In the last decade and, in particular in recent years, the macroscopic porous media theory has made decisive progress concerning the fundamentals of the theory and the development of mathematical models in various fields of engineering and biomechanics. This progress attracted some attention and therefore conferences (colloquia, symposia, etc) devoted almost exclusively to the macroscopic porous media theory have been organized in the last three years in Cambridge, United Kingdom (1996), Prague, the Czech Republic (1997), Essen, Germany (1997), Metz, France (1999), Stuttgart, Germany (1999) and Chicago, USA (2000) in order to collect all findings, to present new results, and to discuss new trends. Also in national and international journals a great number of important contributions have been published which has brought the porous media theory, in some parts, to a close. Therefore, the time seems to be ripe to review the state of the art. The Introduction is devoted to the historical development up to the end of the 1980s and the beginning of the 1990s (readers interested in an extended description of the historical development of the porous media theory are referred to de Boer, 2000). The volume fraction concept is formulated in Section 2. An extensive review of the kinematics in porous media theory is presented in Section 3. The balance equations and the entropy inequality are discussed in Sections 4 and 5. Section 6 is devoted to the investigation of the closure problem and the saturation condition. The constitutive theory with the description of elastic, elastic-plastic, and viscous states of the porous solid as well as some reflexions on the constitutive behavior of the pore fluids are represented in Section 7. Finally, some applications of the porous media theory in various fields (soil mechanics, chemical engineering, biomechanics and building physics as well as in environmental mechanics, soil physics, the petroleum industry, and material science) will demonstrate the usefulness of the macroscopic porous media theory. This review article contains 209 references.

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