Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain

Journal of the Mechanics and Physics of Solids

Volumn 62, Issue 1, 2014, Pages 163-180

  Taylor, Michael ^a   Bertoldi, Katia ^a,c   Steigmann, David J ^b  

^a HARVARD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

Nonlinear elasticity; Thin elastic sheets; Wrinkling

Indexed keywords

ANALYTICAL RESULTS; ELASTIC SHEETS; NONLINEAR ELASTICITY; NONLINEAR PLATE THEORY; NUMERICAL SOLUTION; SPATIAL RESOLUTION; WRINKLING; WRINKLING PATTERNS;

DYNAMICAL SYSTEMS; NUMERICAL METHODS;

ELASTICITY;

EID: 84888288024     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2013.09.024     Document Type: Article

References (48)

1. M. Ben Amar, and J. Dervaux Morphogenesis of growing soft tissues Phys. Rev. Lett. 101 2008 068101
2. E. Cerda, and L. Mahadevan Geometry and physics of wrinkling Phys. Rev. Lett. 90 074302 2003 1 4
3. E. Cerda, K. Ravi-Chandar, and L. Mahadevan Wrinkling of a stretched elastic sheet Nature 419 2002 579
4. P. Ciarlet An Introduction to Differential Geometry with Applications to Elasticity 2005 Springer The Netherlands
5. P.G. Ciarlet, and S. Mardare An intrinsic approach and a notion of polyconvexity for nonlinearly elastic plates C. R. Acad. Sci. Paris 350 I 2012 111 116
6. B. Dacarogna Direct Methods in the Calculus of Variations 1989 Springer Berlin
7. B. Davidovitch, R.D. Schroll, D. Vella, M. Adda-Bedia, and E.A. Cerda Prototypical model for tensional wrinkling in thin sheets Proc. Natl. Acad. Sci. U.S.A. 108 45 2011 18227 18232
8. K. Efimenko, M. Rackaitis, E. Manias, A. Vaziri, L. Mahadevan, and J. Genzer Nested self-similar wrinkling patterns in skins Nat. Mater. 4 2005 293 297
9. G. Friesecke, R. James, and S. Muller A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence Arch. Ration. Mech. Anal. 180 2006 183 236
10. Haseganu, E., 1994. Analytical Investigation of Tension Fields in Lightweight Membrane Structures (Ph.D. thesis). University of Alberta, Edmonton, AB.
11. E. Haseganu, and D. Steigmann Analysis of partly wrinkled membranes by the method of dynamic relaxation Comput. Mech. 14 1994 596 614
12. T. Healey, Q. Li, and R.-B. Cheng Wrinkling behavior of highly stretched rectangular elastic films via parametric global bifurcation J. Nonlinear Sci. 2013 10.1007/s00332-013-9168-3 Online
13. M. Hilgers, and A. Pipkin The graves condition for variational problems of arbitrary order IMA J. Appl. Math. 48 1992 265 269
14. M. Hilgers, and A. Pipkin Elastic sheets with bending stiffness Q. J. Mech. Appl. Math. 45 1992 57 75
15. M. Hilgers, and A. Pipkin Bending energy of highly elastic membranes ii Q. Appl. Math. 54 1996 307 316
16. K. Kareklas, D. Nettle, and T. Smulders Water-induced finger wrinkles improve handling of wet objects Biol. Lett. 9 2013 20120999
17. R.Y. Kezerashvili Proceedings of the Second International Symposium on Solar Sailing 2010
18. D. Kim, J. Ahn, W. Choi, H. Kim, T. Kim, J. Song, Y. Huang, Z. Liu, C. Lu, and J. Rogers Stretchable and foldable silicon integrated circuits Science 320 2008 507 511
19. W. Koiter A consistent first approximation in the general theory of thin elastic shells W. Koiter, Proceedings of the IUTAM Symposium on the Theory of Thin Elastic Shells, Delft 1960 North-Holland Amsterdam 12 33
20. W. Koiter On the nonlinear theory of thin elastic shells Proc. K. Ned. Akad. Wet. B69 1966 1 54
21. H. LeDret, and A. Raoult The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity J. Math. Pures Appl. 75 1995 551 580
