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Birth and decay of tensional wrinkles in hyperelastic sheets

Andreea Panaitescu1, Meng Xin2, Benny Davidovitch2, Julien Chopin3, and Arshad Kudrolli1

  • 1Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
  • 2Department of Physics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
  • 3Instituto de Física, Universidade Federal da Bahia, Salvador-BA 40170-115, Brazil

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Phys. Rev. E 100, 053003 – Published 18 November, 2019

DOI: https://doi.org/10.1103/PhysRevE.100.053003

Abstract

We demonstrate with experiments that wrinkling in stretched latex sheets occurs over finite strains, and that their amplitudes grow and then decay to zero over a greater range of applied strains compared with linear elastic materials. The wrinkles occur provided the sheet is sufficiently thin compared to its width, and only over a finite range of length-to-width ratios. We show with simulations that the Mooney-Rivlin hyperelastic model describes the observed growth and decay of the wrinkles in our experiments. The decrease of wavelength with applied tension is found to be consistent with a far-from-threshold scenario proposed by Cerda and Mahadevan in 2003. However, the amplitude is observed to decrease with increasing tensile load, in contrast with the prediction of their original model. We address the crucial assumption of collapse of compressive stress, as opposed to collapse of compressive strain, underlying the far-from-threshold analysis, and test it by measuring the actual arc-length of the stretched sheet in the transverse direction and its difference from the width of a planar projection of the wrinkled shape. Our experiments and numerical simulations indicate a collapse of the compressive stress and reveal that a proper implementation of the far-from-threshold analysis is consistent with the nonmonotonic dependence of the amplitude on applied tensile load observed in experiments and simulations. Thus, our work support and extend far-from-threshold analysis to the stretching problem of rectangular hyperelastic sheets.

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References (29)

  1. B. Audoly and Y. Pomeau, Elasticity and Geometry (Oxford University Press, Oxford, 2010).
  2. B. Davidovitch, R. D. Schroll, D. Vella, M. Adda-Bedia, and E. A. Cerda, Proc. Natl. Acad. Sci. USA 108, 18227 (2011).
  3. J. Chopin and A. Kudrolli, Phys. Rev. Lett. 111, 174302 (2013).
  4. N. Friedl, F. Rammerstorfer, and F. Fischer, Comput. Struct. 78, 185 (2000).
  5. E. Cerda, K. Ravi-Chandar, and L. Mahadevan, Nature (London) 419, 579 (2002).
  6. E. Cerda and L. Mahadevan, Phys. Rev. Lett. 90, 074302 (2003).
  7. J. Kim, J. A. Hanna, M. Byun, C. D. Santangelo, and R. C. Hayward, Science 335, 1201 (2012).
  8. T. J. Healey, Q. D. Li, and R. B. Cheng, J. Nonlinear Sci. 23, 777 (2013).
  9. L. Zheng, Wrinkling of dielectric elastomer membranes, Ph.D. thesis, California Institute of Technology, 2009.
  10. V. Nayyar, K. Ravi-Chandar, and R. Huang, Intl. J. Solids Struct. 48, 3471 (2011).
  11. T. Y. Kim, E. Puntel, and E. Fried, Intl. J. Solids Struct. 49, 771 (2012).
  12. M. Taylor, K. Bertoldi, and D. J. Steigmann, J. Mech. Phys. Solids 62, 163 (2014).
  13. Q. Li and T. J. Healey, J. Mech. Phys. Solids 97, 260 (2016).
  14. C. Fu, T. Wang, F. Xu, Y. Huo, and M. Potier-Ferry, J. Mech. Phys. Solids 124, 446 (2019).
  15. A. A. Sipos and E. Fehér, Intl. J. Solids Struct. 97–98, 275 (2016).
  16. J. Chopin, V. Demery, and B. Davidovitch, J. Elast. 119, 137 (2015).
  17. J. D. Paulsen, E. Hohlfeld, H. King, J. Huang, Z. Qiu, T. P. Russell, N. Menon, D. Vella, and B. Davidovitch, Proc. Natl. Acad. Sci. USA 113, 1144 (2016).
  18. D. Vella and B. Davidovitch, Phys. Rev. E 98, 013003 (2018).
  19. B. Davidovitch, Y. Sun, and G. M. Grason, Proc. Natl. Acad. Sci. USA 116, 1483 (2019).
  20. V. Nayyar, K. Ravi-Chandar, and R. Huang, Intl. J. Solids Struct. 51, 1847 (2014).
  21. M. Xin and B. Davidovitch (unpublished).
  22. T. Wang, C. Fu, F. Xu, Y. Huo, and M. Potier-Ferry, Intl. J. Eng. Sci. 136, 1 (2019).
  23. J. Chopin, A. Panaitescu, and A. Kudrolli, Phys. Rev. E 98, 043003 (2018).
  24. L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, Oxford, 1975).
  25. D. L. Blair and A. Kudrolli, Phys. Rev. Lett. 94, 166107 (2005).
  26. L. Landau and E. Lifshitz, Theory of Elasticity (Pergamon Press, Oxford, 1970).
  27. M. Stein and J. M. Hedgepth, Analysis of partly wrinkled membranes, NASA (Washington) Technical Note D–813 (1961).
  28. A. C. Pipkin, IMA J. Appl. Math. 36, 85 (1986).
  29. D. J. Steigmann, Proc. R. Soc. London A 429, 141 (1990).

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Phys. Rev. E 100, 053003– Published 18 November, 2019
  • Received 14 June 2019
Article part of CHORUS
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