Abstract
Based on the Theory of Porous Media (TPM), a binary model for the description of saturated thermo-elastic porous solids with different phase temperatures will be presented. The constituents solid and fluid can be compressible or incompressible, i. e. the binary model discussed here includes the compressible model, the hybrid models of first and second type and the incompressible model. For the four different binary models the field equations, the constitutive relations and the dissipation mechanism will be developed and discussed.
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References
Beatty, M. F.: Topics in finite elasticity: Hyperelasticty of rubber, elastomers, and biological tissues–with examples. Appl. Mech. Rev. 40 (1987), 1699–1734.
Biot, M. A., Willis, D. G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24 (1957), 594–601.
Bluhm, J.: A consistent model for saturated and empty porous media. Forschungsberichte aus dem Fachbereich Bauwesen 74, Universität-GH Essen 1997.
de Boer, R.: Theory of porous media - highlights in the historical development and current state. Springer-Verlag, Berlin 2000.
de Boer, R., Bluhm, J.: The influence of compressibility on the stresses of elastic porous solids–semimicroscopic investigations. Int. J. Solids Structures 36 (1999), 4805–4819.
de Boer, R., Didwania, A. K.: The effect of uplift in liquid-saturated porous solids–Karl von Terzaghi’s contributions and recent findings. Géotechnique 47 (2) (1997), 289–298.
de Boer, R., Ehlers, W.: Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme, Teil I. Forschungsberichte aus dem Fachbereich Bauwesen 40, Universität-GH Essen 1986.
Bowen, R. M.: Incompressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 18 (1980), 1129–1148.
Bowen, R. M.: Compressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 20 (1982), 697–735.
Bowen, R. M., Wiese, J. C.: Diffusion in mixtures of elastic materials. Int. J. Eng. Sci. 7 (1969), 689–722.
Coleman, B. D., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13 (1963), 167–178.
Ehlers, W.: Poröse Medien - ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsberichte aus dem Fachbereich Bauwesen 47, Universität-GH Essen 1988.
Ehlers, W.: On the thermodynamics of elasto-plastic porous media. Arch. Mech. 41 (1989), 73–93.
Ehlers, W.: Constitutive equations for granular materials in geomechanical contexts. In Hutter, H. (ed.): Continuum mechanics in environmental sciences and geophysics, CISM Courses and Lecture Notes No. 337, Springer-Verlag, Wien 1993, 313–402.
Green, A. E., Naghdi, P. M.: A dynamical theory of interacting continua. Int. J. Engng. Sci. 3 (1965), 231–241.
Lade, P. V., de Boer, R.: The concept of effective stress for soil, concrete and rock. Géotechnique 47 (1) (1997), 61–78.
Miehe, C.: Zur numerischen Behandlung thermomechanischer Prozesse. Forschungs-und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover, Bericht-Nr. F88/6, Universität Hannover 1988.
Müller, I.: A thermodynamic theory of mixtures of fluids. Arch. Rational Mech. Anal. 28 (1968), 1–39.
Nur, A., Byerlee, J. D.: An exact effective stress law for elastic deformation of rock with fluids. J. Geophys. Res. 76 (1971), 6414–6419.
Simo, J. C., Pister, K. S.: Remarks on rate constitutive equations for finite deformation problems: Computational implications. Comput. Meth. Appl. Mech. Eng. 46 (1984), 201–215.
Suklje, L.: Rheological aspects of soil mechanics. Wiley Interscience, New York 1969.
von Terzaghi, K.: The shearing resistance of saturated soils and the angle between the planes of shear. In Casagrande, A. et al. (eds.): Proceedings of the Internationale Conference on Soil Mechanics and Foundation Engineering, Vol. I, Harvard University 1936, pp. 54–56.
Truesdell, C.: Rational thermodynamics. 2nd. ed., Springer-Verlag, New York 1984.
Truesdell, C., Toupin, R. A.: The classical field theories. In Flügge, S. (ed.): Handbuch der Physik, Band III/1, Springer-Verlag, Berlin 1960.
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Bluhm, J. (2002). Modelling of saturated thermo-elastic porous solids with different phase temperatures. In: Ehlers, W., Bluhm, J. (eds) Porous Media. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04999-0_2
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DOI: https://doi.org/10.1007/978-3-662-04999-0_2
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