Mixture Theory-Based Poroelasticity and the Second Law of Thermodynamics

  • Stephen C. Cowin
Chapter

Abstract

The decisive word in this postulate is the quantifier all it makes the postulate a restrictive condition on the internal constitutive assumptions that can be imposed on systems of the type under consideration.

Keywords

Entropy Porosity Biot Incompressibility Summing 

References

  1. Atkin RJ, Craine RE (1976a) Continuum theories of mixtures: basic theory and historical development. Q J Mech Appl Math XXIX:209–244MathSciNetCrossRefGoogle Scholar
  2. Atkin RJ, Craine RE (1976b) Continuum theories of mixtures: applications. J Inst Math Appl 17:153–207MathSciNetCrossRefMATHGoogle Scholar
  3. Biot MA (1935) Le problème de la consolidation des matières argileuses sous une charge. Ann Soc Sci Bruxelles B55:110–113Google Scholar
  4. Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:155–164CrossRefMATHGoogle Scholar
  5. 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
  6. 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
  7. Biot MA, Willis DG (1957) The elastic coefficients of the theory of consolidation. J Appl Mech 24:594–601MathSciNetGoogle Scholar
  8. Biot MA (1962) Generalized theory of acoustic propagation in porous dissipative media. J Acoust Soc Am 34:1254–1264MathSciNetCrossRefGoogle Scholar
  9. Biot MA (1972) Theory of finite deformation of porous solids. Indiana Univ Math J 21:597–620MathSciNetCrossRefGoogle Scholar
  10. Biot MA (1982) Generalized Lagrangian equations of non-linear reaction-diffusion. Chem Phys 66:11–26MathSciNetCrossRefGoogle Scholar
  11. Bowen RM (1967) Toward a thermodynamics and mechanics of mixtures. Arch Rat Mech Anal 24:370–403MathSciNetCrossRefMATHGoogle Scholar
  12. Bowen RM (1976) Mixtures and EM Field Theories. In: Eringen A.C. (ed) Continum Physics, Vol 3. Academic Press, New YorkGoogle Scholar
  13. Bowen RM (1980) Incompressible porous media models by use of the theory of mixtures. Int J Eng Sci 18:1129–1148CrossRefMATHGoogle Scholar
  14. Bowen RM (1982) Compressible porous media models by use of the theory of mixtures. Int J Eng Sci 20:697–735CrossRefMATHGoogle Scholar
  15. Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction. Arch Ration Mech Anal 13:167–178MathSciNetCrossRefMATHGoogle Scholar
  16. Cowin SC, Cardoso L. (2012) Mixture theory-based poroelasticity as a model of interstitial tissue growth, Mech Mat 44:47–57Google Scholar
  17. De Boer R (1996) Highlights in the historical development of the porous media theory: toward a consistent macroscopic theory. Appl Mech Rev 49:201–262CrossRefGoogle Scholar
  18. De Boer R (2000) Theory of porous media: highlights in the historical development and current state. Springer Verlag, BerlinMATHGoogle Scholar
  19. Goodman MA, Cowin SC (1972) A continuum theory for granular materials. Arch Ration Mech Anal 44:249–266MathSciNetCrossRefMATHGoogle Scholar
  20. Noll W (2009) Thoughts on thermodynamics. 8th International Congress on thermal stressesGoogle Scholar
  21. Truesdell CA (1957) Sulle basi della termomeccania. Rend Lincei 22(33–38):1158–1166MathSciNetGoogle 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

Personalised recommendations