22. V. Nayyar, K. Ravi-Chandar, and R. Huang Stretch-induced stress pattern and wrinkles in hyperelastic thin sheets Int. J. Solids Struct. 48 2011 3471 3483
23. A. Pipkin The relaxed energy density for isotropic membranes IMA J. Appl. Math. 36 1986 85 99
24. E. Puntel, L. Deseri, and E. Fried Wrinkling of a stretched thin sheet J. Elasticity 105 2011 137 170
25. R. Reissner On tension field theory Proc. V Int. Congr. Appl. Mech. 88 1938
26. M. Rezaiee-pajand, M. Kadkhodayan, J. Alamatian, and L. Zhang A new method of fictitious viscous damping determination for the dynamic relaxation method Comput. Struct. 89 2011 783 794
27. J. Rodriguez, G. Rio, J. Cadou, and 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. 49 11 2011 1468 1474
28. D. Roxburgh, D. Steigmann, and R. Tait Azimuthal shearing and transverse deflection of an annular elastic membrane Int. J. Eng. Sci. 33 1994 27 43
29. R. Schroll, E. Katifori, and B. Davidovitch Elastic building blocks for confined sheets Phys. Rev. Lett. 106 074301 2011 1 4
30. Shugar, T., 1990. Automated Dynamic Relaxation Solution Algorithms for Compliant Systems. Technical Report. N-1812, Naval Civil Engineering Laboratory, Port Hueneme, CA.
31. S. Silling Finite difference modelling of phase changes and localization in elasticity Comput. Methods Appl. Mech. Eng. 70 1988 51 73
32. S. Silling Phase changes induced by deformation in isothermal elastic crystals J. Mech. Phys. Solids 37 1989 293 316
33. I.S. Sokolnikoff Tensor Analysis Theory and Applications 1951 John Wiley and Sons, Inc. New York
34. D.J. Steigmann Tension-field theory Proc. R. Soc. Lond. A 429 1990 141 173
35. D.J. Steigmann Thin-plate theory for large elastic deformations Int. J. Non-linear Mech. 42 2007 233 240
36. D.J. Steigmann Applications of polyconvexity and strong ellipticity to nonlinear elasticity and elastic plate theory J. Schroder, P. Neff, CISM Course on Applications of Poly-, Quasi-, and Rank-One Convexity in Applied Mechanics vol. 516 2010 Springer Wien and New York 265 299
37. D.J. Steigmann A well-posed finite-strain model for thin elastic sheets with bending stiffness Math. Mech. Solids 13 2013 103 112
38. D.J. Steigmann, and R.W. Ogden Elastic surface-substrate interactions Proc. R. Soc. Lond. A 455 1999 437 474
39. M. Taylor, and D.J. Steigmann Simulation of laminated thermoelastic membranes J. Therm. Stresses 32 2009 448 476
40. B.H.V. Topping, and A.I. Khan Parallel computation schemes for dynamic relaxation Eng. Comput. 11 6 1994 513 548
41. H. Vandeparre, S. Gabriele, F. Brau, C. Gay, K.K. Parker, and P. Damman Hierarchical wrinkling patterns Soft Matter 6 2010 5751 5756
42. H. Vandeparre, M. Pineirua, F. Brau, B. Roman, J. Bico, C. Gay, W. Bao, C.N. Lau, P.M. Reis, and P. Damman Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains Phys. Rev. Lett. 106 224301 2011 1 4
43. G. Vulpetti, L. Johnson, and G.L. Matloff Solar Sails A Novel Approach to Interplanetary Travel 2008 Copernicus Books, Springer Science+Business Media New York, NY
44. H. Wagner Ebene blechwandtrhger mit sehr diinnem stegblech Z. Flugtech. Motorluftschiffahrt 20 8-12 1929
45. Y. Wong, and S. Pellegrino Winkled membranes. Part 1 experiments J. Mech. Mater. Struct. 1 2006 3 25
46. Y. Wong, and S. Pellegrino Winkled membranes. Part 2 analytical models J. Mech. Mater. Struct. 1 2006 27 61
47. Y. Wong, and S. Pellegrino Winkled membranes. Part 3 numerical simulations J. Mech. Mater. Struct. 1 2006 63 95
48. Zheng, L., 2009. Wrinkling of Dielectric Elastomer Membranes (Ph.D. thesis). California Institute of Technology, Pasadena, CA.