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Unraveling Adhesion Mechanisms: Exploring the Impact of Thickness on Viscoelastic Layers and Wavy Profiles

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Abstract

Contact mechanics theories are commonly developed using the half-space approximation, which may raise concerns when dealing with contact region sizes comparable to or even larger than the size of the contacting bodies. In this study, we examine the normal adhesive contact between a rigid, wavy indenter and a viscoelastic substrate with a finite thickness. To achieve this, we utilize a recently developed finite element model that incorporates adhesive interactions based on the Lennard–Jones potential law. The results demonstrate that adhesive behavior is influenced by a combination of rate and size effects. Additionally, when considering non-negligible viscous effects, an optimal thickness can be determined to maximize the pull-off stress.

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Data Availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

References

  1. Maugis, D., Barquins, M.: Fracture mechanics and the adherence of viscoelastic bodies. J. Phys. D Appl. Phys. 11(14), 1989 (1978)

    Article  ADS  Google Scholar 

  2. Creton, C., Ciccotti, M.: Fracture and adhesion of soft materials: a review. Rep. Prog. Phys. 79(4), 046601 (2016)

    Article  ADS  PubMed  Google Scholar 

  3. Mapari, S., Mestry, S., Mhaske, S.T.: Developments in pressure-sensitive adhesives: a review. Polym. Bull. 78, 4075–4108 (2021)

    Article  CAS  Google Scholar 

  4. Shintake, J., Cacucciolo, V., Floreano, D., Shea, H.: Soft robotic grippers. Adv. Mater. 30(29), 1707035 (2018)

    Article  Google Scholar 

  5. Brodoceanu, D., Bauer, C.T., Kroner, E., Arzt, E., Kraus, T.: Hierarchical bioinspired adhesive surfaces—a review. Bioinspiration Biomimetics 11(5), 051001 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A Math. Phys. Sci. 324(1558), 301–313 (1971)

    ADS  CAS  Google Scholar 

  7. Sridhar, I., Zheng, Z.W., Johnson, K.L.: A detailed analysis of adhesion mechanics between a compliant elastic coating and a spherical probe. J. Phys. D Appl. Phys. 37(20), 2886 (2004)

    Article  ADS  CAS  Google Scholar 

  8. Bradley, R.S.: Lxxix. The cohesive force between solid surfaces and the surface energy of solids. Lond. Edinb. Dublin Philos. Mag. J. Sci. 13(86), 853–862 (1932)

    Article  CAS  Google Scholar 

  9. Li, Q., Pohrt, R., Lyashenko, I.A.F.F., Popov, V.L.: Boundary element method for nonadhesive and adhesive contacts of a coated elastic half-space. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 234(1), 73–83 (2020)

    Article  Google Scholar 

  10. Jiunn-Jong, W.: Adhesive contact between a rigid sphere and a thin elastic layer bonded on a rigid foundation. J. Adhes. Sci. Technol. 34(21), 2292–2315 (2020)

    Article  Google Scholar 

  11. Yang, F.: Asymptotic solution to axisymmetric indentation of a compressible elastic thin film. Thin Solid Films 515(4), 2274–2283 (2006)

    Article  ADS  CAS  Google Scholar 

  12. Argatov, I.I., Mishuris, G.S., Popov, V.L.: Asymptotic modelling of the JKR adhesion contact for a thin elastic layer. Q. J. Mech. Appl. Math. 69(2), 161–179 (2016)

    Article  MathSciNet  Google Scholar 

  13. Borodich, F.M., Galanov, B.A., Perepelkin, N.V., Prikazchikov, D.A.: Adhesive contact problems for a thin elastic layer: asymptotic analysis and the JKR theory. Math. Mech. Solids 24(5), 1405–1424 (2019)

    Article  MathSciNet  Google Scholar 

  14. Müller, C., Müser, M.H.: Analytical and numerical results for the elasticity and adhesion of elastic films with arbitrary Poisson’s ratio and confinement. J. Adhes. 99(4), 648–671 (2023)

    Article  Google Scholar 

  15. Campañá, C., Müser, M.H.: Practical Green’s function approach to the simulation of elastic semi-infinite solids. Phys. Rev. B 74(4), 075420 (2006)

