Skip to main content

Computational Contact Formulations for Soft Body Adhesion

  • Chapter
Advances in Soft Matter Mechanics

Abstract

This article gives an overview of adhesive contact for soft bodies and focuses on a general computational framework that is suitable for treating a large class of adhesion problems. The contact formulation is based on a non-linear continuum approach that is capable of describing bodies down to length scales of several nanometers. Several finite element formulations are presented, that introduce various approximations in order to increase the computational efficiency. The approaches are illustrated by several examples throughout the text. These include carbon nanotube interaction, adhesion of spheres, nanoindentation, thin film peeling, gecko adhesion and self-cleaning surface mechanisms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Johnson K L, Kendall K, Roberts A D. Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A, 324: 301–313, 1971.

    Article  ADS  Google Scholar 

  2. Derjaguin B V, Muller V M, Toporov Y P. Effect of contact deformation on the adhesion of particles. J. Colloid Interface Sci., 53(2): 314–326, 1975.

    Article  Google Scholar 

  3. Maugis D. Adhesion of spheres: The jkr-dmt transition using a dugdale model. L. Colloid Interface Sci., 150(1): 243–269, 1992.

    Article  Google Scholar 

  4. Johnson K L. Contact Mechanics. Johns Hopkins, 1985.

    Google Scholar 

  5. Laursen T A. Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Springer, 2002.

    Google Scholar 

  6. Wriggers P. Computational Contact Mechanics. 2nd ed. Springer, 2006.

    Google Scholar 

  7. Padmanabhan V, Laursen T A. A framework for development of surface smoothing procedures in large deformation frictional contact analysis. Finite Elem. Anal. Des., 37: 173–198, 2001.

    Article  MATH  Google Scholar 

  8. Wriggers P, Krstulovic-Opara L, Korelc J. Smooth C 1-interpolations for twodimensional frictional contact problems. Int. J. Numer. Meth. Engng., 51: 1469–1495, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  9. Stadler M, Holzapfel G A, Korelc J. C n continuous modelling of smooth contact surfaces using nurbs and application to 2D problems. Int. J. Numer. Meth. Engng., 57: 2177–2203, 2003.

    Article  MATH  Google Scholar 

  10. Krstulovic-Opara L, Wriggers P, Korelc J. A C 1-continuous formulation for 3D finite deformation friction contact. Comp. Mech., 29: 27–42, 2002.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Puso M A, Laursen T A. A 3D contact smoothing method using Gregory patches. Int. J. Numer. Meth. Engng., 54: 1161–1194, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  12. Yang B, Laursen T A, Meng X. Two dimensional mortar contact methods for large deformation frictional sliding. Int. J. Numer. Meth. Engng, 62: 1183–1225, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  13. Fischer K A, Wriggers P. Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput. Methods Appl. Mech. Engrg., 195: 5020–5036, 2006.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Puso M A, Laursen T A. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Engrg., 193: 601–629, 2004.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Puso M A, Laursen T A. A mortar segment-to-segment frictional contact method for large deformations. Comput. Methods Appl. Mech. Engrg., 193: 4891–4913, 2004.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Raous M, Cangémi L, Cocu M. A consistent model coupling adhesion, friction, and unilateral contact. Comput. Methods Appl. Mech. Engrg., 177: 383–399, 1999.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Sauer R A, Li S. An atomic interaction-based continuum model for adhesive contact mechanics. Finite Elem. Anal. Des., 43(5): 384–396, 2007.

    Article  MathSciNet  Google Scholar 

  18. Hesch C, Betsch P. A mortar method for energy-momentum conserving schemes in frictionless dynamic contact problems. Int. J. Numer. Methods Engng, doi: 10.1002/nme.2466, 2008.

    Google Scholar 

  19. Wriggers P, Reinelt J. Multi-scale approach for frictional contact of elastomers on rough rigid surfaces. Comput. Methods Appl. Mech. Engrg.. (accepted).

    Google Scholar 

  20. Sauer R A. Multiscale modeling and simulation of the deformation and adhesion of a single gecko seta. Comp. Meth. Biomech. Biomed. Engng., 12(6): 627–640, 2009.

    Article  MathSciNet  Google Scholar 

  21. Temizer I, Wriggers P. A multiscale contact homogenization technique for the modeling of third bodies in the contact interface. Comp. Meth. Appl. Mech. Engrg., 198: 377–396, 2008.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Temizer I, Wriggers P. Thermal contact conductance characterization via computational contact homogenization: A finite deformation theory framework. Int. J. Numer. Meth. Engrg., 83: 27–58, 2009.

