolstr.2010.05.004
31. Counhaye C: Modélisation et contrôle industriel de la géométrie des aciers laminés à froid (modelling and industrial control of the geometry of cold rolled steels). Dissertation: Université de Liège; 2000. (in French)
32. Abdelkhalek S, Montmitonnet P, Legrand N, Buessler P: Coupled approach for flatness prediction in thin strip cold rolling. Int J Mech Sci 2011, 53: 661–675. 10.1016/j.ijmecsci.2011.04.001
33. Damil N, Potier-Ferry M, Hu H: New nonlinear multiscale models for membrane wrinkling. Comptes Rendus Mecanique 2013, 341: 616–624. 10.1016/j.crme.2013.06.001
34. Wesfreid JE, Zaleski S: Cellular Structures in Instabilities. In Lecture Notes in Physics, vol 210. Heidelberg: Springer-Verlag; 1984.
35. Iooss G, Mielke A, Demay Y: Theory of steady Ginzburg-Landau equation in hydrodynamic stability problems. Eur J Mech B Fluids 1989, 8: 229–268.
36. Cross MC, Hohenberg PC: Pattern formation out of equilibrium. Rev Mod Phys 1993, 65: 851–1112. 10.1103/RevModPhys.65.851
37. Hoyle R: Pattern Formation, an Introduction to Methods. Cambridge: Cambrige University Press; 2006.
38. Damil N, Potier-Ferry M: A generalized continuum approach to describe instability pattern formation by a multiple scale analysis. Comptes Rendus Mecanique 2006, 334: 674–678. 10.1016/j.crme.2006.09.002
39. Damil N, Potier-Ferry M: A generalized continuum approach to predict local buckling patterns of thin structures. European Journal of Computational Mechanics 2008, 17: 945–956.
40. Damil N, Potier-Ferry M: Influence of local wrinkling on membrane behaviour: a new approach by the technique of slowly variable Fourier coefficients. J Mech Phys Solids 2010, 58: 1139–1153. 10.1016/j.jmps.2010.04.002
41. Hu H, Damil N, Potier-Ferry M: A bridging technique to analyze the influence of boundary conditions on instability patterns. J Comput Phys 2011, 230: 3753–3764. 10.1016/j.jcp.2011.01.044
42. Segel LA: Distant side walls cause slow amplitude modulation of cellular convection. J Fluid Mech 1969, 38: 203–224. 10.1017/S0022112069000127
43. Newell AC, Whitehead JA: Finite band width, finite amplitude convection. J Fluid Mech 1969, 38: 279–303. 10.1017/S0022112069000176
44. Amazigo JC, Budiansky B, Carrier GF: Asymptotic analyses of the buckling of imperfect columns on non-linear elastic foundations. Int J Solids Struct 1970, 6: 1341–1356. 10.1016/0020-7683(70)90067-3
45. Pomeau Y, Zaleski S: Wavelength selection in one-dimensional cellular structures. J Phys 1981, 42: 515–528. 10.1051/jphys:01981004204051500
46. Potier-Ferry M: Amplitude Modulation, Phase Modulation and Localization of Buckling Patterns. In Collapse: The Buckling of Structure in Theory and Practice. Edited by: Thompson JMT, Hunt GW. Cambridge: Cambridge University Press; 1983:148–159.
47. Hunt GW, Bolt HM, Thompson JMT: Structural localization phenomena and the dynamical phase space analogy. Proc R Soc Lond A 1989, 425: 245–267. 10.1098/rspa.1989.0105
48. Lee SH, Waas AM: Initial post-buckling behavior of a finite beam on an elastic foundation. Int J Non Linear Mech 1996, 31: 313–328. 10.1016/0020-7462(95)00065-8
49. Hunt GW, Peletier MA, Champneys AR, Woods PD, Ahmer Wadee M, Budd CJ, Lord GJ: Cellular buckling in long structures. Nonlinear Dynamics 2000, 21: 3–29. 10.1023/A:1008398006403
50. Coman CD, Bassom AP, Wadee MK: Elasto-plastic localised response in one-dimensional structural models. J Eng Math 2003, 47: 83–100. 10.1023/A:1025856602682
51. Rosen BW: Influence of Fiber and Matrix Characteristics on Mechanics of Deformation and Fracture of Fibrous Composites, in “Fiber Composite Materials, Papers Presented at a Seminar of the American Society for Metals, October 17 and 18, 1964”. Ohio: Metal Parks; 1965:37–75.
