Mechanics of adhesive contact on a power-law graded elastic half-space

Journal of the Mechanics and Physics of Solids

Volumn 57, Issue 9, 2009, Pages 1437-1448

  Chen, Shaohua ^a   Yan, Cong ^a   Zhang, Peng ^b   Gao, Huajian ^c  

^a INSTITUTE OF MECHANICS   (China)

^b Saint Gobain High Performance Materials   (United States)

^c Brown University   (United States)

Author keywords

Contact mechanics; Elastic graded materials; Gibson material; JKR model; Pull off force

Indexed keywords

CONTACT MECHANICS; ELASTIC GRADED MATERIALS; GIBSON MATERIAL; JKR MODEL; PULL-OFF FORCE;

ADHESION; HYDROELASTICITY; POISSON RATIO;

MECHANICS;

EID: 68049083549     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2009.06.006     Document Type: Article

References (51)

1. Artz E., Gorb S., and Spolenak R. From micro to nano contacts in biological attachment devices. Proc. Natl. Acad. Sci. USA 100 (2003) 10603-10606
2. Autumn K., and Peattie A.M. Mechanisms of adhesion in geckos. Integr. Compar. Biol. 42 (2002) 1081-1090
3. Awojobi A.O., and Gibson R.E. Plane strain and axially symmetric problems of a linearly nonhomogeneous elastic half-space. Q. J. Mech. Appl. Math. 26 (1973) 285-302
4. Baney J.M., and Hui C.Y. A cohesive zone model for the adhesion of cylinders. J. Adhes. Sci. Technol. 11 (1997) 393-406
5. Barquins M. Adherence and rolling kinetics of a rigid cylinder in contact with a natural rubber surface. J. Adhes. 26 (1988) 1-12
6. Barthel E. On the description of the adhesive contact of spheres with arbitrary interaction potentials. J. Colloid Interface Sci. 200 (1998) 7-18
7. Booker J.R., Balaam N.P., and Davis E.H. The behavior of an elastic non-homogeneous half-space. Part I. Line and point loads. Int. J. Numer. Anal. Methods Geomech. 9 (1985) 353-367
8. Booker J.R., Balaam N.P., and Davis E.H. The behavior of an elastic non-homogeneous half-space. Part II. Circular and strip footings. Int. J. Numer. Anal. Methods Geomech. 9 (1985) 369-381
9. Brown P.T., and Gibson R.E. Surface settlement of a deep elastic stratum whose modulus increases linearly with depth. Can. Geotech. J. 9 (1972) 467-476
10. Calladine C.R., and Greenwood J.A. Line and point loads on a non-homogeneous incompressible elastic half-space. Q. J. Appl. Match. 28 (1978) 507-529
11. Carpick R.W., Agrait N., Ogletree D.F., and Salmeron M. Variation of the interfacial shear strength and adhesion of a nanometer sized contact. Langmuir 12 (1996) 3334-3340
12. Chaudhury M.K., Weaver T., Hui C.Y., and Kramer E.J. Adhesion contact of cylindrical lens and a flat sheet. J. Appl. Phys. 80 (1996) 30-37
13. Chen B., Wu P.D., and Gao H. Hierarchical modelling of attachment and detachment mechanisms of gecko toe adhesion. Proc. R. Soc. A 464 (2008) 1639-1652
14. Chen S., and Gao H. Non-slipping adhesive contact of an elastic cylinder on stretched substrates. Proc. R. Soc. Lond. A 462 (2006) 211-228
15. Chen S., and Gao H. Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation sensor. J. Mech. Phys. Solids 54 (2006) 1548-1567
16. Chen S., and Gao H. Bio-inspired mechanics of reversible adhesion: orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials. J. Mech. Phys. Solids 55 (2007) 1001-1015
17. Chen S., and Gao H. Non-slipping adhesive contact between mismatched elastic cylinders. Int. J. Solids Struct. 44 (2007) 1939-1948
18. Chen S., and Soh A. Tuning the geometrical parameters of biomimetic fibrillar structures to enhance adhesion. J. Royal Soc. Interface 5 (2008) 373-382
19. Chu Y.S., Dufour S., Thiery J.P., Perez E., and Pincet F. Johnson-Kendall-Robert theory applied to living cells. Phys. Rev. Lett. 94 2 (2005) 028102
20. Derjaguin B.V., Muller V.M., and Toporov Y.P. Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53 (1975) 314-326
21. Dugdale D.S. Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8 (1960) 100-104
22. Gao H., Wang X., Yao H., Gorb S., and Arzt E. Mechanics of hierarchical adhesion structures of gecko. Mech. Mater. 37 (2005) 275-285