    MathSciNet  Google Scholar 

  23. Luan B, Robbins M O. Contact of single asperities with varying adhesion: Comparing continuum mechanics to atomistic simulations. Phys. Rev. E, 74(2): 026111, 2006.

    Article  ADS  Google Scholar 

  24. Sauer R A, Li S. An atomistically enriched continuum model for nanoscale contact mechanics and its application to contact scaling. J. Nanosci. Nanotech., 8(7): 3757–3773, 2008.

    Google Scholar 

  25. Yang C, Persson B N J. Molecular dynamics study of contact mechanics: Contact area and interfacial separation from small to full contact. Phys. Rev. Lett., 100(2): 024303, 2008.

    Article  ADS  Google Scholar 

  26. Tadmor E B, Ortiz M, Phillips R. Quasicontinuum analysis of defects in solids. Phil. Mag. A, 73(6): 1529–1563, 1996.

    Article  ADS  Google Scholar 

  27. Miller R E, Tadmor E B. The quasicontinuum method: Overview, applications and current directions. J. Comp.-Aid. Mat. Design, 9: 203–239, 2002.

    Article  ADS  Google Scholar 

  28. Bradley R S. The cohesive force between solid surfaces and the surface energy of solids. Phil. Mag., 13: 853–862, 1932.

    MATH  Google Scholar 

  29. Hamaker H C. The London-van der Waals attraction between spherical particles. Physica, 4(10): 1058–1072, 1937.

    Article  ADS  Google Scholar 

  30. Sauer R A, Li S. A contact mechanics model for quasi-continua. Int. J. Numer. Meth. Engrg., 71(8): 931–962, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  31. Derjaguin B V. Untersuchungen über die reibung und adhäsion IV: Theorie des anhaftens kleiner teilchen. Kolloid Z., 69: 155–164, 1934.

    Article  Google Scholar 

  32. Sauer R A. An atomic interaction based continuum model for computational multiscale contact mechanics. PhD thesis, University of California, Berkeley, USA, 2006.

    Google Scholar 

  33. Sauer R A, Wriggers P. Formulation and analysis of a 3D finite element implementation for adhesive contact at the nanoscale. Comput. Methods Appl. Mech. Engrg., 198: 3871–3883, 2009.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Agrawal A, Steigmann D. Modeling protein-mediated morphology in biomembranes. Biomech. Model. Mechanobiol., 8(5): 371–379, 2009.

    Article  Google Scholar 

  35. Lanczos C. The Variational Principles of Mechanics. Dover edition, 1986.

    Google Scholar 

  36. Israelachvili J N. Intermolecular and Surface Forces. 2nd ed. Academic Press, 1991.

    Google Scholar 

  37. Belytschko T, Liu W K, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley, 2000.

    Google Scholar 

  38. Wriggers P. Nonlinear Finite Element Methods. Springer, 2008.

    Google Scholar 

  39. Persson B N J. Sliding friction. Surf. Sci. Rep., 33(3): 83–119, 1999.

    Article  ADS  Google Scholar 

  40. Ruoff S R, Tersoff J, Lorents D C, et al. Radial deformation of carbon nanotubes by van der Waals forces. Nature, 364: 514–516, 1993.

    Article  ADS  Google Scholar 

  41. Hertel T, Walkup R E, Avouris P. Deformation of carbon nanotubes by surface van der Waals forces. Phys. Rev. B, 58(20): 13870–13873, 1998.

    Article  ADS  Google Scholar 

  42. Pantano A, Parks D M, Boyce M C. Mechanics of deformation of single-and multi-walled carbon nanotubes. J. Mech. Phys. Solids, 52: 789–821, 2004.

    Article  ADS  MATH  Google Scholar 

  43. Tang T, Jagoda A, Hui C Y, Glassmaker N J. Collapse of single-walled carbon nanotubes. J. Appl. Phys., 97(7): 074310, 2005.

    Article  ADS  Google Scholar 

  44. Sauer R A. A computational contact model for nanoscale rubber adhesion. In Heinrich G, Kaliske M, Lion A and Reese S editors, Constitutive Models for Rubber VI. Taylor & Francis Group, 47–52, 2009.

