Abstract
The paper is concerned with the load transfer problem between two rigid spherical inclusions in an elastic matrix. A reflection-type formula is developed which is accurate up to and including terms ofO(a/R)4, wherea is the maximum radius of the inclusions, andR is the centre-to-centre distance between the two inclusions. Asymptotic results are derived at near touching showing a weak logarithmic singularity in the load transfer. The results are verified by a direct numerical calculation using a boundary collocation method. The numerical method uses Kelvin's general solution as the basis functions for the approximate solution and is highly accurate and efficient, even at near touching.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batchelor, G. K., J. Fluid Mech.44, 545 (1970).
Budianski, B., Hashin, Z. and Sanders, J. L., inProc. 2nd Symp. on Naval Struct. Mechanics. Pergamon, New York 1960.
Dollar, A. and Steif, P. S.,ASME Pressure Vessels and Piping Div. Publication PVP v 146 Adv. in Micromechanics of Composite Material Vessels and Components 1988.
Dvorkin, J., Mavko, G. and Nur, A., Mech. of Materials12, 207 (1991).
Eshelby, J. D., Proc. Roy. Soc. Lond.A241, 376 (1957).
Gluckman, M. J., Pfeffer, R. and Weinbaum, S., J. Fluid Mech.50, 705–740 (1971).
Hashin, Z.,IUTAM Proc. Symposium on Non-Homogeneity in Elasticity and Plasticity, Warsaw, Poland. Pergamon, New York 1959.
Hashin, Z., ASME J. Appl. Mech.58, 444 (1991).
Honein, T. and Herrmann, G.,ASME paper 90-WA/APM-24. Winter Meeting, Dallas 1990. Jeffrey, D. J., Mathematika29, 58 (1982).
Johnson, K. L.,Contact Mechanics. Cambridge University Press, Cambridge 1985.
Kim, S. and Karrila, S. J.,Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann, Boston 1991.
Kim, S. and Phan-Thien, N., in press J. Elasticity, 1993.
Love, A. E. H.,A Treatise on the Mathematical Theory of Elasticity. Dover 1944.
Mura, T.,Micromechanics of Defects in Solids, 2nd Ed. Martinus Nijhoff, Dordrecht 1987.
Nunan, K. C. and Keller, J. B., J. Mech. Phys. Solids32, 259 (1984).
Phan-Thien, N., J. Elasticity, in press (1993).
Phan-Thien, N. and Karihaloo, B. L., ZAMM62, 183 (1982).
Phan-Thien, N. and Tullock, D., J. Mech. Phys. Solids, in press (1993).
Smoluchowski, M., Bull. Acad. Sci. Cracovie A1, 28 (1911).
Stoll, R. D.,Sediment Acoustics. Springer-Verlag, Berlin 1989.
Tu, Y. O. and Gazis, D. G., ASME J. Appl. Mech.31, 659 (1964).
Wallon, K., J. Mech. Phys. Solids26, 139 (1978).
Weinbaum, S., Ganatos, P. and Yan, Z., Ann. Rev. Fluid Mech.22, 275–316 (1990).
Yoon, B. J. and Kim, S., J. Fluid Mech.29, 437 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Phan-Thien, N., Kim, S. The load transfer between two rigid spherical inclusions in an elastic medium. Z. angew. Math. Phys. 45, 177–201 (1994). https://doi.org/10.1007/BF00943501
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00943501