Abstract
Miscible multi-component materials like classical mixtures as well as immiscible materials like saturated and partially saturated porous media can be successfully described on the common basis of the well-founded Theory of Mixtures (TM) or the Theory of Porous Media (TPM). In particular, both the TM and the TPM provide an excellent framework for a macroscopic description of a broad variety of applications ranging, for example, from standard and sophisticated problems in geomechanics via biomechanical applications to electro-chemically active polymers and gels, etc. The present article portrays general multiphasic and multi-component materials, thus reflecting their mechanical and their thermodynamical framework, while furthermore adding electro-chemical effects. Including some constitutive models and illustrative numerical examples, the article can be understood as a reference to theoretical and numerical investigations in the broad field of porous media models.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Acartürk A., Simulation of Charged Hydrated Porous Materials. Dissertation, Report No. II-18 of the Institute of Applied Mechanics (CE), University of Stuttgart (2009)
Bishop A.W., The effective stress principle. Teknisk Ukeblad, 39, 859–863 (1959)
de Boer R., Highlights in the historical development of porous media theory: Toward a consistent macroscopic theory. Applied Mechanics Review, 49, 201–262 (1996)
de Boer R., Theory of Porous Media, Springer, Berlin (2000)
de Boer R. and Ehlers W., Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme. Forschungsberichte aus dem Fachbereich Bauwesen 40, Universität Essen (1986)
de Boer R. and Ehlers W., Uplift, friction and capillarity — three fundamental effects for liquid-saturated porous media, International Journal of Solids Structures, 26, 43–57 (1990)
de Boer R. and Ehlers W., The development of the concept of effective stresses, Acta Mechanica, 83, 77–92 (1990)
Borja R., Bifurcation of elastoplastic solids to shear band mode at finite strain, Computer Methods in Applied Mechanics and Engineering, 191, 5287–5314 (2002)
Bowen R.M., Theory of mixtures, In: Continuum Physics, (Ed.) Eringen A.C., Vol. III, pp. 1–127. Academic Press, New York (1976)
Bowen R.M., Incompressible porous media models by use of the theory of mixtures, International Journal of Engineering Science, 18, 1129–1148 (1980)
Bowen R.M., Compressible porous media models by use of the theory of mixtures, International Journal of Engineering Science, 20, 697–735 (1982)
Brooks R.N. and Corey A.T., Properties of porous media affecting fluid flow, ASCE: Journal of the Irrigation and Draining Division, 92, 61–68 (1966)
Chen Y., Chen X. and Hisada T., Non-linear finite element analysis of mechanical electrochemical phenomena in hydrated soft tissues based on triphasic theory, International Journal for Numerical Methods in Engineering, 65, 147–173 (2006)
Ehlers W., On thermodynamics of elasto-plastic porous media, Archive of Mechanics, 41, 73–93 (1989)
Ehlers W., Poröse Medien — ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie, Habilitation, Forschungsberichte aus dem Fachbereich Bauwesen 47, Universität Essen (1989)
Ehlers W., Constitutive equations for granular materials in geomechanical context, In: Continuum Mechanics in Environmental Sciences and Geophysics, (Ed.) Hutter K., CISM Courses and Lectures No. 337, pp. 313–402. Springer, Wien (1993)
Ehlers W., A single-surface yield function for geomaterials, Archive of Applied Mechanics, 65, 246–259 (1995)
Ehlers W., Grundlegende Konzepte in der Theorie Poröser Medien, Technische Mechanik, 16, 63–76 (1996)
Ehlers W., Foundations of multiphasic and porous materials, In: Porous Media — Theory, Experiments and Numerical Applications, (Eds.) Ehlers W. and Bluhm J., pp. 3–86. Springer, Berlin (2002)
Ehlers W. and Eipper G., Finite elastic deformations in liquid-saturated and empty porous solids, Transport in Porous Media, 34, 179–191 (1999)