    Article  ADS  Google Scholar 

  16. Zhou, Y., Moseler, M., Müser, M.H.: Solution of boundary-element problems using the fast-inertial-relaxation-engine method. Phys. Rev. B 99(14), 144103 (2019)

    Article  ADS  CAS  Google Scholar 

  17. Persson, B.N.J., Albohr, O., Tartaglino, U., Volokitin, A.I., Tosatti, E.: On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J. Phys. Condens. Matter 17(1), R1 (2004)

    Article  PubMed  Google Scholar 

  18. Fuller, K.N.G., Tabor, D.: The effect of surface roughness on the adhesion of elastic solids. Proc. R. Soc. Lond. A Math. Phys. Sci. 345(1642), 327–342 (1975)

    ADS  Google Scholar 

  19. Lyashenko, I.A.F.F., Pohrt, R.: Adhesion between rigid indenter and soft rubber layer: influence of roughness. Front. Mech. Eng. 6, 49 (2020)

    Article  Google Scholar 

  20. Pastewka, L., Robbins, M.O.: Contact between rough surfaces and a criterion for macroscopic adhesion. Proc. Natl Acad. Sci. U.S.A. 111(9), 3298–3303 (2014)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  21. Müser, M.H.: A dimensionless measure for adhesion and effects of the range of adhesion in contacts of nominally flat surfaces. Tribol. Int. 100, 41–47 (2016)

    Article  Google Scholar 

  22. Violano, G., Afferrante, L., Papangelo, A., Ciavarella, M.: On stickiness of multiscale randomly rough surfaces. J. Adhes. 97(6), 509–527 (2021)

    Article  CAS  Google Scholar 

  23. Violano, G., Papangelo, A., Ciavarella, M.: Stickiness of randomly rough surfaces with high fractal dimension: is there a fractal limit? Tribol. Int. 159, 106971 (2021)

    Article  Google Scholar 

  24. Wang, A., Müser, M.H.: Is there more than one stickiness criterion? Friction 11(6), 1027–1039 (2023)

    Article  Google Scholar 

  25. Tiwari, A., Wang, J., Persson, B.N.J.: Adhesion paradox: why adhesion is usually not observed for macroscopic solids. Phys. Rev. E 102(4), 042803 (2020)

    Article  ADS  CAS  PubMed  Google Scholar 

  26. Ghanbarzadeh, A., Faraji, M., Neville, A.: Deterministic normal contact of rough surfaces with adhesion using a surface integral method. Proc. R. Soc. A 476(2242), 20200281 (2020)

    Article  ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  27. Afferrante, L., Violano, G., Dini, D.: How does roughness kill adhesion? J. Mech. Phys. Solids 181, 105465 (2023)

    Article  MathSciNet  Google Scholar 

  28. Violano, G., Dini, D., Di Bari, A., Afferrante, L.: Effect of roughness small scales on the adhesion of randomly rough surfaces with high fractal dimension. IOP Conf. Ser. Mater. Sci. Eng. 1275, 012024 (2023)

    Article  Google Scholar 

  29. Johnson, K.L.: The adhesion of two elastic bodies with slightly wavy surfaces. Int. J. Solids Struct. 32(3–4), 423–430 (1995)

    Article  Google Scholar 

  30. Menga, N., Afferrante, L., Carbone, G.: Adhesive and adhesiveless contact mechanics of elastic layers on slightly wavy rigid substrates. Int. J. Solids Struct. 88, 101–109 (2016)

    Article  Google Scholar 

  31. Wang, A., Müser, M.H.: On the adhesion between thin sheets and randomly rough surfaces. Front. Mech. Eng. 8, 965584 (2022)

    Article  Google Scholar 

  32. Afferrante, L., Violano, G.: The adhesion of viscoelastic bodies with slightly wave surfaces. Tribol. Int. 174, 107726 (2022)

