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The delamination of a growing elastic sheet with adhesion

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A Correction to this article was published on 06 January 2021

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Abstract

We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth causes residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at which the instability occurs. We show that the critical threshold scales with a single dimensionless parameter that comprises information from the geometry of the sheet, the mechanical parameters of material and the adhesive features of the substrate.

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Change history

  • 06 January 2021

    We wish to correct two small errors in our previous article.

References

  1. Goriely A, Geers MGD, Holzapfel GA, Jayamohan J, Jérusalem A, Sivaloganathan S, Squier W, van Dommelen JAW, Waters S, Kuhl E (2015) Mechanics of the brain: perspectives, challenges, and opportunities. Biomech Model Mechanobiol 14:931–965

    Article  Google Scholar 

  2. Ciarletta P, Amar MB (2012) Growth instabilities and folding in tubular organs: a variational method in non-linear elasticity. Int J Non Linear Mech 47(2):248–257

    Article  Google Scholar 

  3. Wilking JN, Zaburdaev V, De Volder M, Losick R, Brenner MP, Weitz DA (2013) Liquid transport facilitated by channels in bacillus subtilis biofilms. Proc Natl Acad Sci 110(3):848–852

    Article  ADS  Google Scholar 

  4. Amar M Ben, Wu M (2014) Patterns in biofilms: from contour undulations to fold focussing. Europhys Lett 108(3):38003

    Article  ADS  Google Scholar 

  5. Gioia G, Ortiz M (1997) Delamination of compressed thin films. Adv Appl Mech 33:119–192

    Article  MATH  Google Scholar 

  6. Gioia G, DeSimone A, Ortiz M, Cuitino AM (2002) Folding energetics in thin-film diaphragms. Proc R Soc Lond A 458(2021):1223–1229

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. Belgacem HB, Conti S, DeSimone A, Müller S (2002) Energy scaling of compressed elastic films-three-dimensional elasticity and reduced theories. Arch Ration Mech Anal 164(1):1–37

    Article  MATH  MathSciNet  Google Scholar 

  8. Wagner TJW, Vella D (2013) The ‘sticky elastica’: delamination blisters beyond small deformations. Soft Matter 9(4):1025–1030

    Article  ADS  Google Scholar 

  9. Stoop N, Müller MM (2015) Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate. Int J Non Linear Mech 75:115–122

    Article  Google Scholar 

  10. Vella D, Bico J, Boudaoud A, Roman B, Reis PM (2009) The macroscopic delamination of thin films from elastic substrates. Proc Natl Acad Sci USA 106(27):10901–10906

    Article  ADS  Google Scholar 

  11. Napoli G, Turzi S (2015) Snap buckling of a confined thin elastic sheet. Proc R Soc A 471(2183):20150444

    Article  ADS  Google Scholar 

  12. Lee AA, Le Gouellec C, Vella D (2015) The role of extensibility in the birth of a ruck in a rug. Extrem Mech Lett 5:81–87

    Article  Google Scholar 

  13. Gelfand IM, Fomin SV (1963) Calculus of variations. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  14. Majidi C (2007) Remarks on formulating an adhesion problem using Euler’s elastica (draft). Mech Res Commun 34(1):85–90

    Article  MATH  MathSciNet  Google Scholar 

  15. Majidi C, Adams GG (2010) Adhesion and delamination boundary conditions for elastic plates with arbitrary contact shape. Mech Res Commun 37(2):214–218

    Article  MATH  Google Scholar 

  16. Landau LD, Lifshitz EM (1975) Elasticity theory. Pergamon Press, Oxford

    MATH  Google Scholar 

  17. Maddocks JH (1987) Stability and folds. Arch Ration Mech Anal 99(4):301–328

    Article  MathSciNet  Google Scholar 

  18. Abramowitz M, Stegun IA (1964) Handbook of mathematical function with formulas, graphs, and mathematical tables. Dover, New York

    MATH  Google Scholar 

  19. De Pascalis R, Napoli G, Turzi SS (2014) Growth-induced blisters in a circular tube. Phys D 283:1–9

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

This research has been carried out within the Young Researchers Project “Morfogenesi e stabilità di film sottili confinati”, supported by the Italian “Gruppo Nazionale per la Fisica Matematica” (GNFM).

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Lecce, Italy

    Gaetano Napoli

  2. Dipartimento di Matematica, Politecnico di Milano, Milan, Italy

    Stefano Turzi

Authors
  1. Gaetano Napoli
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  2. Stefano Turzi
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Correspondence to Stefano Turzi.

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Napoli, G., Turzi, S. The delamination of a growing elastic sheet with adhesion. Meccanica 52, 3481–3487 (2017). https://doi.org/10.1007/s11012-017-0618-0

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  • DOI: https://doi.org/10.1007/s11012-017-0618-0

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