Trends in Continuum Mechanics of Porous Media

Over the last decade and particularly 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 has attracted some attention, and therefore conferences devoted almost exclusively to the macrosopic porous media theory have been organized in order to collect all findings, to present new results, and to discuss new trends. Many important contributions have also been published in national and international journals, which have 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 and to show new trends in the continuum mechanical treatment of saturated and unsaturated capillary and non-capillary porous solids.

This book addresses postgraduate students and scientists working in engineering, physics, and mathematics. It provides an outline of modern theory of porous media and shows some trends in theory and in applications.

Preface. 1. Introduction, 2. Volume Fraction Concept. 3. Kinematics. 1. Basic Relations. 2. Kinematics of Micropolar Constituents. 4. Balance Principles. 1. Balance of Mass. 2. Balance of Momentum and Moment of Momentum. 3. Balance of Energy. 5. Basic inequality (Entropy Principle) 1. Preliminaries. 2. Basic Inequality for Non-Polar Constituents and the Mixture Body. 6. Constitutive theory. 1. Preliminaries. 2. Closure Problems and Constraints. 3. Reformulation of the Entropy Inequality. 4. Exploitation of the Inequality for Ternary and Binary Capillary Porous Models. 5. Elastic Behaviour of the Solid Sceleton a. Finite Theories. b. Linear Theory. c. Other Approaches. 6. Elastic-Plastic Behaviour of the Solid Skeleton a. General Theory. b. Special Stress Strain Relations. 7. Viscous Behaviour of the Solid Skeleton. 8. Thermomechanical Behaviour of Porefluids. a. Inviscid Porefluids. b. Viscous Porefluids. 7. Fundamental Effects in Gas- and Liquid-Filled Porous Solids. 1. Introduction. 2. Basic Equations. 3. Uplift. 4. Friction. 5. Capillarity. a. Basic Relations. b. One-Dimensional Capillary Motion. c. Two-Dimensional Capillary Motion (an Example). 6. Effective Stresses. 7. Phase Transitions. a. Theorethical Foundation. b. Drying Processes. c. Freezing Processes. 8. Poroelasticity. 1. Introduction. 2. The Fundamental Field Equations for Poroelasticity. 3. Main Equations for an Incompressible Binary Model. 4. Basic Solutions for an Incompressible Binary Model. a. Fundamental Solution of the System of Equations of Steady Oscilliations in the Theory of Fluidsaturated Porous Media. b. On the Representations of Solutions in the Theory of Fluidsaturated Porous Media. 5. Wave Propagation. a. Plane Waves in a Semi-Infinite Liquidsaturated Porous medium. b. Propagation of Acceleration Waves in Saturated Porous Solids. c. Growth and Decay of Acceleration Waves. d. Dispersion and Attenuation of Surface Waves in a Saturated Porous Medium. e. Inhomogeneous Plane Waves, Mechanical Energy Flux, and Energy Dissipation in a Two-Phase Porous Medium. f. Propagation and Evolution of Wave Fronts in Saturated Porous Solids. 9. Poroplasticity for Metallic porous Solids. 1. Stress-Strain Realtion a. Rigid Ideal-Plastic Behaviour. b. Elastic-Plastic Behaviour with Hardening. 2. General Theorems for Saturated Porous Solids in the Rigid Ideal-Plastic Range. a. Preliminaries. b. The Uniqueness Theorem for Solutions of Boundary Value Problems. c. Minimum and Maximum Principles for Rigid Ideal-Plastic Behaviour. 10. Applications in Engineering and Biomechanics. 1. Soil Mechanics. a. Consolidation Problem and Localization Phenomena. b. Phase Transitions. c. Dynamics. 2. Chemical Engineering. a. Powder Compaction. b. Drying Processes. 3. Building Physics. a. Transport of Moisture. b. Heat Conduction in a Fluidsaturated Capillary-Porous Solid. 4. Biomechanics. 5. Some other Fields of Application. 11. Conclusions and Outlook. References. Author Index. Subject Index