# Porous Elasticity

Written by: Dr. Ray M. Bowen (Texas A&M University)

The origins of this mechanical engineering textbook go back over 30 years. Dr. Ray M. Bowen was teaching Mechanical Engineering at Rice University. Since then, he has held a variety of positions at Oklahoma State University and Texas A&M University. For eight years, he was President of Texas A&M. This educator is offering his 10 chapter textbook to all students.

Unfortunately, there’s no mention of prerequisites or what specific course this text would generally be tied to. I can tell you, based upon glancing through it quickly, you are going to need a great deal of calculus prior to tackling this one. Bowen lists the subjects as: Porous, Elasticity, Mixtures and Continuum Mechanics. The complete title is Porous Elasticity, Lectures on the Elasticity of Porous Materials as An Application of the Theory of Mixtures.

The text was originally made available in 2008. The current 2014 version corrected some typos and included an index.

CHAPTER 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
References
CHAPTER 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
References
CHAPTER 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
References
CHAPTER 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
References
CHAPTER 5. Models Which Neglect Inertia
5.1. Compressible Models
5.2. Incompressible Models
References
CHAPTER 6. Further Transformations And Material Properties
6.1. Constitutive Equations-Alternate Forms
6.2. Connections With Other Formulations
References
CHAPTER 7. Singular Surfaces And Acceleration Waves
7.1. Singular Surfaces
7.2. Acceleration Waves
References
CHAPTER 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
References
CHAPTER 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
References
CHAPTER 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
10.6. The Use of Green’s Functions
10.7. Biot Problem with Inertia
10.8. Biot Problem with Inertia: Time Dependent External Pressure References
Appendix A Bibliography

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Porous Elasticity