Home Generalized Maugis–Dugdale model of an elastic cylinder in non-slipping adhesive contact with a stretched substrate
Article
Licensed
Unlicensed Requires Authentication

Generalized Maugis–Dugdale model of an elastic cylinder in non-slipping adhesive contact with a stretched substrate

  • Shaohua Chen and Huajian Gao
Published/Copyright: May 31, 2013
Become an author with De Gruyter Brill
Author Information
International Journal of Materials Research
From the journal International Journal of Materials Research Volume 97 Issue 5

Abstract

We have recently developed a generalized JKR model for non-slipping adhesive contact between an elastic cylinder and a stretched substrate where both tangential and normal tractions are transmitted across the contact interface. Here we extend this model to a generalized Maugis–Dugdale model by adopting a Dugdale-type adhesive interaction law to eliminate the stress singularity near the edge of the contact zone. The non-slipping Maugis–Dugdale model is expected to have a broader range of validity in comparison with the non-slipping JKR model. The solution shares a number of common features with experimentally observed behaviors of cell reorientation on a cyclically stretched substrate.

Keywords: Generalized MD model; Generalized JKR model; Adhesive contact; Cell adhesion
* Correspondence address: Professor Huajian Gao, Max Planck Institute for Metals Research, Heisenbergstraße 3, D-70569 Stuttgart, Germany, Tel.: +497116893510, Fax: +497116893512. E-mail:

Dedicated to Professor Dr. Fritz Aldinger on the occasion of his 65th birthday

References

[1] K.L.Johnson, K.Kendall, A.D.Roberts: Proc. Roy. Soc. Lond.A324 (1971) 301.Search in Google Scholar

[2] B.V.Derjaguin, V.M.Muller, Y.P.Toporov: J. Coll. Interface Sci.53 (1975) 314.10.1016/0021-9797(75)90018-1Search in Google Scholar

[3] D.Maugis: J. Coll. Interface Sci.150 (1992) 243.10.1016/0021-9797(92)90285-TSearch in Google Scholar

[4] D.S.Dugdale: J. Mech. Phys. Solids8 (1960) 100.10.1016/0022-5096(60)90013-2Search in Google Scholar

[5] D.Maugis, M.Barquins: J. Phys.D11 (1978) 1989.Search in Google Scholar

[6] V.M.Muller, V.S.Yushenko, B.V.Derjaguin: J. Colloid Interface Sci.77 (1980) 91.10.1016/0021-9797(80)90419-1Search in Google Scholar

[7] R.W.Carpick, N.Agrait, D.F.Ogletree, M.Salmeron: Langmuir12 (1996) 3334.10.1021/la9509007Search in Google Scholar

[8] J.A.Greenwood: Proc. Roy. Soc. Lond. A453 (1997) 1277.10.1098/rspa.1997.0070Search in Google Scholar

[9] K.L.Johnson, J.A.Greenwood: J. Coll. Interface Sci.192 (1997) 326.10.1006/jcis.1997.4984Search in Google Scholar PubMed

[10] J.M.Baney, C.Y.Hui: J. Adhesion Sci. Technol.11 (1997) 393.10.1163/156856197X00778Search in Google Scholar

[11] C.Y.Hui, J.M.Baney, E.J.Kramer: Langmuir14 (1998) 6570.10.1021/la980273wSearch in Google Scholar

[12] E.Barthel: J. Coll. Interface Sci.200 (1998) 7.10.1006/jcis.1997.5309Search in Google Scholar

[13] F.Robbe-Valloire, M.Barquins: Int. J. Adhesion and Adhesives18 (1998) 29.10.1016/S0143-7496(97)00064-XSearch in Google Scholar

[14] J.A.Greenwood, K.L.Johnson: J. Phys. D: Appl. Phys.31 (1998) 3279.10.1088/0022-3727/31/22/017Search in Google Scholar

[15] K.S.Kim, R.M.McMeeking, K.L.Johnson: J. Mech. Phys. Solids46 (1998) 243.10.1016/S0022-5096(97)00070-7Search in Google Scholar

[16] Y.Y.Lin, C.Y.Hui, J.M.Baney: J. Phys. D: Appl. Phys.32 (1999) 2250.10.1088/0022-3727/32/17/316Search in Google Scholar

[17] E.Barthel, G.Haiat: Langmuir18 (2002) 9362.10.1021/la025959+Search in Google Scholar

[18] C.Morrow, M.Lovell, X.Ning: J. Phys. D: Appl. Phys.36 (2003) 534.10.1088/0022-3727/36/5/317Search in Google Scholar

