Boundary Element Modelling of Interface Phenomena

  • A. P. S. Selvadurai
  • M. C. Au
Part of the Topics in Boundary Element Research book series (TBOU, volume 4)

Abstract

In this article we examine the application of the boundary element method to the study of the non-linear interface behaviour between two material regions. The non-linear interface response is modelled either by Coulomb frictional behaviour or by interface plasticity. An incremental formulation is adopted for the analysis of the non-linear pheonomena. The incremental non-linear analysis is used to examine the two-dimensional problem of a finite elastic region which contains a circular rigid inclusion. The numerical results presented in the paper illustrates the manner in which the non-linear phenomena at the inclusion-elastic medium interface contributes to the global non-linear responses in the composite.

Keywords

Strain Hardening Como Geomechanics Pentech 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duvaut, G. and Lions, J.L.,Inequalities in Mechanics and Physics Springer Verlag, Berlin (1975).Google Scholar
  2. 2.
    Gudehus, G., (Ed.), Finite Elements in Geomechanics John Wiley, New York, (1977).Google Scholar
  3. 3.
    Desai, C.S. and Christian, J.T., (Eds.), Numerical Methods in Geomechanics McGraw-Hill, New York, (1977).Google Scholar
  4. 4.
    de Pater, A.D. and Kalker, J.J., (Eds.)., The Mechanics of Contact Between Deformable Media Proc. IUTAM Symposium, Enschede, Deflt Univ. Press, Delft (1975).Google Scholar
  5. 5.
    Selvadurai, A.P.S., Elastic Analysis of Soil-Foundation Interaction, Developments in Geotechnical Engineering Vol. 17, Elsevier Scientific Publ. Co., Amsterdam, (1979).Google Scholar
  6. 6.
    Gladwell, G.M.L., Contact Problems in the Classical Theory of Elasticity Sijthoff and Noordhoft, The Netherlands, (1980).MATHGoogle Scholar
  7. 7.
    Kikuchi, N. and Oden, J.T., Contact Problems in Elasticity Texas Institute for Computational Mechanics, Rept. 79–8, The University of Texas, Austin, (1979).Google Scholar
  8. 8.
    Panagiotopoulos, P.D., Inequality Problems in Mechanics and Applications Birkhauser Verlag, Basel (1985).MATHCrossRefGoogle Scholar
  9. 9.
    Johnson, K.L., Contact Mechanics Cambridge University Press, U.K., (1985).MATHGoogle Scholar
  10. 10.
    Selvadurai, A.P.S. and Voyiadijs, G.Z. (Eds.), Mechanics of Material Interfaces Studies in Applied Mechanics, Vol. 11, Elsevier Scientific Publ. Co., Amsterdam, (1986).Google Scholar
  11. 11.
    Bowden, F.P. and Tabor, D., Friction and Lubrication of Solids, Vols. I and II, Oxford University Press, Oxford, (1964).Google Scholar
  12. 12.
    Ufliand, la. S, Survey of Articles on the Application of Integral Transforms in the Theory of Elasticity English Transi. Sneddon, I.N. (Ed.), Raleigh, North Carolina State University, (1965).Google Scholar
  13. 13.
    Galin, L.A.,Contact Problems in the Theory of Elasticity English Transi., Sneddon, Z.N. (Ed.), Raleigh, North Carolina State University, (1961).Google Scholar
  14. 14.
    Dundurs, J. and Stippes, M., ’Role of elastic constants in certain contact problems’, J. Appl. Mech., 37 pp. 965–970 (1970).CrossRefGoogle Scholar
  15. 15.
    Sneddon, I.N., Application of Integral Transforms in The Theory of Elasticity, CISM Courses and Lectures No. 220, Springer Verlag, Wein, (1975).Google Scholar
  16. 16.
