Tortuosity and objective relative accelerations in the theory of porous materials

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 461, Issue 2057, 2005, Pages 1533-1561

  Wilmanski, Krzysztof ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Added mass; Material objectivity; Poroelastic materials; Tortuosity

Indexed keywords

EID: 26944501609     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2004.1423     Document Type: Article

References (23)

1. Allard, J. F. 1993 Propagation of sound in porous media: Modelling sound absorbing materials. Essex: Elsevier.
2. Berryman, J. G. 1980 Confirmation of Biot's theory. Appl. Phys. Lett. 37, 382-384.
3. Biot, M. A. 1956 Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. JASA 28, 168-178.
4. Bourbie, T., Coussy, O. & Zinszner, B. 1987 Acoustics of porous media. Paris: Technip.
5. Coussy, O. 1991 Mécanique des Milieux Poreux. Paris: Technip.
6. Drew, D., Cheng, L. & Lahey, R. T., Jr 1979 The analysis of virtual mass effects in two-phase flow. Int. J. Multiphase Flow 5, 233-242.
7. Frenkel, Y. 1944 On the theory of seismic and seismoelectric phenomena in moist soils. J. Phys. 8(4), 230-241.
8. Johnson, D. L., Koplik, J. & Dashen, R. 1987 Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mech. 176, 379-402.
9. Kirchner, N. P. 2002 Thermodynamically consistent modelling of abrasive granular materials. Part I: nonequilibrium Theory. Proc. R. Soc. A 458, 2153-2176.
10. Kosinski, W., Kubik, J. & Hutter, K. 2002 On the added mass effect for porous media. Arch. Mech. 54(5-6), 479-495.
11. Liu, I.-S. 2002 Continuum mechanics. Berlin: Springer.
12. Müller, I. 1985 Thermodynamics. Boston: Pitman.
13. Stoll, R. D. 1989 Sediment acoustics Lecture notes in earth sciences, vol. 26. New York: Springer.
14. Tisza, L. 1938 Transport phenomena in He II. Nature 141, 913.
15. Tolstoy, I. 1991 Acoustics, elasticity and thermodynamics of porous media: twenty-one papers by M.A. Biot, Acoustical Society of America.
16. Wilmanski, K. 1998 A thermodynamic model of compressible porous materials with the balance equation of porosity. Transport Porous Media 32, 21-47.
17. Wilmanski, K. 1998 Thermomechanics of continua. Berlin: Springer.
18. Wilmanski, K. 1999 Waves in porous and granular materials. Kinetic and continuum theories of granular and porous media (ed. K. Hutter & K. Wilmanski), pp. 131-186. Vienna: Springer.
19. Wilmanski, K. 2001 Some questions on material objectivity arising in models of porous materials. Rational continua, classical and new (ed. P. Podio-Guidugli & M. Brocato), pp. 149-161. Milan: Springer.
20. Wilmanski, K. 2002 Thermodynamical admissibility of Biot's model of poroelastic saturated materials. Arch. Mech. 54(5-6), 709-736.
21. Wilmanski K. 2004a On a micro-macro transition for poroelastic Biot's model and corresponding Gassmann-type relations. Géotechnique 54(9), 593-603.
22. Wilmanski, K. 2004b Thermodynamics of simple two-component thermo-poroelastic media, WIAS-Preprint #901. In Recent trends in the applications of mathematics to mechanics (ed. G. Romano & S. Rionero), STAMM 2002. Milan: Springer.
23. Wilmanski, K. & Albers, B. 2003 Acoustic waves in porous solid-fluid mixtures. In Dynamic response of granular and porous materials under large and catastrophic deformations (ed. K. Hutter & N. Kirchner). Lecture Notes in Applied and Computational Mechanics, vol. 11, pp. 285-314. Berlin: Springer.