Effective moduli of particulate solids: The completed double layer boundary element method with lubrication approximation

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 51, Issue 1, 2000, Pages 92-113

  Qi, F ^a   Phan Thien, N ^a   Fan, X J ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Boundary element method; Completed double layer BEM; Contitutive equations; Effective moduli; Lubrication approximation; Micromechanics; Particulate solids

Indexed keywords

EID: 0034340224     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001509     Document Type: Article

References (49)

1. Banerjee, P. K. and Butterfield, R., Boundary Element Methods in Engineering Science, McGraw Hill, New York 1981.
2. Batchelor, G. K., The stress system in a suspension of force-free particles, J. Fluid Mech. 44 (1970), 545-570.
3. Bergman, D. J., Exactly solvable microscopic geometries and rigorous bounds for the complex dielectric constant of two-component composite material, Phys. Rev. Lett 44 (1980), 1285-1287.
4. Brebbia, C. A., Tellers, J. C. F. and Wrobel, L. C , Boundary Element Techniques: Theory and Applications in Engineering, Springer-Verlag, Berlin 1984.
5. Budianski, B., Hashin, Z. and Sanders, J. L., in Proc. 2nd. Symp. on Naval Struct. Mechanics, Pergamon New York 1960.
6. Chen, H. S. and Acrivos, A., The solution of the equations of linear elasticity for an infinite region containing two spherical inclusions, Int. J. Solids Structures, 14 (1978), 331-348; The effective elastic moduli of composite materials containing spherical inclusions at nondilute concentrations, Int. J. Solids Structures, 14 (1978), 349-364.
7. Chen, H. S. and Acrivos, A., The solution of the equations of linear elasticity for an infinite region containing two spherical inclusions, Int. J. Solids Structures, 14 (1978), 331-348; The effective elastic moduli of composite materials containing spherical inclusions at nondilute concentrations, Int. J. Solids Structures, 14 (1978), 349-364.
8. Fan, X. J., Phan-Thien, N. and Zheng, R., Completed double layer boundary element method for periodic suspensions, ZAMP 48 (1997), 1-12.
9. Garland, D. K. and Tanner, D. B., Electrical transport and optical properties of inhomogenous media, Amer. Inst. Phys., New York 1978.
10. Hale, D. K., The physical properties of compos te materials, J. Matl. Sci., 11 (1976), 2105-2141.
11. Hashin, Z., IUTAM Proc. Symposium on non-homogeneity in elasticity and plasticity, Warsaw, Poland; Pergamon, New York 1959.
12. Hashin, Z. and Shtrikman, S., A variational approach to the theory of the elastic behaviour of multiphase materials, J. Mech. Phys.Solids, 11 (1963), 127-140.
13. Ingber, M. S., Dynamic simulation of the hydrodynamic interaction among immersed particles in Stokes flow, Int J. Num. Method. Fluids 10 (1990), 791-809.
14. Ingber, M. S. and Mondy L. A., Direct second kind boundary integral formulation for Stokes flow problems, Comp. Mech., 11 (1993), 11-27.
15. Ishai, O. and Cohen, L. J., Elastic properties of filled and porous epoxy composites, Int. J. Mech. Sci., 9 (1967), 539-546.
16. Kim, S. and Karrila, S. J. (1991), Microhydrodynamics: Principles and Selected Applications, Butterworth-Heinemann, Boston 1991.
17. Landau, L. D. and Lifshitz, E. M., Theory of Elasticity, 2nd Ed., Pergamon Press, New York 1970.
18. McCoy, J. J., in Mechanics Today, ed. Nemat-Nasser, S., Vol. 6, Pergamon, New York 1981.
19. McPhedran, R. C., McKenzie, D. R. and Phan-Thien, N., in Advances in the Mechanics and the Flow of Granular Materials, McGraw-Hill, New York 1983.
20. Milton, G. W., Concerning bounds on the transport and mechanical properties of multicomponent composite materials. Appl. Phys., A 26 (1981), 125-130: and (1982), Bounds on the elastic and transport properties of two-component composites, J. Mech. Phys. Solids, 30 (1981), 177-191.
21. Milton, G. W., Concerning bounds on the transport and mechanical properties of multicomponent composite materials. Appl. Phys., A 26 (1981), 125-130: and (1982), Bounds on the elastic and transport properties of two-component composites, J. Mech. Phys. Solids, 30 (1981), 177-191.
22. Milton, G. W. and Phan-Thien, N., New bounds on effective elastic moduli of two-component materials. Proc. Roy. Soc., London A 380 (1982), 305-331.
23. Nasseri, S. and Phan-Thien, N. (1996), On the path and efficiency of two micromachines with rigid tails, Comp. Mech., 18(3) (1996), 192-199; Modelling micromachines with elasticparts in a viscous environment, Comp. Mech., 20(3) (1997), 242-246; Geometric optimization of a micromachine with spiral tail, Comp. Mech. 20(3) (1997), 267-271.
