Abstract
Based on the Theory of Porous Media (TPM), a formulation of a fluid-saturated porous solid is presented where both constituents, the solid and the fluid, are assumed to be materially incompressible. Therefore, the so-called point of compaction exists. This deformation state is reached when all pores are closed and any further volume compression is impossible due to the incompressibility constraint of the solid skeleton material. To describe this effect, a new finite elasticity law is developed on the basis of a hyperelastic strain energy function, thus governing the constraint of material incompressibility for the solid material. Furthermore, a power function to describe deformation dependent permeability effects is introduced.
After the spatial discretization of the governing field equations within the finite element method, a differential algebraic system in time arises due to the incompressibility constraint of both constituents. For the efficient numerical treatment of the strongly coupled nonlinear solid-fluid problem, a consistent linearization of the weak forms of the governing equations with respect to the unknowns must be used.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bowen, R. M.: 1976, Theory of mixtures, In: A. C. Eringen (ed.), Continuum Physics, Vol. 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.
de Boer, R. and Ehlers, W.: 1986, Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme, Teil I, Forschungsberichte aus dem Fachbereich Bauwesen der Universität-GH-Essen 40, Essen.
Brenan, K. E., Campbell, S. L. and Petzold, L. R.: 1989, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Elsevier Science, New York.
Ehlers, W.: 1989, Poröse Medien-ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie, Forschungsberichte aus dem Fachbereich Bauwesen der Universität-GH-Essen 47, Essen.
Ehlers, W.: 1993, Constitutive equations for granular materials in geomechanical context, In: K. Hutter (ed.), Continuum Mechanics in Environmental Sciencies and Geophysics, CISM Courses and Lecture Notes No. 337, Springer-Verlag, Wien, pp. 313-402.
Ehlers, W. and Eipper, G.: 1997, Finite Elastizität bei fluidgesättigten hochporösen Festkörpern, ZAMM 77, S79-S80.
Marsden, J. E. and Hughes, T. J. R.: 1983, Mathematical Foundations of Elasticity, Prentice Hall, Englewood Cliffs, N.J.
Ogden, R. W.: 1972, Large deformation isotropic elasticity: On the correlation of theory and experiment for compressible rubberlike solids, Proc. Royal Soc. London, Series A 328, 567-583.
Ogden, R. W.: 1984, Non-Linear Elastic Deformations, Ellis Horwood, Chichester, U.K.
Rivlin, R. S.: 1948, Large elastic deformations of isotropic materials: I. Fundamental concepts, Proc. Royal Soc. London, Series A 240, 459-490.
Zienkiewicz, O. C. and Taylor, R. L.: 1984, The Finite Element Method, Vol. 1, 4th edn, McGraw-Hill, London.
Wriggers, P.: 1989, Konsistente Linearisierung in der Kontinuumsmechanik und ihre Anwendung auf die Finite-Element-Methode, Bericht F88/4, Institut für Baumechanik und Numerische Mechanik, Universität Hannover.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ehlers, W., Eipper, G. Finite Elastic Deformations in Liquid-Saturated and Empty Porous Solids. Transport in Porous Media 34, 179–191 (1999). https://doi.org/10.1023/A:1006565509095
Issue Date:
DOI: https://doi.org/10.1023/A:1006565509095