Exact Solutions for Two-Dimensional Time-Dependent Flow and Deformation Within a Poroelastic Medium

J. Appl. Mech 66(2), 536-540 (Oct 25, 1999) (5 pages) doi:10.1115/1.2791080 History: Received September 01, 1996; Revised August 10, 1998


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.

COPYRIGHT © 1999 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.


ArmstrongCGLaiWMMowVC1984An Analysis of the Unconfined Compression of Articular CartilageASME Journal of Biomechanical Engineering662165173 [CrossRef]
AteshianGALaiWMZhuWBMowVC1994An asymptotic solution for the contact of two cartilage layersJournal of Biomechanics66213471360 [CrossRef]
BarrySIAldisGK1990Comparison of models for flow induced deformation of soft biological tissuesJournal of Biomechanics662647654 [CrossRef]
BarrySIAldisGK1991Deformation of soft biological tissue due to an unsteady fluid flowInternational Journal of Non-Linear Mechanics662687699 [CrossRef]
BarrySIAldisGK1993Radial flow through deformable porous shellsJournal of the Australian Mathematics Society, Series B662333354 [CrossRef]
BarrySIAldisGKMercerGN1995Injection of fluid into a layer of deformable porous mediumASME Applied Mechanics Reviews662722726 [CrossRef]
BarrySIMercerGNZoppouC1997Approximate and Analytic Solutions for Deformation of Finite Porous FiltersASME JOURNAL OF APPLIED MECHANICS662929934 [CrossRef]
BiotMA1941General theory of three dimensional consolidationJournal of Applied Physics662155164 [CrossRef]
BookerJRCarterJP1986Long term subsidence due to fluid extraction from a saturated, anisotropic, elastic soil massQuarterly Journal of Mechanics and Applied Mathematics6628597 [CrossRef]
BookerJRCarterJP1987Withdrawal of a compressible pore fluid from a point sink in an isotropic elastic half space with anisotropic permeabilityInternational Journal Solids and Structures662369385 [CrossRef]
BowenRM1980Incompressible porous media models by the theory of mixturesInternational Journal of Engineering Science66211291148 [CrossRef]
GibsonRESchiffmanRLPuSL1970Plane strain and axially symmetric consolidation of a clay layer on a smooth impervious baseQuarterly Journal of Mechanics and Applied Mathematics662505520 [CrossRef]
HeinrichGDesoyerK1961Theorie dreidimensionaler Setzungsvorgaenge in TonshichtenIngenieur-Archiv662225253 [CrossRef]
HolmesMH1983A nonlinear diffusion equation arising in the study of soft tissueQuarterly of Applied Mathematics662209220
HolmesMHLaiWMMowVC1985Singular Perturbation Analysis of the Nonlinear, Flow-dependent Compressive Stress Relaxation Behaviour of Articular CartilageASME Journal of Biomechanical Engineering662206218
JensenOEGlucksbergMRSachsJRGrotbergJB1994Weakly Nonlinear Deformation of a Thin Poroelastic Layer With a Free SurfaceASME JOURNAL OF APPLIED MECHANICS662729731 [CrossRef]
KenyonDE1976Transient Filtration in a Porous Elastic CylinderASME JOURNAL OF APPLIED MECHANICS662594598 [CrossRef]
KenyonDE1979A mathematical model of water flux through aortic tissueBulletin of Mathematical Biology6627990 [CrossRef]
KlancharMTarbellJM1987Modeling water flow through arterial tissueBulletin of Mathematical Biology662651669 [CrossRef]
LaiWMMowVC1980Drag induced compression of articular cartilage during a permeation experimentBiorheology662111123
MakAFLaiWMMowVC1987Biphasic indentation of articular cartilage: I. Theoretical analysisJournal of Biomechanics662703714 [CrossRef]
MowVCLaiWM1980Recent Developments in synovial joint biomechanicsSIAM Review662275317 [CrossRef]
ParkerKHMehtaRVCaroCG1987Steady flow in porous, elastically deformable materialsASME JOURNAL OF APPLIED MECHANICS662794800 [CrossRef]
RudnickiJW1987Plane Strain Dislocations in Linear Elastic Diffusive SolidsASME JOURNAL OF APPLIED MECHANICS662545552 [CrossRef]
SachsJRGlucksbergMRJensenOEGrotbergJB1994Linear Flow and Deformation in a Poroelastic Disk With a Free SurfaceASME JOURNAL OF APPLIED MECHANICS662726728 [CrossRef]
YangMTaberLA1991The possible role of poroelasticity in the apparent viscoelastic behaviour of passive cardiac muscleJournal of Biomechanics662587597 [CrossRef]




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In