Dynamic Poroelasticity

  • Stephen C. Cowin
Chapter

Abstract

The modern theory of the motion of the water in the soil based on Darcy’s law does not take into account the fact that the particles of the soil can be elastically compressed and extended, assuming that the external forces and the hydrostatic pressure act on the liquid filling these pores only. This simplifying assumption necessitates a correction even in the case of problems on the steady flow of soil water under the influence of given external forces.

Keywords

Permeability Porosity Anisotropy Crest Biot 

References

  1. Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:155–164CrossRefMATHGoogle Scholar
  2. Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182–185MathSciNetCrossRefMATHGoogle Scholar
  3. Biot MA (1956a) Theory of propagation of elastic waves in a fluid saturated porous solid I low frequency range. J Acoust Soc Am 28:168–178MathSciNetCrossRefGoogle Scholar
  4. Biot MA (1956b) Theory of propagation of elastic waves in a fluid saturated porous solid II higher frequency range. J Acoust Soc Am 28:179–191MathSciNetCrossRefGoogle Scholar
  5. Biot MA (1962a) Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33:1482–1498MathSciNetCrossRefMATHGoogle Scholar
  6. Biot MA (1962b) Generalized theory of acoustic propagation in porous dissipative media. J Acoust Soc Am 28:1254–1264MathSciNetCrossRefGoogle Scholar
  7. Cardoso L, Cowin SC (2011) Fabric dependence of quasi-waves in anisotropic porous media. J Acoust Soc Am 129(5):3302–3316CrossRefGoogle Scholar
  8. Cardoso L, Cowin SC (2012) Role of the structural anisotropy of biological tissues on poroelastic wave propagation. Mech Mater 44:174–188CrossRefGoogle Scholar
  9. Cardoso L, Teboul F, Sedel L, Meunier A, Oddou C (2003) In vitro acoustic waves propagation in human and bovine cancellous bone. J Bone Miner Res 18(10):1803–1812CrossRefGoogle Scholar
  10. Cardoso L, Meunier A, Oddou C (2008) In vitro acoustic wave propagation in human and bovine cancellous bone as predicted by the Biot’s theory. J Mech Med Biol 8(2):1–19CrossRefGoogle Scholar
  11. Cowin SC (1985) The relationship between the elasticity tensor and the fabric tensor. Mechanics of Materials 4: 137–47.CrossRefGoogle Scholar
  12. Cowin SC (2003) A recasting of anisotropic poroelasticity in matrices of tensor components. Trans Porous Med 50:35–56MathSciNetCrossRefGoogle Scholar
  13. Cowin SC (2004) Anisotropic poroelasticity: fabric tensor formulation. Mech Mater 36:665–677CrossRefGoogle Scholar
  14. Cowin S, Cardoso L (2011) Fabric dependence of poroelastic wave propagation in anisotropic porous media. Biomech Model Mechanobiol 10:39–65CrossRefGoogle Scholar
  15. Frenkel J (1944) On the theory of seismic and seismo-electric phenomena in moist soils. J Phys USSR 8:230–241MathSciNetGoogle Scholar
  16. Plona TJ, Johnson DL (1983) Acoustic properties of porous systems: I. phenomenological description. In: Johnson DL, Sen PN (eds) Physics and chemistry of porous media. AIP Conference Proceedings No. 107, pp 89–104Google Scholar
  17. Sharma MD (2005) Propagation of inhomogeneous plane waves in dissipative anisotropic poroelastic solids. Geophys J Int 163:981–990CrossRefGoogle Scholar
  18. Sharma MD (2008) Propagation of harmonic plane waves in a general anisotropic porous solid. Geophys J Int 172:982–994CrossRefGoogle Scholar
  19. Yang G, Kabel J, van Rietbergen B, Odgaard A, Huiskes R, Cowin SC (1999) The anisotropic Hooke’s law for cancellous bone and wood. J Elast 53:125–146.CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Stephen C. Cowin
    • 1
  1. 1.Department of Biomedical EngineeringThe City CollegeNew YorkUSA

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