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.

References

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
.
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