[19] U.D.Schwarz: J. Coll. Interface Sci.261 (2003) 99.10.1016/S0021-9797(03)00049-3Search in Google Scholar

[20] G.Haiat, M.C.P.Huy, E.Barthel: J. Mech. Phys. Solids51 (2003) 69.10.1016/S0022-5096(02)00059-5Search in Google Scholar

[21] H.Gao, X.Wang, H.Yao, S.Gorb, E.Arzt: Mech. Mater.37 (2005) 275.10.1016/j.mechmat.2004.03.008Search in Google Scholar

[22] H.Gao, H.Yao: Proc. Nat. Acad. Sci. USA101 (2004) 7851.10.1073/pnas.0400757101Search in Google Scholar PubMed PubMed Central

[23] N.J.Glassmaker, A.Jagota, C.Y.Hui, J.Kim: J. R. Soc. Interface1 (2004) 23.10.1098/rsif.2004.0004Search in Google Scholar

[24] C.Y.Hui, N.J.Glassmaker, T.Tang, A.Jagota: J. R. Soc. Interface1 (2004) 35.10.1098/rsif.2004.0005Search in Google Scholar

[25] S.Chen, H.Gao: Proc. Roy. Soc. Lond. A462 (2006) 211.10.1098/rspa.2005.1553Search in Google Scholar

[26] Y.-S.Chu, S.Dufour, J.P.Thiery, E.Perez, F.Pincet: Phys. Rev. Let.94 (2005) 028102–1.10.1103/PhysRevLett.94.028102Search in Google Scholar

[27] R.C.Buck: Exp. Cell. Res.127 (1980) 470.10.1016/0014-4827(80)90456-5Search in Google Scholar

[28] P.C.Dartsch, H.Hammerle: Eur. J. Cell Biol.41 (1986) 339.Search in Google Scholar

[29] V.P.Shirinsky, A.S.Antonov, K.Birukov, A.Sobolevsky, Y.Romanov, N.Kabaeva, G.Antonova, V.Smirnov: J. Cell. Biol.109 (1989) 331.10.1083/jcb.109.1.331Search in Google Scholar

[30] C.Neidlinger-Wilke, H.J.WilkeL.Claes: J. Orthop. Res.12 (1994) 70.10.1002/jor.1100120109Search in Google Scholar

[31] J.H.C.Wang: J. Theor. Biol.202 (2000) 33.10.1006/jtbi.1999.1035Search in Google Scholar

[32] A.D.Roberts, A.G.Thomas: Wear33 (1975) 45.10.1016/0043-1648(75)90223-9Search in Google Scholar

[33] M.Barquins: J. Adhesion26 (1988) 1.10.1080/00218468808071271Search in Google Scholar

[34] M.K.Chaudhury, T.Weaver, C.Y.Hui, E.J.Kramer: J. Appl. Phys80 (1996) 30.10.1063/1.362819Search in Google Scholar

[35] O.T.Sari, G.G.Adams, S.Muftu: J. Appl. Mech.72 (2005) 633.10.1115/1.1831291Search in Google Scholar

[36] K.L.Johnson: Contact Mechanics. Cambridge University Press (1985).10.1017/CBO9781139171731Search in Google Scholar

[37] J.Durdurs: Appl. Mech.36 (1969) 650.10.1115/1.3564739Search in Google Scholar

[38] Z.Suo: Proc. Roy. Soc. Lond. A427 (1990) 331.10.1098/rspa.1990.0016Search in Google Scholar

[39] G.F.Carrier, M.Krook, C.E.Pearson: Functions of a complex variable. Hod brooks, Ithaca, New York (1983).Search in Google Scholar

Received: 2005-11-23
Accepted: 2006-1-15
Published Online: 2013-05-31
Published in Print: 2006-05-01

