0
Research Papers

2014 Drucker Medal Paper: A Derivation of the Theory of Linear Poroelasticity From Chemoelasticity

[+] Author and Article Information
Lallit Anand

Professor
Fellow ASME
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: anand@mit.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 21, 2015; final manuscript received July 3, 2015; published online August 20, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(11), 111005 (Aug 20, 2015) (11 pages) Paper No: JAM-15-1334; doi: 10.1115/1.4031049 History: Received June 21, 2015

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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

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(2), pp. 155–164. [CrossRef]
Biot, M. , and Willis, D. , 1957, “The Elastic Coefficients of the Theory of Consolidation,” ASME J. Appl. Mech., 24, pp. 594–601.
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.
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. [CrossRef]
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.
Wang, H. , 2000, Theory of Linear Poroelasticity With Applications to Geomechanics and Hydrogeology, Princeton University Press, Princeton, NJ.
Rudnicki, J. , 2001, “Coupled Deformation–Diffusion Effects in the Mechanics of Faulting and Geomaterials,” ASME Appl. Mech. Rev., 54(6), pp. 483–502. [CrossRef]
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.
Cowin, S. , 1999, “Bone Poroelasticity,” J. Biomech., 32(3), pp. 217–302. [CrossRef] [PubMed]
Bowen, R. , 1969, “Thermochemistry of a Reacting Mixture of Elastic Materials With Diffusion,” Arch. Ration. Mech. Anal., 34(2), pp. 97–217. [CrossRef]
Coussy, O. , 1995, Mechanics of Porous Media, Wiley, Chichester, UK.
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.
Biot, M. , 1972, “Theory of Finite Deformation of Porous Solids,” Indiana Univ. Math. J., 21(7), pp. 597–620. [CrossRef]
Biot, M. , 1973, “Nonlinear and Semilinear Rheology of Porous Solids,” J. Geophys. Res., 78(23), pp. 4924–4937. [CrossRef]
Gurtin, M. , Fried, E. , and Anand, L. , 2010, The Mechanics and Thermodynamics of Continua, Cambridge University Press, Cambridge, UK.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Fick, A. , 1855, “Über Diffusion,” Poggendorff's Ann. Phys. Chem., 94, pp. 59–86. [CrossRef]
Terzaghi, K. , and Froölicj, O. , 1936, Theories der Setzung von Tonschicheten, Franz Deuticke, Leipzig, Wien, Austria.
Darcy, H. , 1856, Les Fontaines de la Ville de Dijon, Victor Dalmont, Paris.

Figures

Tables

Errata

Discussions

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