Deformation and fluid flow due to a source in a poro-elastic layer

Applied Mathematical Modelling

Volumn 21, Issue 11, 1997, Pages 681-689

  Barry, S I ^a   Mercer, G N ^b   Zoppou, C ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b NONE

Author keywords

Deformable; Filter; Poro elastic; Porous

Indexed keywords

BOUNDARY CONDITIONS; DEFORMATION; ELASTICITY; FLOW OF FLUIDS; NUMERICAL ANALYSIS; POROUS MATERIALS; SWELLING;

FILTERS (FOR FLUIDS);

FILTER; FLUID FLOW; POROUS MEDIUM; SOIL;

FILTER; FLUID FLOW; POROUS MEDIUM; SOIL WATER;

EID: 0031277732     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(97)00097-8     Document Type: Article

References (27)

1. Scott, R. F. Subsidence - A review. Evaluation and Prediction of Subsidence, ed. S. K. Saxena, A.S.C.E., New York, 1978, pp. 1-25
2. Bear, J. and Corapcioglu, M. Y. A mathematical model for consolidation in a thermoelastic aquifer due to hot water injection or pumping. Water Resources Res. 1981, 17, 723-736
3. Terzaghi, K. Erdbaumechanik auf Bodenphysikalischen Grundlagen. Wien, Deuticke 1925
4. Biot, M. A. General theory of three-dimensional consolidation. J. Appl. Phys. 1941, 12, 155-164
5. Kenyon, D. E. The theory of an incompressible solid-fluid mixture. Arch. Rat. Mech. Anal. 1976, 62, 131-147
6. Bowen, R. M. Incompressible porous media models by the theory of mixtures. Int. J. Eng. Sci. 1980, 18, 1129-1148
7. Mow, V. C. and Lai, W. M. Recent developments in synovial joint biomechanics. SIAM Rev. 1980, 22, 275-317
8. Mow, V. C., Hou, J. S., Owens, J. M., and Ratcliffe, A. Biphasic and quasilinear viscoelastic hydrated soft tissues. Biomechanics of Diarthrodial Joints, eds. V. C. Mow, A. Ratcliffe, and S. L-Y. Woo, Springer-Verlag, New York, 1990, pp. 215-260
9. Booker, J. R. and Carter, J. P. Long term subsidence due to fluid extraction from a saturated, anisotropic, elastic soil mass. Q. J. Mech. Appl. Math. 1986, 39, 85-97
10. Booker, J. R. and Carter, J. P. Withdrawal of a compressible pore fluid from a point sink in an isotropic elastic half space with anisotropic permeability. Int. J. Solids Struct. 1987, 23, 369-385
11. Heinrich, G. and Desoyer, K. Theorie dreidimensionaler Setzungsvorgaenge in Tonshichten. Ing.-Arch. 1961, 30, 225-253
12. Gibson, R. E., Schiffman, R. L., and Pu, S. L. Plane strain and axially symmetric consolidation of a clay layer on a smooth impervious base. Q. J. Mech. Appl. Math. 1970, 23, 505-520
13. Mak, A. F., Lai, W. M., and Mow, V. C. Biphasic indentation of articular cartilage - I. Theoretical analysis. J. Biomech. 1987, 20, 703-714
14. Spilker, R. L., Sun, J.-K., and Mow, V. C. A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage. J. Biomech. Eng. 1992, 114, 191-201
15. Suh, J.-K. and Spilker, R. L. Indentation analysis of biphasic articular cartilage: nonlinear phenomena under finite deformation. J. Biomech. Eng. 1994, 116, 1-9
16. Sachs, J. R., Glucksberg, M. R., Jensen, O. E., and Grotberg, J. B. Linear flow and deformation in a poroelastic disc with a free surface. J. Appl. Mech. 1994, 61, 726-728
17. Jensen, O. E., Glucksberg, M. R., Sachs, J. R., and Grotberg, J. B. Weakly nonlinear deformation of a thin poroelastic layer with a free surface. J. Appl. Mech. 1994, 61, 729-731
18. Vardoulakis, I. and Harnpattanapanich, T. Numerical Laplace-Fourier transform inversion technique for layered-soil consolidation problems: 1. Fundamental solutions and validation. Int. J. Num. Anal. Meth. Geomech. 1986, 10, 347-365
19. Barry, S. I., Aldis, G. K., and Mercer, G. N. Injection of fluid into a layer of deformable porous medium. Appl. Mech. Rev. 1995, 48, 722-726
20. Lai, W. M. and Mow, V. C. Drag induced compression of articular cartilage during a permeation experiment. Biorheology 1980, 17, 111-123
21. Holmes, M. H. A theoretical analysis for determining the nonlinear hydraulic permeability of a soft tissue from a permeation experiment. Bull. Math. Biol. 1985, 47, 669-683
22. Barry, S. I. and Aldis, G. K. Comparison of models for flow induced deformation of soft biological tissue. J. Biomech. 1990, 23, 647-654
23. Barry, S. I. and Aldis, G. K. Unsteady flow induced deformation of porous materials. Int. J. Non-Linear Mech. 1991, 26, 687-699
24. Barry, S. I. and Aldis, G. K. Radial flow through deformable porous shells. J. Austral. Math. Soc. Ser. B 1993, 34, 333-354
25. Bedford, A. and Drumheller, D. S. Recent advances, theory of immiscible and structured mixtures. Int. J. Eng. Sci. 1983, 21, 863-960
26. Hou, J. S., Holmes, M. H., Lai, W. M., and Mow, V. C. Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. J. Biomech. Eng. 1989, 111, 78-87
27. Gradshteyn, I. S. and Ryzhik, I. M. Table of Integrals, Series, and Products. Academic Press, New York, 1980