Exact analytic solutions are derived for the time-dependent deformation of a poroelastic medium within a two-dimensional finite domain. Solutions are given with a specific set of boundary conditions for the case of a source of fluid at an arbitrary point and for an applied pressure on the boundary. These solutions are ideal for testing numerical schemes for poroelastic flow and deformations due to their relative simplicity.
Issue Section:
Technical Papers
1.
Armstrong
CG
Lai
WM
Mow
VC
1984
An Analysis of the Unconfined Compression of Articular Cartilage
, ASME Journal of Biomechanical Engineering
, vol. 66
2
(pg. 165
-173
)2.
Ateshian
GA
Lai
WM
Zhu
WB
Mow
VC
1994
An asymptotic solution for the contact of two cartilage layers
, Journal of Biomechanics
, vol. 66
2
(pg. 1347
-1360
)3.
Barry
SI
Aldis
GK
1990
Comparison of models for flow induced deformation of soft biological tissues
, Journal of Biomechanics
, vol. 66
2
(pg. 647
-654
)4.
Barry
SI
Aldis
GK
1991
Deformation of soft biological tissue due to an unsteady fluid flow
, International Journal of Non-Linear Mechanics
, vol. 66
2
(pg. 687
-699
)5.
Barry
SI
Aldis
GK
1993
Radial flow through deformable porous shells
, Journal of the Australian Mathematics Society, Series B
, vol. 66
2
(pg. 333
-354
)6.
Barry
SI
Aldis
GK
Mercer
GN
1995
Injection of fluid into a layer of deformable porous medium
, ASME Applied Mechanics Reviews
, vol. 66
2
(pg. 722
-726
)7.
Barry
SI
Mercer
GN
Zoppou
C
1997
Approximate and Analytic Solutions for Deformation of Finite Porous Filters
, ASME JOURNAL OF APPLIED MECHANICS
, vol. 66
2
(pg. 929
-934
)8.
Biot
MA
1941
General theory of three dimensional consolidation
, Journal of Applied Physics
, vol. 66
2
(pg. 155
-164
)9.
Booker
JR
Carter
JP
1986
Long term subsidence due to fluid extraction from a saturated, anisotropic, elastic soil mass
, Quarterly Journal of Mechanics and Applied Mathematics
, vol. 66
2
(pg. 85
-97
)10.
Booker
JR
Carter
JP
1987
Withdrawal of a compressible pore fluid from a point sink in an isotropic elastic half space with anisotropic permeability
, International Journal Solids and Structures
, vol. 66
2
(pg. 369
-385
)11.
Bowen
RM
1980
Incompressible porous media models by the theory of mixtures
, International Journal of Engineering Science
, vol. 66
2
(pg. 1129
-1148
)12.
Gibson
RE
Schiffman
RL
Pu
SL
1970
Plane strain and axially symmetric consolidation of a clay layer on a smooth impervious base
, Quarterly Journal of Mechanics and Applied Mathematics
, vol. 66
2
(pg. 505
-520
)13.
Heinrich
G
Desoyer
K
1961
Theorie dreidimensionaler Setzungsvorgaenge in Tonshichten
, Ingenieur-Archiv
, vol. 66
2
(pg. 225
-253
)14.
Holmes
MH
1983
A nonlinear diffusion equation arising in the study of soft tissue
, Quarterly of Applied Mathematics
, vol. 66
2
(pg. 209
-220
)15.
Holmes
MH
Lai
WM
Mow
VC
1985
Singular Perturbation Analysis of the Nonlinear, Flow-dependent Compressive Stress Relaxation Behaviour of Articular Cartilage
, ASME Journal of Biomechanical Engineering
, vol. 66
2
(pg. 206
-218
)16.
Jensen
OE
Glucksberg
MR
Sachs
JR
Grotberg
JB
1994
Weakly Nonlinear Deformation of a Thin Poroelastic Layer With a Free Surface
, ASME JOURNAL OF APPLIED MECHANICS
, vol. 66
2
(pg. 729
-731
)17.
Kenyon
DE
1976
Transient Filtration in a Porous Elastic Cylinder
, ASME JOURNAL OF APPLIED MECHANICS
, vol. 66
2
(pg. 594
-598
)18.
Kenyon
DE
1979
A mathematical model of water flux through aortic tissue
, Bulletin of Mathematical Biology
, vol. 66
2
(pg. 79
-90
)19.
Klanchar
M
Tarbell
JM
1987
Modeling water flow through arterial tissue
, Bulletin of Mathematical Biology
, vol. 66
2
(pg. 651
-669
)20.
Lai
WM
Mow
VC
1980
Drag induced compression of articular cartilage during a permeation experiment
, Biorheology
, vol. 66
2
(pg. 111
-123
)21.
Mak
AF
Lai
WM
Mow
VC
1987
Biphasic indentation of articular cartilage: I. Theoretical analysis
, Journal of Biomechanics
, vol. 66
2
(pg. 703
-714
)22.
Mow
VC
Lai
WM
1980
Recent Developments in synovial joint biomechanics
, SIAM Review
, vol. 66
2
(pg. 275
-317
)23.
Parker
KH
Mehta
RV
Caro
CG
1987
Steady flow in porous, elastically deformable materials
, ASME JOURNAL OF APPLIED MECHANICS
, vol. 66
2
(pg. 794
-800
)24.
Rudnicki
JW
1987
Plane Strain Dislocations in Linear Elastic Diffusive Solids
, ASME JOURNAL OF APPLIED MECHANICS
, vol. 66
2
(pg. 545
-552
)25.
Sachs
JR
Glucksberg
MR
Jensen
OE
Grotberg
JB
1994
Linear Flow and Deformation in a Poroelastic Disk With a Free Surface
, ASME JOURNAL OF APPLIED MECHANICS
, vol. 66
2
(pg. 726
-728
)26.
Yang
M
Taber
LA
1991
The possible role of poroelasticity in the apparent viscoelastic behaviour of passive cardiac muscle
, Journal of Biomechanics
, vol. 66
2
(pg. 587
-597
)
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