Theory of Porous Media

Mayer, the Discoverer of the Mechanical Equivalent of Heat.- 3.8.4 The Contributions of Mohr, Seguin, Colding, Holtzmann, and Helmholtz.- 3.8.5 The Decisive Investigations of Joule.- 3.8.6 The Foundation of Thermodynamics by Clausius, Rankine and Thomson.- 3.8.7 Discussions on the Correct Form of the Mechanical Theory of Heat and Further Developments.- 3.8.8 Biographical Notes.- 4 The Modern Era.- 4.1 Discovery of Fundamental Effects of Liquid-Saturated Rigid Porous Solids.- 4.2 The Treatment of the Liquid-Saturated Deformable Porous Solid by von Terzaghi.- 4.3 The Foundation of Modern Porous Media Theory by Fillunger.- 4.4 The Tragic Controversy Between the Viennese Professors Fillunger and von Terzaghi in 1936/37.- 4.5 The Further Development of the Viennese Affair and in Soil Mechanics.- 4.6 Biographical Notes.- 4.7 The Followers of von Terzaghi and Fillunger: Biot, Heinrich and Frenkel.- 4.7.1 Biot's Theory.- 4.7.2 Heinrich's Theory.- 4.7.3 Frenkel's Description of Moist Soil.- 4.7.4 Further Developments.- 4.7.5 Biographical Notes.- 4.8 Further Development of the Elasticity and Plasticity Theories..- 4.8.1 Elasticity Theory.- 4.8.2 Plasticity Theory.- 4.9 Modern Continuum Mechanics and Mixture Theory.- 4.10 Theories of Immiscible Mixtures.- 5 Current State of Porous Media Theory.- 5.1 Introductory Remarks to Porous Media Theory.- 5.2 The Volume Fraction Concept.- 5.3 Kinematics.- 5.4 Balance Equations.- 5.4.1 Balance of Mass.- 5.4.2 Balance of Momentum and Moment of Momentum.- 5.4.3 Balance of Energy.- 5.5 Entropy Inequality.- 5.6 The Closure Problem and the Saturation Constraint.- 5.7 Principle of Virtual Work.- 5.8 Constitutive Theory.- 5.8.1 Principle of Material Objectivity.- 5.8.2 The Introduction and Evaluation of the Entropy Inequality for a General Binary Porous Medium Model.- a) The Introduction and Evaluation of the Entropy Inequality for a Binary Porous Medium Model with Incompressible Constituents.- b) The Introduction and Evaluation of the Entropy Inequality for a Binary Porous Model with Compressible Constituents.- c) The Introduction and Evaluation of the Entropy Inequality for a Binary Porous Medium Model with Compressible Solid and Incompressible Fluid Constituents (Hybrid Model of First Type).- d) The Introduction and Evaluation of the Entropy Inequality for a Binary Porous Medium Model with Incompressible Solid and Compressible Fluid Constituents (Hybrid Model of Second Type).- e) Additional Remarks.- 5.8.3 Thermoelastic Compressible Porous Solid Filled with an Incompressible Viscous Fluid.- 5.8.4 Rigid Ideal-Plastic Porous Solid Filled with an Inviscid Compressible Fluid.- 5.8.5 Elastic-Plastic Behavior of an Incompressible Porous Solid Filled with an Incompressible Inviscid Fluid.- 5.8.6 Constitutive Relations and Transport Phenomena in Fluid-Saturated Rigid Porous Solids.- a) Heat Conduction.- b) Motion of an Incompressible, Viscous Fluid.- c) Further Transport Phenomena: Diffusion, Capillarity, Filtration, and Motion of Moisture.- 5.9 Applications.- 5.9.1 Uplift, Friction and Capillarity: three Fundamental Effects for Liquid-Saturated Porous Solids.- 5.9.2 One-Dimensional Transient Wave Propagation in Fluid-Saturated Incompressible Porous Media.- a) Field Equations.- b) One-Dimensional Transient Wave Propagation Solution.- c) General Properties of the Analytical Solution.- d) An Illustrative Example of a One-Dimensional Soil Column Subject to three Different Surface Loadings.- 5.9.3 One-Dimensional Consolidation (von Terzaghi's Differential Equation).- 5.9.4 The Elastic-Plastic Compaction of Metallic Powders.- 5.9.5 Further Solutions.- 6 Conclusions and Outlook.- A Evaluation of the Entropy Inequality.- B Introduction to the Vector- and Tensor Calculus for Engineers.- B 1. Introduction.- B 2. Basic Concepts.- B 2.1 Symbols.- B 2.2 Einstein's Summation Convention.- B 2.3 Kronecker Symbol.- B 3. Vector Algebra.- B 3.1 Vector Notion and Vector Operations.- B 3.2 Base System.- B 3.3 Reciprocal Base System.- B 3.4 Covariant and Contravariant Coefficients of the Vector Components.- B 3.5 Physical Coefficients of a Vector.- B 4. Tensor Algebra.- B 4.1 Tensor Notion (Linear Mapping).- B 4.2 Algebra in Base Systems.- B 4.3 Scalar Product of Tensors.- B 4.4 Tensor Product.- B 4.5 Special Tensors and Operations.- B 4.5.1 Inverse Tensor..- B 4.5.2 Transposed Tensor.- B 4.5.3 Symmetrical and Skew-Symmetrical Tensors..- B 4.5.4 Orthogonal Tensor.- B 4.5.5 Trace of the Tensor.- B 4.6 Decomposition of the Tensor.- B 4.6.1 Additive Decomposition.- B 4.6.2 Multiplicative Decomposition (Polar Decomposition).- B 4.7 Change of the Base.- B 4.8 Higher-Order Tensors.- B 4.8.1 Introduction of Higher-Order Tensors.....- B 4.8.2 Special Operations and Tensors.- B 4.8.3 Algebra in Base Systems.- B 4.9 Cross Product.- B 4.9.1 Cross Product of Vectors.- B 4.9.2 Cross Tensor Product of Vector and Tensor..- B 4.9.3 Cross Tensor Product of Tensors.- B 4.9.4 Cross Vector Product of Tensors.- B 4.9.5 Special Tensors and Operations.- B 4.10 Fundamental Tensors.- B 5. Vector and Tensor Analysis.- B 5.1 Functions of Scalar Parameters.- B 5.2 Field Theory.- B 5.2.1 Gradient.- B 5.2.2 Derivatives of Higher-Order.- B 5.2.3 Special Operations (Divergence, Rotation, and the Laplace-Operator).- B 5.3 Functions of Vector and Tensor Variables.- B 5.4 Integral Theorems.- B 5.4.1 Transformation of Surface Integrals into Volume Integrals.- B 5.4.2 Transformation of Line Integrals into Surface Integrals.- C Geometric Representation of the Principal Stresses, the Stress Invariants and the Mohr-Coulomb Theory.- C 1. Preliminaries.- C 2. Triaxial Plane.- C 3. Octahedral Plane.- C 4. Geometric Representation of Yield Functions.- C 5. Subspace of the Stress State.- C 6. Mohr-Coulomb Theory.- C 6.1 Coulomb's Strength Hypothesis for Arbitrarily Oriented Surfaces.- C 6.2 Failure Surfaces.- C 7. Failure Condition in Invariant Formulation.- References.- Author Index.