The thermodynamic structure and constitutive equations for fluid-saturated compressible and incompressible elastic porous solids

Abstract The macroscopic porous media theory consists of the mixture theory, restricted by the volume fraction concept. The incorporation of this concept leads to major difficulties in constructing a consistent macroscopic theory. With the help of thermodynamic restrictions, in addition with the multiplicative decomposition of the deformation gradient as well as experimental observations it will be shown, as to how a consistent phenomenological porous media theory for compressible and incompressible elastic porous solid models filled with an incompressible fluid can be developed which is mathematically and physically well balanced.

[1]  L. Šuklje,et al.  Rheologic aspects of soil mechanics , 1969 .

[2]  D. S. Drumheller,et al.  Theories of immiscible and structured mixtures , 1983 .

[3]  R. D. Boer,et al.  Thermodynamics of fluid-saturated porous media with a phase change , 1995 .

[4]  S. L. Passman,et al.  A Theory of Multiphase Mixtures , 1984 .

[5]  R. M. Bowen,et al.  Incompressible porous media models by use of the theory of mixtures , 1980 .

[6]  R. Clausius,et al.  Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie , 1865 .

[7]  R. D. Boer,et al.  Development of porous media theories — A brief historical review , 1992 .

[8]  G. Heinrich,et al.  Hydromechanische Grundlagen für die Behandlung von stationären und instationären Grundwasserströmungen , 1955 .

[9]  R. Balian,et al.  From Microphysics to Macrophysics: Methods and Applications of Statistical Physics , 1992 .

[10]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[11]  Amos Nur,et al.  An exact effective stress law for elastic deformation of rock with fluids , 1971 .

[12]  Reint Boer,et al.  Vektor- und Tensorrechnung für Ingenieure , 1982 .

[13]  Wolfgang Ehlers,et al.  Uplift, friction and capillarity: Three fundamental effects for liquid-saturated porous solids , 1990 .

[14]  R. Baierlein.  How entropy got its name , 1992 .

[15]  M. Biot,et al.  THE ELASTIC COEFFICIENTS OF THE THEORY OF CONSOLIDATION , 1957 .

[16]  J. Nunziato,et al.  On ideal multiphase mixtures with chemical reactions and diffusion , 1980 .