    Article  Google Scholar 

  33. Violano, G., Afferrante, L.: Size effects in adhesive contacts of viscoelastic media. Eur. J. Mech. A Solids 96, 104665 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  34. Afferrante, L., Violano, G.: On the effective surface energy in viscoelastic Hertzian contacts. J. Mech. Phys. Solids 158, 104669 (2022)

    Article  MathSciNet  Google Scholar 

  35. Papangelo, A., Ciavarella, M.: Detachment of a rigid flat punch from a viscoelastic material. Tribol. Lett. 71(2), 48 (2023)

    Article  Google Scholar 

  36. Dokkum, J.S.V., Pérez-Rafols, F., Dorogin, L., Nicola, L.: On the retraction of an adhesive cylindrical indenter from a viscoelastic substrate. Tribol. Lett. 164, 107234 (2021)

    Article  Google Scholar 

  37. Violano, G., Afferrante, L.: On the long and short-range adhesive interactions in viscoelastic contacts. Tribol. Lett. 70(3), 68 (2022)

    Article  CAS  Google Scholar 

  38. Carbone, G., Pierro, E., Recchia, G.: Loading-unloading hysteresis loop of randomly rough adhesive contacts. Phys. Rev. E 92(6), 062404 (2015)

    Article  ADS  Google Scholar 

  39. Violano, G., Afferrante, L.: Roughness-induced adhesive hysteresis in self-affine fractal surfaces. Lubricants 9(1), 7 (2021)

    Article  Google Scholar 

  40. Wang, A., Zhou, Y., Müser, M.H.: Modeling adhesive hysteresis. Lubricants 9(2), 17 (2021)

    Article  CAS  Google Scholar 

  41. Dalvi, S., Gujrati, A., Khanal, S.R., Pastewka, L., Dhinojwala, A., Jacobs, T.D.B.: Linking energy loss in soft adhesion to surface roughness. Proc. Natl Acad. Sci. U.S.A. 116(51), 25484–25490 (2019)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  42. Lorenz, B., Krick, B.A., Mulakaluri, N., Smolyakova, M., Dieluweit, S., Sawyer, W.G., Persson, B.N.J.: Adhesion: role of bulk viscoelasticity and surface roughness. J. Phys. Condens. Matter 25(22), 225004 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Violano, G., Chateauminois, A., Afferrante, L.: Rate-dependent adhesion of viscoelastic contacts, part I: contact area and contact line velocity within model randomly rough surfaces. Mech. Mater. 160, 103926 (2021)

    Article  Google Scholar 

  44. Violano, G., Chateauminois, A., Afferrante, L.: Rate-dependent adhesion of viscoelastic contacts. part II: numerical model and hysteresis dissipation. Mech. Mater. 158, 103884 (2021)

    Article  Google Scholar 

  45. Pérez-Ràfols, F., Dokkum, J.S.V., Nicola, L.: On the interplay between roughness and viscoelasticity in adhesive hysteresis. J. Mech. Phys. Solids 170, 105079 (2023)

    Article  MathSciNet  Google Scholar 

  46. Müller, C., Samri, M., Hensel, R., Arzt, E., Müser, M.H.: Revealing the coaction of viscous and multistability hysteresis in an adhesive, nominally flat punch: a combined numerical and experimental study. J. Mech. Phys. Solids 174, 105260 (2023)

    Article  MathSciNet  Google Scholar 

  47. Das, D., Chasiotis, I.: Rate dependent adhesion of nanoscale polymer contacts. J. Mech. Phys. Solids 156, 104597 (2021)

    Article  MathSciNet  CAS  Google Scholar 

  48. Violano, G., Chateauminois, A., Afferrante, L.: Aff 2023 JKR-like solution for viscoelastic adhesive contacts. Front. Mech. Eng. 7, 664486 (2021)

    Article  Google Scholar 

  49. Müser, M.H., Persson, B.N.J.: Crack and pull-off dynamics of adhesive, viscoelastic solids. Europhys. Lett. 137(3), 36004 (2022)

    Article  ADS  Google Scholar 

  50. Li, D., Li, R., Zhang, W.: Combined effects of viscoelasticity and surface roughness on the adhesion behavior of a flat-end cylindrical microstructure. Int. J. Solids Struct. 251, 111753 (2022)

