Abstract
The behaviour of porous media can be described in a continuum mechanical setting by the Theory of Porous Media, i. e. by a mixture theory extended by the concept of volume fractions. In addition to the volume fractions, micropolarity is taken into account to model the internal structure of porous media on the macroscopic scale. After a microscopic motivation of the approach, which shows that it is physically motivated to deal with micropolar mixture models, the kinematics, the balance relations, and the constitutive framing of such a theory are discussed. A set of model equations is formulated within the presented frame and applied to some boundary value problems showing the evidence of the theoretical approach.
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References
Bauer, G.: Thermodynamische Betrachtung einer gesättigten Mischung. Dissertation, Technische Hochschule Darmstadt 1997.
Bluhm, J.: A consistent model for saturated and empty porous media. Forschungsberichte aus dem Fachbereich Bauwesen, 74, Universität-GH-Essen 1997.
Bluhm, J., de Boer, R.: Effective stress — a clarification. Arch. Appl. Mech. 66 (1996), 479–492.
de Boer, R.: Theory of porous media — highlights in the historical development and current state. Springer-Verlag, Berlin 2000.
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. Engng. Sci. 18 (1980), 1129–1148.
Coleman, B. D., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rat. Mech. Anal. 13 (1963), 167–178.
Cundall, P. A, Strack, O. D. L.: A discrete numerical model for granular assemblies. Géotechnique 29 (1979), 47–65.
Diebels, S.: A micropolar theory of porous media: Constitutive modelling. Transport in Porous Media 34 (1999), 193–208.
Diebels, S.: Mikropolare Zweiphasenmodelle: Formulierung auf der Basis der Theorie Poröser Medien. Habilitationsschrift, Bericht Nr. II-4, Institut für Mechanik (Bauwesen), Lehrstuhl II, Universität Stuttgart 2000.
Diebels, S., Ehlers, W.: On basic equations of multiphase micropolar materials. Technische Mechanik 16 (1996), 77–88.
Diebels, S., Ehlers, W., Michelitsch, T.: Particle simulations as a microscopic approach to a Cosserat continuum. J. Phys. IV France (2001), submitted.
Ehlers, W.: Poröse Medien — ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsberichte aus dem Fachbereich Bauwesen, 47, Universität-GH-Essen 1988.
Ehlers, W.: Compressible, incompressible and hybrid two-phase models in porous media theories. In Angel, Y. C. (ed.): Anisotropy and Inhomogeneity in Elasticity and Plasticity, AMD-Vol. 158, ASME 1993, pp. 25–38.
Ehlers, W.: Constitutive equations for granular materials in geomechanical context. In Hutter, K. (ed.): Continuum mechanics in environmental sciences and geophysics, CISM Courses and Lectures No. 337, Springer-Verlag, Wien 1993, pp. 313–402.
Ehlers, W., Diebels, S., Michelitsch, T.: Microscopic modeling of granular materials taking into account particle rotations. In Vermeer, P. A. et al. (eds.): Continuous and discontinuous modelling of cohesive frictional materials, Springer-Verlag, Berlin 2001, pp. 259–274.
Ehlers, W., Ellsiepen, P.: Theoretical and numerical methods in environmental continuum mechanics based on the theorie of porous media. In Schrefler, B. A. (ed.): Environmental mechanics, CISM Courses and Lectures No. 417, Springer-Verlag, Wien 2001.
Eipper, G.: Theorie und Numerik finiter elastischer Deformationen in fluidgesättigten porösen Festkörpern. Dissertation, Bericht Nr. II-1, Institut für Mechanik (Bauwesen), Lehrstuhl II, Universität Stuttgart 1998.
Ellsiepen, P. (ed.): PANDAS — Benutzer- und Referenzhandbuch. Bericht Nr. 97-II-9, Institut für Mechanik (Bauwesen), Lehrstuhl II, Universität Stuttgart 1997.
Eringen, A. C.: Simple microfluids. Int. J. Engng. Sci. 2 (1964), 205–217.
Eringen, A. C., Kafadar, C. B.: Polar field theories. In Eringen, A. C. (ed.): Continuum Physics, Vol IV — Polar and nonlocal field theories, Academic Press, New York 1976, pp. 1–73.
Gibson, L. J., Ashby, M. F.: Cellular solids — structure and properties. 2nd ed., Cambridge University Press, Cambridge 1997.
Hassanizadeh, S. M., Gray, W. G.: General conservation equations for multiphase systems: 2. Mass, momentena, energy, and entropy equations. Advances in Water Resources 2 (1979), 191–208.
Hutter, K.: The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics. Acta Mech. 27 (1977), 1–54.
Lade, P., de Boer, R.: The concept of effective stress for soil, concrete and rock. Géotechnique 47 (1997), 61–78.
Lewis, R. W., Schrefier, B. A.: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. 2nd ed., John Wiley Sons, Chichester 1998.
Liu, I-S.: Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rat. Mech. Anal. 46 (1972), 131–148.
Liu, I-S., Müller, I.: Thermodynamics of mixtures of fluids. In Truesdell, C. (ed.): Rational Thermodynamics, 2nd ed., Springer-Verlag, New York 1984, pp. 264–285.
Müller, I.: Thermodynamik — Grundlagen der Materialtheorie. Bertelsmann Universitätsverlag, Düsseldorf 1973.
Onck, P. O.: Notch-strengthening in two-dimensional foams. J. Phys IV France (2001), submitted.
Simio, J. C., Taylor, R. L.: Penalty function formulations for incompressible nonlinear elastostatics. Comp. Meth. Appl. Mech. Engng. 35 (1982), 107–118.
Steinmann, P.: Lokalisierungsprobleme in der Plasto-Mechanik. Dissertation, Universität Karlsruhe 1992.
Steinmann, P.: A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity. Int. J. Solids Struct. 31 (1994), 1063–1084.
Suklje, L.: Rheological Aspects of Soil Mechanics. Wiley Interscience, London 1969.
Svendsen, B., Hutter, K.: On the thermodynamics of a mixture of isotropic materials with constraints. Int. J. Engng. Sci. 33 (1995), 2021–2054.
von Terzaghi, K.: Zur Berechnung der Durchlässigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen. Sitzungsber. Akad. Wiss. Wien 132 (1923), 125–138.
Truesdell, C.: Thermodynamics of diffusion. In Truesdell, C. (ed.): Rational Thermodynamics, 2nd ed., Springer-Verlag, New York 1984, pp. 219–236.
Truesdell, C., Toupin, R. A.: The classical field theories. In Flügge, S. (ed.): Handbuch der Physik, III/1, Springer-Verlag, Berlin 1960, pp. 226–793.
Volk, W.: Untersuchung des Lokalisierungsverhaltens mikropolarer poröser Medien. Dissertation, Bericht Nr. II-2, Institut für Mechanik (Bauwesen), Lehrstuhl II, Universität Stuttgart 1999.
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Diebels, S. (2002). Micropolar mixture models on the basis of the Theory of Porous Media. In: Ehlers, W., Bluhm, J. (eds) Porous Media. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04999-0_3
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DOI: https://doi.org/10.1007/978-3-662-04999-0_3
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