    Google Scholar 

  45. Sauer R A. A computational model for nanoscale adhesion between deformable solids and its application to gecko adhesion. J. Adhes. Sci. Technol., 24: 1807–1818, 2010.

    Article  Google Scholar 

  46. Huber G, Mantz H, Spolenak R, et al. Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements. Proc. Natl. Acad. Sci. USA, 102(45): 16293–16296, 2005.

    Article  ADS  Google Scholar 

  47. Sun W, Neuzil P, Kustandi T S, et al. The nature of the gecko lizard adhesive force. Biophys. J., 89(2): L14–L17, 2005.

    Article  Google Scholar 

  48. Autumn K, Liang Y A, Hsieh S T, et al. Adhesive force of a single gecko foot-hair. Nature, 405: 681–684, 2000.

    Article  ADS  Google Scholar 

  49. Kendall K. Thin-film peeling-the elastic term. J. Phys. D: Appl. Phys., 8: 1449–1452, 1975.

    Article  ADS  Google Scholar 

  50. Zhao Y P, Wang L S, Yu T X. Mechanics of adhesion in MEMS: A review. J. Adhesion Sci. Technol., 17(4): 519–546, 2003.

    Article  ADS  Google Scholar 

  51. Lane M. Interface fracture. Annu. Rev. Mater. Res., 33: 29–54, 2003.

    Article  ADS  Google Scholar 

  52. Liu Y, Zhang L, Wang X, et al. Coupling of navier-stokes equations with protein molecular dynamics and its application to hemodynamics. Int. J. Numer. Methods Fluids, 46: 1237–1252, 2004.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. McGarry J P, Murphy B P, McHugh P E. Computational mechanics modelling of cell-substrate contact during cyclic substrate deformation. J. Mech. Phys. Solids, 53: 2597–2637, 2005.

    Article  ADS  MATH  Google Scholar 

  54. Zeng X, Li S. Multiscale modeling and simulation of soft adhesion and contact of stem cells. J. Mech. Behav. Biomed. Mater., doi: 10.1016/j.jmbbm.2010.06.002, 2010.

    Google Scholar 

  55. Krasovitski B, Marmur A. Particle adhesion to drops. J. Adhes., 81(7-8):869–880, 2005.

    Article  Google Scholar 

  56. Persson B N J, Albohr O, Tartaglino U, et al. On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J. Phys. Condens. Matter, 17(3): R1–R62, 2005.

    Article  ADS  Google Scholar 

  57. Kendall K, Amal R, Jiang X, et al. Effect of adhesion on aggregation in nanoparticle dispersions. J. Adhes., 83: 573–585, 2007.

    Article  Google Scholar 

  58. Qu L, Dai L, Stone M, et al. Carbon nanotube arrays with strong shear binding-on and easy normal lifting-off. Science, 322: 238–242, 2008.

    Article  ADS  Google Scholar 

  59. Wei Y, Hutchinson J W. Interface strength, work of adhesion and plasticity in the peel test. Int. J. Fracture, 93: 315–333, 1998.

    Article  Google Scholar 

  60. Crisfield M A, Alfano G. Adaptive hierarchical enrichment for delamination fracture using a decohesive zone model. Int. J. Numer. Meth. Engrg., 54(9): 1369–1390, 2002.

    Article  MATH  Google Scholar 

  61. Diehl T. On using a penalty-based cohesive-zone finite element approach, part I: Elastic solution benchmarks. Int. J. Adhesion Adhesives, 28: 237–255, 2008.

    Article  Google Scholar 

  62. Lorenzis L D, Zavarise G. Modeling of mixed mode debonding in the peel test applied to superficial reinforcements. Int. J. Solids Struc., 45: 5419–5436, 2008.

    Article  MATH  Google Scholar 

  63. Sauer R A. Enriched contact finite elements for stable peeling computations. Int. J. Numer. Meth. Engrg.. (in press)

    Google Scholar 

  64. Puso M A, Laursen T A, Solberg J. A segment-to-segment mortar contact method for quadratic elements and large deformations. Comput. Methods Appl. Mech. Engrg., 197: 555–566, 2008.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. Sauer R A. The peeling behavior of thin films with finite bending stiffness and the implications on gecko adhesion. J. Adhes.. (accepted)

    Google Scholar 

  66. Sauer R A, Holl M. A 3d finite element analysis of the peeling behavior of a gecko spatula. Comp. Meth. Biomech. Biomed. Engng.. (submitted)

