Porous Elasticity
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TOC
1. Some Classical Porous Media Models
1.1. Preliminary Definitions
1.2. Rigid Isentropic Solid Containing One Incompressible Fluid
1.3. Rigid Isotropic Solid Containing One Compressible Fluid
1.4. Rigid Isotropic Solid Containing N – 1 Incompressible Fluids
1.5. Linear Elastic Incompressible Isotropic Solid Containing An Incompressible Fluid
1.6. Linear Elastic Isotropic Solid Containing A Compressible Fluid
2. Elements of The Theory of Mixtures
2.1. Kinematics
2.2. Equations of Balance
2.3. Field Equations
2.4. Balance of Mass-Special Forms
2.5. Balance of Momentum-Special Forms
2.6. Entropy Inequality
2.7. Rigid Isotropic Solid Containing Incompressible Fluids
3. Porous Elasticity Models
3.1. Immiscible Mixtures
3.2. Immiscible Mixtures-Linearized Isotropic Models
3.3. Immiscible Mixtures-Field Equations for the Linearized Model
4. Porous Elasticity Models With Pore Pressures
4.1. Immiscible Mixtures-Definition of Pore Pressure
4.2. Binary Immiscible Porous Materials with Pore Pressure
4.3. Stability of Equilibrium-Classes of Initial-Boundary Value
4.4. Incompressible Immiscible Mixtures
4.5. Binary Incompressible Immiscible Mixtures
5. Models Which Neglect Inertia
5.1. Compressible Models
5.2. Incompressible Models
6. Further Transformations And Material Properties
6.1. Constitutive Equations-Alternate Forms
6.2. Connections With Other Formulations
7. Singular Surfaces And Acceleration Waves
7.1. Singular Surfaces
7.2. Acceleration Waves
8. Plane Harmonic Waves
8.1. One Dimensional Governing Equations
8.2. Plane Progressive Waves: Dispersion Relation
8.3. High Frequency Approximation
8.4. Low Frequency Approximation
8.5. High and Low Frequency Approximation for Nonconductors
8.6. Phase Velocities
8.7. Numerical Example
9. Boundary Initial Value Problems: Inertia Neglected
9.1. Governing Partial Differential Equations
9.2. Some Properties of the Space Part of the Operator
9.3. Boundary Initial Value Problems
9.4. A One Dimensional Example
9.5. Biot Problem
9.6. Modified Biot Problem: Time Dependent External Pressure
9.7. The Use of Green’s Functions
10. Boundary Initial Value Problems: Inertia Included
10.1. Governing Partial Differential Equations
10.2. Boundary Initial Value Problems
10.3. A One Dimensional Example
10.4. Properties of the Roots of
10.5. Inversion of ( ) n K s
10.6. The Use of Green’s Functions
10.7. Biot Problem with Inertia
10.8. Biot Problem with Inertia: Time Dependent External Pressure
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