© 2006, Carl Hanser Verlag, München

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. Editorial
  5. Basic
  6. Three-dimensional printing of TiAl3/Al2O3 composites
  7. Microemulsion mediated synthesis of nanocrystalline BaTiO3: possibilities, potential and perspectives
  8. Solid-State 17O NMR studies on Yttria-stabilized zirconia
  9. Twinning in ultrathin silicon nanowires
  10. Re-optimization of the Mg–Sb system under topological constraints
  11. Mg-rich phase equilibria of Mg–Mn–Zn alloys analyzed by computational thermochemistry
  12. The In–Pt–Sb phase diagram
  13. Thermodynamic evaluation of the Al–Cr–C system
  14. Thermodynamic description of the Ni–Si–Ti ternary system
  15. Enthalpies of formation measurements and thermodynamic description of the Ag–Cu–Zn system
  16. Thermodynamic assessment of the Mn–Cr–O system for solid oxide fuel cell (SOFC) materials
  17. Subsolidus phase equilibria in the CeO2−x–SiO2–ZrO2 system: An experimental study
  18. Generalized Maugis–Dugdale model of an elastic cylinder in non-slipping adhesive contact with a stretched substrate
  19. Implications of linear relationships between local and macroscopic flow stresses in the composite model
  20. Applied
  21. Gas-phase surface alloying under “kinetic control”: A novel approach to improving the surface properties of titanium alloys
  22. Thin film formation by oriented attachment of polymer-capped nanocrystalline ZnO
  23. The sintering mechanism and microstructure evolution in SiC–AlN ceramics studiedby EFTEM
  24. Thermal evolution of free volumes and of crystallization in amorphous Si–B–C–N ceramics
  25. High-temperature deformation behavior of nanocrystalline precursor-derived Si–B–C–N ceramics in controlled atmosphere
  26. Nanopowder dispersion and spray-drying process: the case of Cr2O3
  27. Electroless deposition of brushite (CaHPO4 · 2H2O) crystals on Ti–6Al–4V at room temperature
  28. The role of chemisorbed anions in the aqueous processing of AlN powder
  29. The influence of porosity on the electrical properties of liquid-phase sintered silicon carbide
  30. Development of high-temperature thermoelectric materials based on SrTiO3-layered perovskites
  31. The influence of the preparation method on the microstructure and properties of Al2O3/TiN nanocomposites
  32. Infrared properties of sintered α-MnSe
  33. Quasi-equilibrium sintering of particle clusters containing Bernal holes
  34. Design of metal ceramic composites
  35. Notifications
  36. DGM News
https://doi.org/10.3139/146.101275
Keywords for this article
Generalized MD model; Generalized JKR model; Adhesive contact; Cell adhesion

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. Editorial
  5. Basic
  6. Three-dimensional printing of TiAl3/Al2O3 composites
  7. Microemulsion mediated synthesis of nanocrystalline BaTiO3: possibilities, potential and perspectives
  8. Solid-State 17O NMR studies on Yttria-stabilized zirconia
  9. Twinning in ultrathin silicon nanowires
  10. Re-optimization of the Mg–Sb system under topological constraints
  11. Mg-rich phase equilibria of Mg–Mn–Zn alloys analyzed by computational thermochemistry
  12. The In–Pt–Sb phase diagram
  13. Thermodynamic evaluation of the Al–Cr–C system
  14. Thermodynamic description of the Ni–Si–Ti ternary system
  15. Enthalpies of formation measurements and thermodynamic description of the Ag–Cu–Zn system
  16. Thermodynamic assessment of the Mn–Cr–O system for solid oxide fuel cell (SOFC) materials
  17. Subsolidus phase equilibria in the CeO2−x–SiO2–ZrO2 system: An experimental study
  18. Generalized Maugis–Dugdale model of an elastic cylinder in non-slipping adhesive contact with a stretched substrate
  19. Implications of linear relationships between local and macroscopic flow stresses in the composite model
  20. Applied
  21. Gas-phase surface alloying under “kinetic control”: A novel approach to improving the surface properties of titanium alloys
  22. Thin film formation by oriented attachment of polymer-capped nanocrystalline ZnO
  23. The sintering mechanism and microstructure evolution in SiC–AlN ceramics studiedby EFTEM
  24. Thermal evolution of free volumes and of crystallization in amorphous Si–B–C–N ceramics
  25. High-temperature deformation behavior of nanocrystalline precursor-derived Si–B–C–N ceramics in controlled atmosphere
  26. Nanopowder dispersion and spray-drying process: the case of Cr2O3
  27. Electroless deposition of brushite (CaHPO4 · 2H2O) crystals on Ti–6Al–4V at room temperature
  28. The role of chemisorbed anions in the aqueous processing of AlN powder
  29. The influence of porosity on the electrical properties of liquid-phase sintered silicon carbide
  30. Development of high-temperature thermoelectric materials based on SrTiO3-layered perovskites
  31. The influence of the preparation method on the microstructure and properties of Al2O3/TiN nanocomposites
  32. Infrared properties of sintered α-MnSe
  33. Quasi-equilibrium sintering of particle clusters containing Bernal holes
  34. Design of metal ceramic composites
  35. Notifications
  36. DGM News
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 3.10.2025 from https://www.degruyterbrill.com/document/doi/10.3139/146.101275/html?lang=en
Scroll to top button