Ehlers W., Ellsiepen P., Blome P., Mahnkopf D. and Markert B., Theoretische und numerische Studien zur Lösung von Rand- und Anfangswertproblemen in der Theorie Poröser Medien. Technical Report No. 99-II-1, Institute of Applied Mechanics (CE), Universität Stuttgart (1999)
Ehlers W., Ellsiepen P. and Ammann M., Time- and space-adaptive methods applied to localization phenomena in empty and saturated micropolar and standard porous materials, International Journal for Numerical Methods in Engineering, 52, 503–526 (2001)
Ehlers W. and Markert B., A linear viscoelastic biphasic model for soft tissues based on the theory of porous media, ASME Journal of Biomechanical Engineering, 123, 418–424 (2001)
Ehlers W., Ammann M. and Diebels S., h-adaptive FE methods applied to single- and multiphase problems, International Journal for Numerical Methods in Engineering, 54, 219–239 (2002)
Ehlers W. and Graf T., On partially saturated soil as a triphasic material, In: Poromechanics II, Proceedings of the 2 nd Biot Conference on Poromechanics, (Eds.) Auriault J.-L., Geindreau C., Royer P., Bloch J.-L., Boutin C. and Lewandowska J., pp. 419–424. Balkema at Swets & Zeitlinger, Lisse (2002)
Ehlers W., Markert B. and Acartürk A., Large strain viscoelastic swelling of charged hydrated porous media, In: Poromechanics II, Proceedings of the 2 nd Biot Conference on Poromechanics, (Eds.) Auriault J.-L., Geindreau C., Royer P., Bloch J.-L., Boutin C. and Lewandowska J., pp. 185–191. Balkema at Swets & Zeitlinger, Lisse (2002)
Ehlers W., Graf T. and Ammann M., Deformation and localization analysis of partially saturated soil, Computer Methods in Applied Mechanics and Engineering, 193, 2885–2910 (2004)
Ehlers W., Markert B. and Acartürk A., Swelling phenomena of hydrated porous materials. In: Poromechanics III, Proceedings of the 3 rd Biot Conference on Poromechanics, (Eds.) Abousleiman Y.N., Cheng A.H.-D. and Ulm F.J., pp. 781–786. Balkema Publishers, Leiden (2005)
Ehlers W., Karajan, N. and Markert B., A porous media model describing the inhomogeneous behaviour of the human intervertebral disc, Materials Science and Engineering Technology, 37, 546–551 (2006)
Ehlers W. and Scholz B., An inverse algorithm for the identification and the sensitivity analysis of the parameters governing micropolar elasto-plastic granular material, Archive of Applied Mechanics, 77, 911–931 (2007)
Ehlers W. and Acartürk A., The role of weakly imposed Dirichlet boundary conditions for numerically stable computations of swelling phenomena, Computational Mechanics, 43, 545–557 (2009)
Ehlers W., Karajan N. and Markert B., An extended biphasic model for charged hydrated tissues with application to the inter-vertebral disc, Biomechanics and Modeling in Mechanobiology, 8, 233–251 (2009)
Ehlers W. and Karajan N., Advances in modelling saturated biological soft tissues and chemically active gels, Archive of Applied Mechanics, submitted
Eipper G., Theorie und Numerik finiter elastischer Deformationen in fluidgesättigten porösen Medien, Dissertation, Bericht Nr. II-1 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart (1998)
Ellsiepen P., Zeit- und ortsadaptive Verfahren angewandt auf Mehrphasenprobleme poröser Medien, Dissertation, Bericht Nr. II-3 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart (1999)
Finsterle S., Inverse Modellierung zur Bestimmung hydrogeologischer Parameter eines Zweiphasensystems, Dissertation, Technischer Bericht der Versuchsanstalt für Wasserbau, Hydrologie und Graziologie der ETH Zürich (1993)
Frijns A.J.H., Huyghe J.M., Kaasschieter E.F. and Wijlaars M.W., Numerical simulation of deformations and electrical potentials in a cartilage substitute, Biorheology, 40, 123–131 (2003)
Ghadiani S. R., A multiphasic Continuum-Mechanical Model for Design Investigations of an Effusion-Cooled Rocket Thrust Chamber, Dissertation, Report No. II-13 of the Institute of Applied Mechanics (CE), University of Stuttgart (2005)
Graf T., Multiphasic Flow Processes in Deformable Porous Media under Consideration of Fluid Phase Transitions. Dissertation, Report No. II-17 of the Institute of Applied Mechanics (CE), University of Stuttgart (2008)