52. Léotoing L, Drapier S, Vautrin A: Nonlinear interaction of geometrical and material properties in sandwich beam instabilities. Int J Solids Struct 2002, 39: 3717–3739. 10.1016/S0020-7683(02)00181-6
53. Chen X, Hutchinson JW: Herringbone buckling patterns of compressed thin films on compliant substrates. J Appl Mech 2004, 71: 597–603. 10.1115/1.1756141
54. Audoly B, Boudaoud A: 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 2008, 56: 2422–2443. 10.1016/j.jmps.2008.03.002
55. Wang S, Song J, Kim DH, Huang Y, Rogers JA: Local versus global buckling of thin films on elastomeric substrates. Appl Phys Lett 2008, 93: 023126. 10.1063/1.2956402
56. Fischer FD, Rammerstorfer FG, Friedl N, Wieser W: Buckling phenomena related to rolling and levelling of sheet metal. Int J Mech Sci 2000, 42: 1887–1910. 10.1016/S0020-7403(99)00079-X
57. Abdelkhalek S, Montmitonnet P, Potier-Ferry M, Zahrouni H, Legrand N, Buessler P: Strip flatness modelling including buckling phenomena during thin strip cold rolling. Ironmak Steelmak 2010, 37: 290–297. 10.1179/030192310X12646889255708
58. Grandidier JC, Ferron G, Potier-Ferry M: Microbuckling and strength in long-fiber composites: theory and experiments. Int J Solids Struct 1992, 29: 1753–1761. 10.1016/0020-7683(92)90168-S
59. Kyriakides S, Arseculeratne R, Perry EJ, Liechti KM: On the compressive failure of fiber reinforced composites. Int J Solids Struct 1995, 32: 689–738. 10.1016/0020-7683(94)00157-R
60. Waas AM, Schultheisz CR: Compressive failure of composites. 2 Experimental studies. Prog Aerosp Sci 1996, 32: 43–78. 10.1016/0376-0421(94)00003-4
61. Drapier S, Grandidier JC, Potier-Ferry M: A structural approach of plastic microbuckling in long fibre composites: comparison with theoretical and experimental results. Int J Solids Struct 2001, 38: 3877–3904. 10.1016/S0020-7683(00)00247-X
62. Mhada K, Braikat B, Hu H, Damil N, Potier-Ferry M: About macroscopic models of instability pattern formation. Int J Solids Struct 2012, 49: 2978–2989. 10.1016/j.ijsolstr.2012.05.033
63. Boucif M, Wesfreid JE, Guyon E: Experimental study of wavelength selection in the elastic buckling instability of thin plates. Eur J Mech A Solids 1991, 10: 641–661.
64. Feyel F, Chaboche JL: FE2 multiscale approach for modeling the elastoviscoplastic behavior of long fiber SiC/Ti composite materials. Comput Methods Appl Mech Eng 2000, 183: 309–330. 10.1016/S0045-7825(99)00224-8
65. Geymonat G, Muller S, Triantafyllidis N: Homogenization of nonlinearly elastic materials: microscopic bifurcation and macroscopic loss of rank-one convexity. Archives for Rational Mechanics and Analysis 1993, 122: 231–290. 10.1007/BF00380256
66. Liu Y, Yu K, Hu H, Belouettar S, Potier-Ferry M: A Fourier-related double scale analysis on instability phenomena of sandwich beams. Int J Solids Struct 2012, 49: 3077–3088. 10.1016/j.ijsolstr.2012.06.005
67. Yu K, Hu H, Chen S, Belouettar S, Potier-Ferry M: Multi-scale techniques to analyze instabilities in sandwich structures. Compos Struct 2013, 96: 751–762.
68. Koiter WT: On the Stability of Elastic Equilibrium. Dissertation, Delft. NASA Technical Translation F-10. US Dept. of Commerce/Nat. Bur. of Standards N67–25033: 833, Clearinghouse; 1945. 1967 1967
69. Budiansky B: Theory of buckling and post-buckling behaviour of elastic structures. Adv Appl Mech 1974, 14: 1–65.
70. Cochelin B, Damil N, Potier-Ferry M: Méthode Aymptotique Numérique. Paris: Hermes-Lavoisier; 2007.
71. Jacques N, Potier-Ferry M: On mode localization in tensile plate bukling. Comptes Rendus Mecanique 2005, 333: 804–809. 10.1016/j.crme.2005.10.013
72. Nayfeh AH: Perturbation Methods. New York: John Wiley and Sons; 1973.
73. Sanchez-Palencia E: Non-Homogeneous Media and Vibration Theory. In Lecture Notes in Physics, vol 127. Heidelberg: Springer-Verlag; 1980.