Abstract
We revisit the delamination of a solid adhesive sheet under uniaxial compression from a flat, rigid substrate. Using energetic considerations and scaling arguments, we show that the phenomenology is governed by three dimensionless groups, which characterize the level of confinement imposed on the sheet, as well as its extensibility and bendability. Recognizing that delamination emerges through a subcritical bifurcation from a planar, uniformly compressed state, we predict that the dependence of the threshold confinement level on the extensibility and bendability of the sheet, as well as the delaminated shape at threshold, varies markedly between two asymptotic regimes of these parameters. For sheets whose bendability is sufficiently high, the delaminated shape is a large-slope “fold,” where the amplitude is proportional to the imposed confinement. In contrast, for lower values of the bendability parameter, the delaminated shape is a small-slope “ruck,” whose amplitude increases more moderately upon increasing confinement. Realizing that the instability of the fully laminated state requires a finite extensibility of the sheet, we introduce a simple model that allows us to construct a bifurcation diagram that governs the delamination process.
Graphic abstract
Similar content being viewed by others
References
D. Vella, Nat. Rev. Phys. 1, 425 (2019)
J. Bico, É. Reyssat, B. Roman, Annu. Rev. Fluid Mech. 50, 629 (2018)
D.P. Holmes, Current Opin. Colloid Inter. Sci. Particle Syst. 40, 118 (2019)
J.D. Paulsen, Ann. Rev. Condens. Matter Phys. 10, 431 (2019)
D. Vella, J. Bico, A. Boudaoud, B. Roman, P.M. Reis, Proc. Natl. Acad. Sci. USA 106, 10901 (2009)
T.J.W. Wagner, D. Vella, Phys. Rev. Lett. 107, 044301 (2011)
O. Oshri, Y. Liu, J. Aizenberg, A.C. Balazs, Phys. Rev. E 97, 062803 (2018)
T.J.W. Wagner, D. Vella, Soft Matter 9, 1025 (2013)
D. Vella, A. Boudaoud, M. Adda-Bedia, Phys. Rev. Lett. 103, 174301 (2009)
J.M. Kolinski, P. Aussillous, L. Mahadevan, Phys. Rev. Lett. 103, 174302 (2009)
G. Gioia, M. Ortiz, Adv. Appl. Mech. 33, 119 (1997)
E.A. Jagla, Phys. Rev. B 75, 085405 (2007)
J. Bedrossian, R.V. Kohn, Commun. Pure Appl. Math. 68, 472 (2015)
J.W. Hutchinson, M.D. Thouless, E.G. Liniger, Acta Metall. Mater. 40, 295 (1992)
M.W. Moon, K.R. Lee, K.H. Oh, J.W. Hutchinson, Acta Mater. 52, 3151 (2004)
C. Majidi, R.S. Fearing, Proc. Royal Soc. A: Math. Phys. Eng. Sci. 464, 1309 (2008)
H. Bense, M. Tani, M. Saint-Jean, E. Reyssat, B. Roman, J. Bico, Soft Matter (2020)
J. Hure, B. Roman, J. Bico, Phys. Rev. Lett. 106, 174301 (2011)
J. Hure, B. Audoly, J. Mech. Phys. Solids 61, 450 (2013)
E. Hohlfeld, B. Davidovitch, Phys. Rev. E 91, 012407 (2015)
G. Napoli, S. Turzi, Meccanica 52, 3481 (2017)
A.A. Lee, C. Le Gouellec, D. Vella, Extreme Mech. Lett. 5, 81 (2015)
S. Singamaneni, M.E. McConney, V.V. Tsukruk, Adv. Mater. 22, 1263 (2010)
O. Ortiz, A. Vidyasagar, J. Wang, R. Toomey, Langmuir 26, 17489 (2010). (( PMID: 20929198))
S.S. Velankar, V. Lai, R.A. Vaia, ACS Appl. Mater. Interfaces 4, 24 (2012)
T. Tanaka, S.T. Sun, Y. Hirokawa, S. Katayama, J. Kucera, Y. Hirose, T. Amiya, Nature 325, 796 (1987)
D. Kumar, T.P. Russell, B. Davidovitch, N. Menon, Nat. Mater. 19, 690 (2020)
B. Davidovitch, R.D. Schroll, D. Vella, M. Adda-Bedia, E.A. Cerda, Proc. Nat. Acad. Sci. 108, 18227 (2011)
V. Démery, B. Davidovitch, C.D. Santangelo, Phys. Rev. E 90, 042401 (2014)
A.E. Cohen, L. Mahadevan, Proc. Nat. Acad. Sci. 100, 12141 (2003)
C. Py, P. Reverdy, L. Doppler, J. Bico, B. Roman, C.N. Baroud, Phys. Rev. Lett. 98, 156103 (2007)
M. Kothari, Z.S. Lemon, C. Roth, T. Cohen, Controlled Propagation and Jamming of a Delamination Front (2020)
F. Brau, P. Damman, H. Diamant, T.A. Witten, Soft Matter 9, 8177 (2013)
Y. Ebata, A.B. Croll, A.J. Crosby, Soft Matter 8, 9086 (2012)
H. Son, A.L. Chau, C.S. Davis, Soft Matter 15, 6375 (2019)
L. Pocivavsek, R. Dellsy, A. Kern, S. Johnson, B. Lin, K.Y.C. Lee, E. Cerda, Science 320, 912 (2008)
H. Diamant, T.A. Witten, Phys. Rev. Lett. 107, 164302 (2011)
J. Huang, B. Davidovitch, C.D. Santangelo, T.P. Russell, N. Menon, Phys. Rev. Lett. 105, 038302 (2010)
B. Audoly, Phys. Rev. E 84, 011605 (2011)
Acknowledgements
We thank D. Vella for many discussions and invaluable comments and D. Vella and O. Oshri for their critical reading of this manuscript. BD acknowledges support by the National Science Foundation under grant DMR 1822439.
Author information
Authors and Affiliations
Contributions
B. Davidovitch and V. Démery have contributed equally.
Corresponding author
Rights and permissions
About this article
Cite this article
Davidovitch, B., Démery, V. Rucks and folds: delamination from a flat rigid substrate under uniaxial compression. Eur. Phys. J. E 44, 11 (2021). https://doi.org/10.1140/epje/s10189-021-00020-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/s10189-021-00020-1