Abstract
The extension of the classical mixture theory by the concept of volume fractions leads to the theory of porous media. In this article, the theory of porous media is generalised to micropolar constituents. The kinematic relations and the balance equations for a porous medium are developed without restricting the number of constituents. Based on the entropy inequality, the general form of the constitutive equations are derived for a binary medium consisting of a porous elastic skeleton saturated by a viscous pore-fluid. Both constituents are assumed to be compressible. Handling the saturation constraint by a Lagrangian multiplier leads to a compatibility of the proposed model to so-called hybrid and incompressible models.
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References
Besdo, D.: 1974, Ein Beitrag zur nichtlinearen Theorie des Cosserat-Kontinuums, Acta Mech. 20, 105–131.
de Boer, R.: 1982, Vektor-und Tensorrechnung fiir Ingenieure, Springer-Verlag, Berlin
de Boer, R. and Ehlers, W.: 1986, Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Problemi, Forschungsberichte aus dem Fachbereich Bauwesen 40, Universität-GH-Essen, Essen.
de Borst, R.: 1991, Numerical modelling of bifurcation and localisation in cohesive-frictional materials, Pageoph. 137, 368–390.
Bowen, R. M.: 1976, Theory of mixtures, In: A. C. Eringen (ed.), Continuum Physics III, Academic Press, New York, pp. 1–127.
Bowen, R. M.: 1980, Incompressible porous media models by use of the theory of mixtures, Int. J. Engng.Sci. 18, 1129–1148.
Bowen, R. M.: 1982, Compressible porous media models by use of the theory of mixtures, Int. J. Engng. Sci. 20, 697–735.
Coleman, B. C. and Noll, W.: 1963, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rat. Mech. Anal. 13, 167–178.
Cosserat, E. and Cosserat, F.: 1909, Théorie des Corps Déformable, A. Herman, Paris.
Diebels, S.: 1997, Materialtheorie für granuläre Materialien, ZAMM (submitted).
Diebels, S. and Ehlers, W.: 1996, On basic equations of multiphase micropolar materials, Technische Mechanik 16, 77–88.
Dietsche, A., Steinmann, P. and Willam, K.: 1993, Micropolar elasticity and its role in localization, Int. J. Plast. 9, 813–831.
Ehlers, W.: 1989, Poröse Medien — ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie, Forschungsberichte aus dem Fachbereich Bauwesen 47, Universität-GH-Essen, Essen.
Ehlers, W.: 1993, Constitutive equations for granular materials in geomechanical context, In: K. Hutter (ed.), Continuum Mechanics in Environmental Sciences and Geophysics, CISM Courses and Lecture Notes No. 337, Springer-Verlag, Wien, pp. 313–402.
Ehlers, W.: 1996, Grundlegende Konzepte in der Theorie Poröser Medien, Technische Mechanik 16, 63–76.
Eringen, A. C.: 1964, Simple microfluids, Int. J. Engng. Sci. 3, 205–217.
Eringen, A. C. and Kafadar, C. B.: 1976, Polar field theories, In: A. C. Eringen (ed.), Continuum Physics TV, Academic Press, New York, pp. 1–73.
Haupt, P.: 1993, Foundations of continuum mechanics, In: K. Hutter (ed.), Continuum Mechanics in Environmental Sciences and Geophysics, CISM Courses and Lecture Notes No. 337, Springer-Verlag, Wien, pp. 1–77.
Hemmingsson, J., Herrmann, H. J. and Roux, S.: 1996, Vectorial cellular automaton for the stress in granular media, J. de Physique (submitted).
Lade, P. V. and de Boer, R.: 1997, The concept of effective stress for soil, concrete, and rock, Geotechnique 47, 61–78.
Svendsen, B. and Hutter, K.: 1995, On the thermodynamics of a mixture of isotropic materials with constraints, Int. J. Engng. Sci. 33, 2021–2054.
Tejchmann, J. and Wu, W.: 1993, Numerical study on patterning of shear bands in a Cosserat continuum, Acta Mech. 99, 61–74.
Truesdell, C.: 1984, Rational Thermodynamics, Springer-Verlag, New York, p. 221.
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Diebels, S. (1999). A Micropolar Theory of Porous Media: Constitutive Modelling. In: De Boer, R. (eds) Porous Media: Theory and Experiments. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4579-4_12
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DOI: https://doi.org/10.1007/978-94-011-4579-4_12
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