Haupt P., Continuum Mechanics and Theory of Materials, Springer, Berlin (2000)
Huyghe J.M. and Janssen J.D., Thermo-chemo-electromechanical formulation of saturated charged porous solids, Transport in Porous Media, 34, 129–141 (1999)
Huyghe J.M., Molenaar M.M. and Baaijens F.P.T., Poromechanics of compressible charged porous media using the theory of mixtures, ASME Journal of Biomechanics, 129, 776–785 (2007)
Kaasschieter E.F., Frijns A.J.H. and Huyghe J.M.R.J., Mixed finite element modelling of cartilaginous tissues, Mathematics and Computers in Simulation, 61, 549–560 (2003)
Karajan N., An Extended Biphasic Description of the Inhomogeneous and Anisotropic Intervertebral Disc. Dissertation, Report No. II-19 of the Institute of Applied Mechanics (CE), University of Stuttgart (2009)
Lade P.V. and Duncan J.M., Cubical triaxial tests on cohesionless soil, ASCE: Journal of Soil Mechanics and Foundations Division, 99, 793–812 (1973)
Lewis R.W. and Schrefler B.A., The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, 2 nd Edition. Wiley, Chichester (1998)
Loret B., Hueckel T. and Gajo A., Chemo-mechanical coupling in saturated porous media: elastic-plastic behaviour of homoionic expansive clays, International Journal of Solids and Structures, 39, 2273–2806 (2002)
Mahnkopf D., Lokalisierung fluidgesättigter poröser Festkörper bei finiten elastoplastischen Deformationen. Dissertation, Bericht Nr. II-5 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart (2000)
Müllerschön H., Spannungs-Verzerrungsverhalten granularer Materialien am Beispiel von Berliner Sand. Dissertation, Bericht Nr. II-6 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart (2000)
Perzyna P., Fundamental problems in viscoplasticity, Advances in Applied Mechanics, 9, 243–377 (1966)
Samson E., Marchand J., Robert J.-L. and Bournazel J.-P., Modelling ion diffusion mechanisms in porous media, International Journal for Numerical Methods in Engineering, 46, 2043–2060 (1999)
Scholz B., Application of a Micropolar Model to the Localization Phenomena in Granular Materials: General Model, Sensitivity Analysis and Parameter Optimization. Dissertation, Report No. II-15 of the Institute of Applied Mechanics (CE), University of Stuttgart (2007)
Skempton A.W., Significance of Terzaghi’s concept of effective stress (Terzaghi’s discovery of effective stress), In: From Theory to Practice in Soil Mechanics, (Eds.) Bjerrum L., Casagrande A., Peck R.B. and Skempton A.W., pp. 42–53. Wiley, New York (1960)
Truesdell C., Sulle basi delle termomeccanica, Rendiconti Lincei, 22, 158–166 (1957)
Truesdell C., Thermodynamics of diffusion, In: Rational Thermodynamics, (Ed.) Truesdell C., 2nd Edition, pp. 219–236. Springer, New York (1984)
Truesdell C. and Toupin R.A., The classical field theories, In: Handbuch der Physik, (Ed.) Flügge S., Vol. III/1, pp. 226–902. Springer, Berlin (1960)
van Genuchten M.T., A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Science Society of America Journal, 44, 892–898 (1980)
Wallmersperger T., Modellierung und Simulation stimulierbarer polyelektrischer Gele. Dissertation, Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universität Stuttgart (2003)
Wieners C., Ammann M., Diebels S. and Ehlers W., Parallel 3-d simulations for porous media models in soil mechanics, Computational Mechanics, 29, 73–87 (2002)
Wieners C., Ammann M., Graf T. and Ehlers W., Parallel Krylov methods and the application to 3-d simulations of a triphasic porous media model in soil mechanics, Computational Mechanics, 36, 409–420 (2005)
Wieners C., Ammann M. and Ehlers W., Distributed point objects: a new concept for parallel finite elements applied to a geomechanical problem, Future Generation Computer Systems, 22, 532–535 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ehlers, W. Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels. Int J Adv Eng Sci Appl Math 1, 1–24 (2009). https://doi.org/10.1007/s12572-009-0001-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12572-009-0001-z