    Article  Google Scholar 

  51. Müser, M.H., Nicola, L.: Modeling the surface topography dependence of friction, adhesion, and contact compliance. MRS Bull. 47(12), 1221–1228 (2022)

    Article  ADS  PubMed  Google Scholar 

  52. Argatov, I.I., Lyashenko, I.A., Popov, V.L.: Rate-dependent JKR-type decohesion of a cylindrical punch from an elastic substrate. Phys. Scr. 98(5), 055905 (2023)

    Article  ADS  Google Scholar 

  53. Carbone, G., Mandriota, C., Menga, N.: Theory of viscoelastic adhesion and friction. Extreme Mech. Lett. 56, 101877 (2022)

    Article  Google Scholar 

  54. Creton, C., Lakrout, H.: Micromechanics of flat-probe adhesion tests of soft viscoelastic polymer films. J. Polym. Sci. Part B Polym. Phys. 38(7), 965–979 (2000)

    Article  ADS  CAS  Google Scholar 

  55. Putignano, C., Carbone, G., Dini, D.: Mechanics of rough contacts in elastic and viscoelastic thin layers. Int. J. Solids Struct. 69, 507–517 (2015)

    Article  Google Scholar 

  56. Menga, N., Afferrante, L., Carbone, G.: Effect of thickness and boundary conditions on the behavior of viscoelastic layers in sliding contact with wavy profiles. J. Mech. Phys. Solids 95, 517–529 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  57. Menga, N., Afferrante, L., Demelio, G.P., Carbone, G.: Rough contact of sliding viscoelastic layers: numerical calculations and theoretical predictions. Tribol. Int. 122, 67–75 (2018)

    Article  Google Scholar 

  58. Persson, B.N.J., Brener, E.A.: Crack propagation in viscoelastic solids. Phys. Rev. E 71(3), 036123 (2005)

    Article  ADS  CAS  Google Scholar 

  59. Ramond, G., Pastor, M., Maugis, D., Barquins, M.: Mesure du module complexe par poinçonnement. Cahiers du Groupe Français de Rhéologie 6(67), 3–3 (1985)

    Google Scholar 

  60. Carbone, G., Mangialardi, L.: Analysis of the adhesive contact of confined layers by using a Green’s function approach. J. Mech. Phys. Solids 56(2), 684–706 (2008)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  61. Derjaguin, B.: Untersuchungen ueber die reibung und adhaesion, IV: Theorie des anhaftens kleiner teilchen. Kolloid-Zeitschrift 69, 155–164 (1934)

    Article  Google Scholar 

  62. Baney, J.M., Hui, C.-Y.: A cohesive zone model for the adhesion of cylinders. J. Adhes. Sci. Technol. 11(3), 393–406 (1997)

    Article  CAS  Google Scholar 

  63. Gent, A.N., Schultz, J.: Effect of wetting liquids on the strength of adhesion of viscoelastic material. J. Adhes. 3(4), 281–294 (1972)

    Article  CAS  Google Scholar 

  64. Thomas, T.R.: Trends in surface roughness. Int. J. Mach. Tools Manuf. 38(5–6), 405–411 (1998)

    Article  Google Scholar 

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Acknowledgements

G. Violano and L. Afferrante acknowledge the Italian Ministry of University and Research under the Program “Department of Excellence” L. 232/2016 (Grant No. CUP - D93C23000100001).

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  1. Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Via E. Orabona, 70126, Bari, Italy

    Guido Violano & Luciano Afferrante

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  1. Guido Violano
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  2. Luciano Afferrante
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GV contributed to conceptualization; investigation; methodology; numerical modeling; writing of the original-draft; and writing, reviewing, and editing of the manuscript. LA contributed to conceptualization; investigation; methodology; numerical modeling; and writing, reviewing, and editing of the manuscript.

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Correspondence to Guido Violano.

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Violano, G., Afferrante, L. Unraveling Adhesion Mechanisms: Exploring the Impact of Thickness on Viscoelastic Layers and Wavy Profiles. Tribol Lett 72, 14 (2024). https://doi.org/10.1007/s11249-023-01807-3

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