    Spence, D., ’Self similar solutions to adhesive contact problems’, Proc. Roy. Soc., Ser. A., 305 pp. 55–80(1968).Google Scholar
  17. 17.
    Kalker, J J, ’Variational principles of contact elastostatics’, J. Inst. Math. Applies., 20 pp. 199–219 (1977).MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Turner, J.R., ’The frictional unloading problem on a linear elastic halfspace’, J. Inst. Math. Applies., 24 pp. 439–469 (1979).MATHCrossRefGoogle Scholar
  19. 19.
    Goodman, R.E., Taylor, R.L. and Brekke, T.L., ’A model for the mechanics of jointed rock’, J. Soil Mech. Fdn. Div. Proc. ASCE, 94 pp. 637–659 (1968).Google Scholar
  20. 20.
    Goodman, R.E. and Dubois, J., ’Duplications of dilatancy in analysis of jointed rocks’, J. Soil Mech. Fdn. Div., Proc. ASCE, 98 pp. 399–422 (1972).Google Scholar
  21. 21.
    Ghabbousi, J., Wilson, E.L. and Isenberg, J, ’Finite Elements for rock joints and interfaces’, J. Soil Mech. Fdn. Div. Proc. ASCE, 99 pp. 833–848 (1973).Google Scholar
  22. 22.
    Zienkiewicz, O.C., Best, B., Dullage, C. and Stagg, K., ’Analysis of non-linear problems in rock mechanics with particular reference to jointed rock systems’, Proc. 2nd Congress Int. Soc. Rock Mech. Belgrade, Yugoslavia, 3 pp. 501–509 (1970).Google Scholar
  23. 23.
    Fredriksson, G., ’Finite element solution of surface non-linearities in structural mechanics’,Computers and Structures, 6 pp. 281–290 (1976).MATHCrossRefGoogle Scholar
  24. 24.
    Boulon, M., Darve, F., Desrues, J. and Foray, P., ’Soil-structure coupling, nonlinear rheological relationships and boundary conditions in soil mechanics’, Computers and Structures, 9 pp. 293–303 (1978).MATHCrossRefGoogle Scholar
  25. 25.
    Pande, G.N. and Sharma, K.G., ’On joint/interface elements and associated problems of numerical ill-conditioning’, Int. J. Num. Anal. Meth. Geomech., 3, pp. 293–300 (1979).CrossRefGoogle Scholar
  26. 26.
    Ito, Y.M., England, R.H. and Nelson, R.B., ’Computational methods for soil-structure interaction problems’,Computers and Structures, 13 pp. 157–162 (1981).MATHCrossRefGoogle Scholar
  27. 27.
    Selvadurai, A.P.S. and Faruque, M.O., ’The influence of interface friction on the performance of cable jacking tests of rock masses’, Proc. Impl. Comp. Procedures and Stress-Strain Laws in Geotech Eng. Desai, C.S. and Saxena, S.K., Eds., Illinois, Runcorn Press, 1, pp. 169–183 (1981).Google Scholar
  28. 28.
    Desai, C.S., ’Behaviour of interfaces between structural and geologic media’, Proc. Int. Conf on Recent Advances in Geotech. Earthq. Eng. and Soil Dynamics (Prakash, S., Ed.), St. Louis, Mo., 2, pp. 619–638, (1981).Google Scholar
  29. 29.
    Desai, C.S. and Nagaraj, B.K., ’Constitutive modelling for interfaces under cyclic loading’ in Mechanics of Material Interfaces (Selvadurai, A.P.S. and Vorjiadjis, G.Z., Eds.), Vol. II, Studies in Applied Mechanics, Elsevier Scientific Publ. Co, pp. 97–108, (1986).Google Scholar
  30. 30.
    Goodman, R.E., ’Analysis of jointed rocks’, Ch. 11 in Finite Elements in Geomechanics (Gudehus, G, Ed.), John Wiley, New York, pp. 351–376 (1977).Google Scholar
  31. 31.
    Desai, C.S, ’Soil-structure interaction and simulation problems’, Ch. 7 in Finite Elements in Geomechanics (Gudehus, G, Ed.), John Wiley, New York, pp. 209–250 (1977).Google Scholar
  32. 32.
    Herrmann, L.R, ’Finite element analysis of contact problems’, J. Eng. Mech. Div. Proc. ASCE, 104 1042–1057(1978).Google Scholar
  33. 33.