    Google Scholar 

  67. Persson B N J. Contact mechanics for randomly rough surfaces. Surf. Sci. Rep., 61(4): 201–227, 2006.

    Article  ADS  Google Scholar 

  68. Timoshenko S P, Goodier J N. Theory of Elasticity. 3rd ed. McGraw-Hill, 1970.

    Google Scholar 

  69. Greenwood J A, Williamson J B P. Contact of nominally at surfaces. Proc. Roy. Soc. A, 295(1442): 300–319, 1966.

    Article  ADS  Google Scholar 

  70. Chang W R, Etsion L, Bogy D B. Adhesion model for metallic rough surfaces. J. Trib., 110: 50–56, 1988.

    Article  Google Scholar 

  71. Persson B N J. Elastoplastic contact between randomly rough surfaces. Phys. Rev. Lett., 87(11): 116101–1, 2001.

    Article  ADS  Google Scholar 

  72. Chowdhury S K R, Ghosh P. Adhesion and adhesional friction at the contact between solids. Wear, 174: 9–19, 1994.

    Article  ADS  Google Scholar 

  73. Lai W T, Cheng H S. Computer simulation of elastic rough contacts. Trib. Trans, 28: 172–180, 1985.

    Google Scholar 

  74. Webster MN, Sayles R S. A numerical model for the elastic frictionless contact of real rough surfaces. J. Trib, 108: 314–320, 1986.

    Article  Google Scholar 

  75. Ren N, Lee S C. Contact simulation of three-dimensional rough surfaces using moving grid method. J. Tribol.-T. ASME, 115(4): 597–601, 1993.

    Article  Google Scholar 

  76. Tian X, Bhushan B. A numerical three-dimensional model for the contact of rough surface by variational principle. J. Tribol.-T. ASME, 118(1): 33–42, 1996.

    Article  Google Scholar 

  77. Karpenko Y A, Akay A. A numerical model of friction between rough surfaces. Tribol. Int., 34(8): 531–545, 2001.

    Article  Google Scholar 

  78. Carbone G, Mangialardi L. Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface. J. Mech. Phys. Solids, 52(6): 1267–1287, 2004.

    Article  ADS  MATH  Google Scholar 

  79. Tworzydlo WW, Cecot W, Oden J T, et al. Computational micro-and macroscopic models of contact and friction: Formulation, approach and applications. Wear, 220(2): 113–140, 1998.

    Article  Google Scholar 

  80. Haraldsson A, Wriggers P. A strategy for numerical testing of friction laws with application to contact between soil and concrete. Comp. Meth. Appl. Mech. Engrg., 190: 963–977, 2000.

    Article  MATH  Google Scholar 

  81. Zhuravlev V A. On the question of theoreticsl justification of the Amontons-Coulomb law for friction of unlubricated surfaces. Proc. Inst. Mech. Eng. J-J. Eng. Trib., 221(J8): 895–898, 2007.

    Google Scholar 

  82. Borodich F M. Comment on “elastoplastic contact between randomly rough surfaces”. Phys. Rev. Lett., 88(6): 069601, 2002.

    Article  ADS  Google Scholar 

  83. Autumn K, Dittmore A, Santos, D, et al. Frictional adhesion: A new angle on gecko attachment. J. Exp. Biol., 209: 3569–3579, 2006.

    Article  Google Scholar 

  84. Singer I L. Friction and energy dissipation at the atomic scale: A review. J. Vac. Sci. Technol. A, 12(5): 2605–2616, 1994.

    Article  ADS  Google Scholar 

  85. Morita S, Fujisawa S, Sugawara Y. Spatially quantized friction with a lattice periodicity. Surf. Sci. Rep., 23(1): 1–41, 1996.

    Article  Google Scholar 

  86. Luan B Q, Hyun S, Molinari J F, et al. Multiscale modeling of two-dimensional contacts. Phys. Rev. E, 74(4): 046710, 2006.

    Article  ADS  Google Scholar 

  87. Barthlott W, Neinhuis C. Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta, 202: 1–8, 1997.

    Article  Google Scholar 

  88. Sauer R A, Osman M. A computational contact model for liquid droplets. (under preparation).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sauer, R.A. (2012). Computational Contact Formulations for Soft Body Adhesion. In: Advances in Soft Matter Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19373-6_2

Download citation

Publish with us

Policies and ethics