Abstract
The theme of this chapter is contained in a quote from the 1941 paper of M.A. Biot that clearly describes an RVE: “Consider a small cubic element of soil, its sides being parallel with the coordinate axes. This element is taken to be large enough compared to the size of the pores so that it may be treated as homogeneous, and at the same time small enough, compared to the scale of the macroscopic phenomena in which we are interested, so that it may be considered as infinitesimal in the mathematical treatment.”
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References
Armstrong GC, Lai WM, Mow VC. 1984. An analysis of the unconfined compression of articular cartilage. J Biomech Eng 106:165–173.
Bear J. 1972. Dynamics of fluids in porous media. New York: Elsevier.
Biot MA. 1941. General theory of three-dimensional consolidation. J Appl Phys 12:155–164.
Carroll MM. 1979. An effective stress law for anisotropic elastic deformation. J Geophys Res 84:7510–7512.
Cohen, B, Lai, WM, Mow VC. 1998. A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis. J Biomech Eng 120:491–496.
Coussy O. 1995. Mechanics of porous continua. New York: Wiley.
Cowin SC. 2003. A recasting of anisotropic poroelasticity in matrices of tensor components. Transport Porous Media 50:35–56.
Cowin SC. 2004. Anisotropic poroelasticity: fabric tensor formulation. Mech Mater 36:665–677.
Cowin SC, Mehrabadi MM. 2006. Compressible and incompressible constituents in anisotropic poroelasticity: the problem of unconfined compression of a disk. J Mech Phys Solids. In press.
de Boer R. 2000. Theory of porous media. Berlin: Springer.
Detournay E, Cheng H-DA. 1993. Fundamentals of poroelasticity. In Comprehensive rock engineering: principles, practice and projects. ed. JA Hudson, pp. 113–171. Oxford: Pergamon.
Geertsma J. 1957. The effect of fluid pressure decline on volumetric changes of porous rocks. J Appl Mech 24:594–601.
Kachanov M. 1999. Solids with cracks and non-spherical pores: proper parameters of defect density and effective elastic properties. Int J Fracture 97:1–32.
Nur A, Byerlee JD. 1971. An exact effective stress law for elastic deformation of rock with fluids. J Geophys Res 76:6414.
Rice JR, Cleary MP. 1976. Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev Geophys Space Phys 14:227–241.
Rudnicki JW. 1985. Effect of pore fluid diffusion on deformation and failure of rock. In Mechanics of geomaterials, ed. Z Bazant, pp. 315–347. New York: Wiley.
Shafiro B, Kachanov M. 1997. Materials with fluid filled pores of various shapes: effective elastic properties and fluid pressure polarization. Int J Solids Struct 34:3517–3540.
Skempton AW. 1954. The pore pressure coefficients A and B. Géotechnique 4:143–147.
Skempton AW. 1961. Effective stress in soils, concrete and rock. In Pore pressure and suction in soils, pp. 4–16. Butterworths, London.
Sevostianov I, Kachanov M. 2001. Author’s response. J Biomech 34:709–710.
Thompson M, Willis JR. 1991. A reformation of the equations of anisotropic poroelasticity. J Appl Mech 58:612–616.
Thomson WT. 1960. Laplace transformation, 2nd ed. Engelwood Cliffs, NJ Prentice-Hall.
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(2007). Poroelasticity. In: Cowin, S.C., Doty, S.B. (eds) Tissue Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49985-7_9
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