    Wilson, E.L, ’Finite elements for foundations, joints and fluids’, Ch. 10 in Finite Elements in Geomechanics (Gudehus, G, Ed.), John Wiley, New York, pp. 319–350 (1977).Google Scholar
  34. 34.
    Gaertner, R, ’Investigation of plane elastic contact allowing for friction’, Computers and Structures 7, pp. 59–63 (1977).CrossRefGoogle Scholar
  35. 35.
    Okamoto, N. and Nabazawa, M, ’Finite element incremental contact analysis with various frictional conditions’, Int. J. Num. Meth. Eng., 14 pp. 337–357 (1979).MATHCrossRefGoogle Scholar
  36. 36.
    Zienkiewicz, O.C., The Finite Element Method in Engineering Science McGraw-Hill, New York (1978).Google Scholar
  37. 37.
    Andersson, T., The boundary element method applied to two-dimensional contact problems with friction’, in Boundary Element Methods Proc. 3rd Int. Seminar, Irvine, California (Brebbia, C.A., Ed.), Springer-Verlag, Berlin (1981).Google Scholar
  38. 38.
    Andersson, T., ’The second generation boundary element contact program’ in Boundary Element Methods in Engineering Proc. 4th Int. Seminar, Southampton, U.K. (Brebbia, C.A. Ed.) Springer- Verlag, Berlin (1982).Google Scholar
  39. 39.
    Andersson, T., and Allan Persson, B.G., ’The boundary element method applied to two-dimensional contact problems’, Ch. 5 inProgress in Boundary Element Methods (Brebbia, C.A., Ed.), CML Publications, U.K., 2, pp. 136–157 (1983).Google Scholar
  40. 40.
    Paris, F. and Garrido, J.A., ’On the use of discontinuous elements in two-dimensional contact problems’, Proc. 7th Boundary Element Conference (Brebbia, C.A. and Maier, G., Eds.) Como, Springer-Verlag, Berlin, pp. 13.27–13.39 (1985).Google Scholar
  41. 41.
    Selvadurai, A.P.S. and Au., M.C., ’Response of inclusions with interface separation, friction and slip’, Proc. 7th Boundary Element Conference (Brebbia, C.A. and Maier, G., Eds.), Como, Springer-Verlag, Berlin, pp. 14.109–14.127 (1985).Google Scholar
  42. 42.
    Brebbia, C., The Boundary Element Method for Engineers Pentech Press, 2nd. ed., (1980).Google Scholar
  43. 43.
    Teiles, J.C.F., ’The Boundary Element Method Applied to Inelastic Problems’ Lecture notes in Engineering, 1, Springer-Verlag, Berlin, (1983).Google Scholar
  44. 44.
    Banerjee, P.K. and Butterfield, R.,’Boundary Element Methods in Engineering Science’, McGraw-Hill, New York, (1981).Google Scholar
  45. 45.
    Brebbia, C.A., Tells, J.C.P. and Wrobel, L.C.,’Boundary Element Techniques, Theory and Applications in Engineering’, Springer-Verlag, (1984).MATHCrossRefGoogle Scholar
  46. 46.
    Haslinger, J. and Janovsky, V., ’Contact problems with friction’, in Trends in Application of Pure Mathematics to Mechanics (Brilla, J., Ed.) IV, pp. 74–100 (1983).Google Scholar
  47. 47.
    Martins, J.A.C. and Oden, J.T., ’Interface models, variational principles and numerical solutions for dynamic friction problems’, in Mechanics of Material Interfaces (Selvadurai, A.P.S. and Voyiadjis, G.Z., Eds.), Studies in Applied Mechanics, Vol. II, Elsevier Scientific Publ. Co., pp. 3–22 (1986).Google Scholar
  48. 48.
    Chen, W.-F., Limit Analysis and Soil Plasticity Developments in Geotechnical Engineering, Vol. 7, Elsevier Scientific Publ. Co., Amsterdam, (1975)Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1987

Authors and Affiliations

  • A. P. S. Selvadurai
  • M. C. Au

There are no affiliations available

Personalised recommendations