24. Nasseri, S. and Phan-Thien, N. (1996), On the path and efficiency of two micromachines with rigid tails, Comp. Mech., 18(3) (1996), 192-199; Modelling micromachines with elasticparts in a viscous environment, Comp. Mech., 20(3) (1997), 242-246; Geometric optimization of a micromachine with spiral tail, Comp. Mech. 20(3) (1997), 267-271.
25. Nasseri, S. and Phan-Thien, N. (1996), On the path and efficiency of two micromachines with rigid tails, Comp. Mech., 18(3) (1996), 192-199; Modelling micromachines with elasticparts in a viscous environment, Comp. Mech., 20(3) (1997), 242-246; Geometric optimization of a micromachine with spiral tail, Comp. Mech. 20(3) (1997), 267-271.
26. Nunan, K. C. and Keller, J. B., Effective elasticity tensor of a periodic composite, J. Mech. Phys Solids, 32 (1984), 259-280.
27. Pakddel, P. and Kim, S., Mobility and stresslet functions of particles with rough surface: A numerical study, J. Rheology, 35 (1991), 797-823.
28. Pham, D. C. and Phan-Thien, N., On the optimal bounds for the effective conductivity of isotropic quasi-symmetric multiphase media, 1996.
29. Phan-Thien, N. and Fan, X. J., Traction based completed adjoint double layer boundary element method in elasticity, Comp. Mech., 16 (1995), 360-367.
30. Phan-Thien, N. and Kim, S., Microstructures in Elastic Media: Principles and Computational Methods, Oxford University Press, New York 1994.
31. Phan-Thien, N. and Kim, S., On the elastic double layer: some exact solutions and the spectrum on the sphere, J. Mech. Phys. Solids, 42(8) (1994), 1177-1197.
32. Phan-Thien, N. and Milton, G. W., New third order bounds on the effective moduli of N-phase composites, Quart. Appl. Math., XLI (1983), 59-74. New bounds on the effective thermal conductivity of n-phase materials, Proc. Roy. Soc., London A 380 (1983), 333-348.
33. Phan-Thien, N. and Milton, G. W., New third order bounds on the effective moduli of N-phase composites, Quart. Appl. Math., XLI (1983), 59-74. New bounds on the effective thermal conductivity of n-phase materials, Proc. Roy. Soc., London A 380 (1983), 333-348.
34. Phan-Thien, N., Tran-Cong, T. and Graham, A. L., Shear flow of periodic arrays of particles clusters, J. Fluid Mech., 228 (1991), 275-293.
35. Phan-Thien, N. Tullock, D. L. and Kim, S., Completed double layer in half-space: A boundary element method, Comp, Mech. 9 (1992), 121-135.
36. Phan-Thien, N. and Tullock, D. L., Completed double layer boundary element method in elasticity, J. Mech. Solids, 41 (1993), 1067-1086.
37. Phan-Thien, N. and Tullock, D. L., Completed double layer boundary element method in elasticity and Stokes flow: Distributed computing through PVM, Comp. Mech., 14 (1994), 370-383.
38. Power, H. and Miranda, G., Second kind integral equation formulation of Stokes' flows past a particles arbitrary shape. SIAM J. Appl. Math., 47 (1987), 689-698.
39. Rallison, J. M., A numerical study of the deformation and burst of a viscous drop in general shear flow, J. Fluid Mech., 109 (1981), 465-482; The deformations of small viscous drops and bubbles in shear flows, Ann. Rev. Fluid Mech., 16 (1984), 45-66.
40. Rallison, J. M., A numerical study of the deformation and burst of a viscous drop in general shear flow, J. Fluid Mech., 109 (1981), 465-482; The deformations of small viscous drops and bubbles in shear flows, Ann. Rev. Fluid Mech., 16 (1984), 45-66.
41. Rider, P. F. and Phan-Thien, N., A numerical viscometer via distributed computing and the completed double layer boundary element method, Engineering Analysis with Boundary Elements, 19 (1997), 57-65.
42. Sadd, Y. and Schultz, M. H., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. Research Report, YALEU/DCS/RR-254, Department of Computer Science, Yale University 1983.
43. Shakib, F., Hughes, T. J. R. and Johan, Z., A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis. Comp. Mech. Eng., 75 (1989), 415-456.
44. Spanoudakis, J. and Young, R. J., Crack propagation in a glass particle-filled epoxy resin, J. Mater. Sci., 19 (1984), 473-486.
45. Stoll, R. D., Sediment Acoustics, Springer-Verlag, Berlin 1989.
46. Stone, H. A., Dynamics of drop deformation and breakup in viscous fluids, Ann. Rev. Fluid Mech., 26 (1994), 65-102.
47. Tran-Cong, T. and Phan-Thien, N., Stokes problems of multi-particle systems: A numerical method for arbitrary flows, Phys. Fluid, A 1(3) (1989), 453-461.
48. Walpole, L. J., On bounds for the overall elastic moduli of inhomogeneous systems-I and II, J. Mech. Phys. Solids, 14 (1966), 151-151-162 and 289-301.
49. Watt, J. P., Davies, G. F. and O'Connell, R. J., Rev. Geophy., 14 (1976), 541.