The purpose of this brief paper is to present a new derivation of Biot's theory of linear poroelasticity (Biot, M., 1935, “Le Probleḿe de la Consolidation des Matiéres Argileuses Sous une Charge,” Ann. Soc. Sci. Bruxelles,B55, pp. 110–113; Biot, M., 1941, “General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., 12, pp. 155–164; and Biot, M., and Willis, D., 1957, “The Elastic Coefficients of the Theory of Consolidation,” J. Appl. Mech., 24, pp. 594–601) in a modern thermodynamically consistent fashion, and show that it may be deduced as a special case of a more general theory of chemoelasticity.
Issue Section:
Research Papers
References
1.
Biot
, M.
, 1935
, “Le Probleḿe de la Consolidation des Matiéres Argileuses Sous une Charge
,” Ann. Soc. Sci. Bruxelles
, B55
, pp. 110
–113
.2.
Biot
, M.
, 1941
, “General Theory of Three-Dimensional Consolidation
,” J. Appl. Phys.
, 12
(2), pp. 155
–164
.3.
Biot
, M.
, and Willis
, D.
, 1957
, “The Elastic Coefficients of the Theory of Consolidation
,” ASME J. Appl. Mech.
, 24
, pp. 594
–601
.4.
Lehner
, F.
, 2011
, “The Linear Theory of Anisotropic Poroelastic Solids
,” Mechanics of Crustal Rocks
(CISM Courses and Lectures, Vol. 533
), Y.
Leroy
and F.
Lehner
, eds., Springer
, New York
, pp. 1
–41
.5.
Rice
, J.
, and Cleary
, M.
, 1976
, “Some Basic Stress Diffusion Solutions for Fluid Saturated Elastic Porous Media With Compressible Constituents
,” Rev. Geophys. Space Phys.
, 14
(2), pp. 227
–241
.6.
Detournay
, E.
, and Cheng
, A. H.-D.
, 1993
, “Fundamentals of Poroelasticity
,” Comprehensive Rock Engineering: Principles Practices and Projects
, J.
Hudson
and C.
Fairhurst
, eds., Pergamon Press
, Elmsford, NY, pp. 113
–171
.7.
Wang
, H.
, 2000
, Theory of Linear Poroelasticity With Applications to Geomechanics and Hydrogeology
, Princeton University Press
, Princeton
, NJ
.8.
Rudnicki
, J.
, 2001
, “Coupled Deformation–Diffusion Effects in the Mechanics of Faulting and Geomaterials
,” ASME Appl. Mech. Rev.
, 54
(6), pp. 483
–502
.9.
Guéguen
, Y.
, Dormieux
, L.
, and Boutéca
, M.
, 2004
, “Fundamentals of Poromechanics
,” Mechanics of Fluid-Saturated Porous Materials
(International Geophysics Series, Vol. 89
), Y.
Guéguen
and M.
Boutéca
, eds., Elsevier Academic Press
, Burlington
, MA
.10.
Cowin
, S.
, 1999
, “Bone Poroelasticity
,” J. Biomech.
, 32
(3), pp. 217
–302
.11.
Bowen
, R.
, 1969
, “Thermochemistry of a Reacting Mixture of Elastic Materials With Diffusion
,” Arch. Ration. Mech. Anal.
, 34
(2), pp. 97
–217
.12.
Coussy
, O.
, 1995
, Mechanics of Porous Media
, Wiley
, Chichester, UK
.13.
Gibbs
, J.
, 1878
, “On the Equilibrium of Heterogeneous Substances
,” Transactions of the Connecticut Academy of Arts and Sciences
, Vol. III
, Connecticut Academy of Arts and Sciences, New Haven, CT, pp. 108
–248
.14.
Biot
, M.
, 1972
, “Theory of Finite Deformation of Porous Solids
,” Indiana Univ. Math. J.
, 21
(7), pp. 597
–620
.15.
Biot
, M.
, 1973
, “Nonlinear and Semilinear Rheology of Porous Solids
,” J. Geophys. Res.
, 78
(23), pp. 4924
–4937
.16.
Gurtin
, M.
, Fried
, E.
, and Anand
, L.
, 2010
, The Mechanics and Thermodynamics of Continua
, Cambridge University Press
, Cambridge, UK
.17.
Hong
, W.
, Zhao
, X.
, Zhou
, J.
, and Suo
, Z.
, 2008
, “A Theory of Coupled Diffusion and Large Deformation in Polymeric Gel
,” J. Mech. Phys. Solids
, 56
(5), pp. 1779
–1793
.18.
Duda
, F.
, Souza
, A.
, and Fried
, E.
, 2010
, “A Theory for Species Migration in Finitely Strained Solid With Application to Polymer Network Swelling
,” J. Mech. Phys. Solids
, 58
(4), pp. 515
–529
.19.
Chester
, S.
, and Anand
, L.
, 2010
, “A Coupled Theory of Fluid Permeation and Large Deformations for Elastomeric Materials
,” J. Mech. Phys. Solids
, 58
(11), pp. 1879
–1906
.20.
Chester
, S.
, and Anand
, L.
, 2011
, “A Thermo-Mechanically Coupled Theory for Fluid Permeation in Elastomeric Materials: Application to Thermally Responsive Gels
,” J. Mech. Phys. Solids
, 59
(10
), pp. 1978
–2006
.21.
Chester
, S.
, Di Leo
, C.
, and Anand
, L.
, 2015
, “A Finite Element Implementation of a Coupled Diffusion–Deformation Theory for Elastomeric Gels
,” Int. J. Solids Struct.
, 52
, pp. 1
–18
.22.
Fick
, A.
, 1855
, “Über Diffusion
,” Poggendorff's Ann. Phys. Chem.
, 94
, pp. 59
–86
.23.
Terzaghi
, K.
, and Froölicj
, O.
, 1936
, Theories der Setzung von Tonschicheten
, Franz Deuticke
, Leipzig, Wien, Austria
.24.
Darcy
, H.
, 1856
, Les Fontaines de la Ville de Dijon
, Victor Dalmont
, Paris
.Copyright © 2015 by ASME
You do not currently have access to this content.