23. Gao H., and Yao H. Shape insensitive optimal adhesion of nanoscale fibrillar structures. Proc. Nat. Acad. Sci. USA 101 (2004) 7851-7856
24. Giannakopoulos A.E., and Pallot P. Two-dimensional contact analysis of elastic graded materials. J. Mech. Phys. Solids 48 (2000) 1597-1631
25. Giannakopoulos A.E., and Suresh S. Indentation of solids with gradients in elastic properties: part I. Point force. Int. J. Solids Struct. 34 (1997) 2357-2392
26. Giannakopoulos A.E., and Suresh S. Indentation of solids with gradients in elastic properties: part II. Axisymmetric indentors. Int. J. Solids Struct. 34 (1997) 2393-2428
27. Gibson R.E. Some results concerning displacements and stresses in a non-homogeneous elastic half-space. Geotechnique 17 (1967) 58-67
28. Gibson R.E., Brown P.T., and Andrew K.R.F. Some results concerning displacements in a non-homogeneous elastic layer. ZAMP 22 (1971) 855-864
29. Gibson R.E., and Sills G.C. Settlement of a trip load on a non-homogeneous orthotropic incompressible elastic half-space. Quart. J. Mech. Appl. Math. 28 (1975) 233-243
30. Glassmaker N.J., Jagota A., Hui C.Y., and Kim J. Design of biomimetic fibrillar interface: 1. Making contact. J. R. Soc. Interface 1 (2004) 23-33
31. Greenwood J.A., and Johnson K.L. The mechanics of adhesion of viscoelastic solids. Philo. Mag. 43 (1981) 697-711
32. Greenwood J.A. Adhesion of elastic spheres. Proc. R. Soc. London A 453 (1997) 1277-1297
33. Greenwood J.A., and Johnson K.L. An alterative to the Maugis model of adhesion between elastic spheres. J. Phys. D: Appl. Phys. 31 (1998) 3279-3290
34. Hertz H. On the contact of elastic solids. J. Reine Angew. Math. 92 (1882) 156-171
35. Holl D.L. Stress transmission in earths. Proc. High Res. Board 20 (1940) 709-721
36. Hruban K. The basic problem of a no-linear and non-homogeneous half-space. Non-Homogeneity in Elasticity and Plasticity, IUTAM Symposium (1958), Pergamon Press, Warsaw 53-61
37. Hui C.Y., Glassmaker N.J., Tang T., and Jagota A. Design of biomimetic fibrillar interface: 2. Mechanics of enhanced adhesion. J. R. Soc. Interface 1 (2004) 35-48
38. Johnson K.L. Contact Mechanics (1985), Cambridge University Press, Cambridge
39. Johnson K.L., and Greenwood J.A. An adhesion map for the contact of elastic spheres. J. Colloid Interface Sci. 192 (1997) 326-333
40. Johnson K.L., Kendall K., and Roberts A.D. Surface energy and the contact of elastic solids. Proc. R. Soc. London A 324 (1971) 301-313
41. Kim K.S., McMeeking R.M., and Johnson K.L. Adhesion, slip cohesive zone and energy fluxes for elastic spheres in contact. J. Mech. Phys. Solids 46 (1998) 243-266
42. Lekhnitskii S.G. Radial distribution of stresses in a wedge and in a half-plane with variable modulus of elasticity. PMM 26 (1962) 146-151
43. Maugis D. Adhesion of spheres: The JKR-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150 (1992) 243-269
44. Morrow C., Lovell M., and Ning X. A JKR-DMT transition solution for adhesive rough surface contact. J. Phys. D: Appl. Phys. 36 (2003) 534-540
45. Muller V.M., Yushenko V.S., and Derjaguin B.V. On the influence of molecular forces on the deformation of an elastic sphere and its sticking to s rigid contact. J. Colloid Interface Sci. 77 (1980) 91-101
46. Spolenak R., Gorb S., Gao H., and Artz E. Effects of contact shape on the scaling of biological attachments. Proc. R. Soc. A 461 (2005) 305-319
47. Tabor D. Surface forces and surface interactions. J. Colloid Interface Sci. 58 (1976) 2-23
48. Yao, H., 2006. Mechanics of robust and releasable adhesion in biology. Ph.D. Dissertation, Max-Planck Institute for Metals Research, Stuttgart.
49. Yao H., and Gao H. Bio-inspired mechanics of robust and releasable adhesion on rough surface. J. Mech. Phys. Solids 54 (2006) 1120-1146
50. Yao H., and Gao H. Mechanical principles of robust and releasable adhesion of gecko. J. Adhes. Sci. Tech. 21 (2007) 1185-1212
51. Yao H., Ciavarella M., and Gao H. Adhesion maps of spheres corrected for strength limit. J. Colloid Interface Sci. 315 (2007) 786-790