Machine generated contents note: ch. 1 Elementary Tensor Analysis -- 1.1.Introduction -- 1.2.General Tensors, Cartesian Tensors, and Tensor Rank -- 1.3.A Brief Review of Vector Analysis -- 1.4.Dyadic Form of Second-Order Tensors -- 1.5.Derivatives of Tensors -- 1.6.Divergence and Stokes Theorems -- 1.6.1.Divergence Theorem or Gauss Theorem -- 1.6.2.Stokes Theorem -- 1.7.Some Formulas in Cylindrical Coordinates -- 1.8.Some Formulas in Spherical Coordinates -- 1.9.Summary and Further Reading -- 1.10.Problems -- ch. 2 Elasticity and Its Applications -- 2.1.Introduction -- 2.2.Basic Concepts for Stress Tensor -- 2.3.Piola-Kirchhoff Stresses -- 2.4.Coordinate Transformation of Stress -- 2.5.Basic Concepts for Strain Tensor -- 2.6.Rate of Deformation -- 2.7.Compatibility Equations -- 2.8.Hill's Work-Conjugate Stress Measures -- 2.9.Constitutive Relation -- 2.10.Isotropic Solids -- 2.11.Transversely Isotropic Solids -- 2.12.Equations of Motion and Equilibrium --

Contents note continued: 2.13.Compatibility Equation in Terms of Stress Tensor -- 2.14.Strain Energy Density -- 2.15.Complementary Energy -- 2.16.Hyperelasticity and Hypoelasticity -- 2.17.Plane Stress, Plane Strain, and the Airy Stress Function -- 2.18.Stress Concentration at a Circular Hole -- 2.19.Force Acting at the Apex of a Wedge -- 2.20.Uniform Vertical Loading on Part of the Surface -- 2.21.Solution for Indirect Tensile Test (Brazilian Test) -- 2.22.Jaeger's Modified Brazilian Test -- 2.23.Edge Dislocation -- 2.24.Dislocation Pile-up and Crack -- 2.25.Screw Dislocation and Faulting -- 2.26.Mura Formula for Curved Dislocation -- 2.27.Summary and Further Reading -- 2.28.Problems -- ch. 3 Complex Variable Methods for 2-D Elasticity -- 3.1.Introduction -- 3.2.Coordinate Transformation in Complex Variable Theory -- 3.3.Homogeneous Stresses in Terms Analytic Functions -- 3.4.A Borehole Subject to Internal Pressure -- 3.5.Kirsch Solution by Complex Variable Method --

Contents note continued: 3.6.Definiteness and Uniqueness of the Analytic Function -- 3.7.Boundary Conditions for the Analytic Functions -- 3.8.Single-valued Condition for Multi-connected Bodies -- 3.9.Multi-connected Body of Infinite Extend -- 3.10.General Transformation of Quantities -- 3.11.Elastic Body with Holes -- 3.12.Stress Concentration at a Square Hole -- 3.13.Mapping Functions for Other Holes -- 3.14.Summary and Further Reading -- 3.15.Problems -- ch. 4 Three-Dimensional Solutions in Elasticity -- 4.1.Introduction -- 4.2.Displacement Formulation -- 4.2.1.Helmholtz Decomposition -- 4.2.2.Lame's Strain Potential for Incompressible Solids -- 4.2.3.Galerkin Vector -- 4.2.4.Love's Displacement Potential for Cylindrical Solids -- 4.2.5.Papkovitch-Neuber Displacement Potential -- 4.2.6.2-D Papkovitch-Neuber vs. Kolosov-Muskhelisvili Methods -- 4.3.Stress Formulations -- 4.3.1.Beltrami and Beltrami-Schaefer Stress Functions -- 4.3.2.Maxwell Stress Functions --

Contents note continued: 4.3.3.Morera Sress Function -- 4.3.4.Other Beltrami Stress Functions -- 4.4.Some 3-D Solutions in Geomechanics -- 4.4.1.Hollow Sphere Subject to Internal and External Pressures -- 4.4.2.Kelvin's Fundamental Solution -- 4.4.2.1.Papkovitch-Neuber Potential Method -- 4.4.2.2.Love's Displacement Potential Method -- 4.4.3.Boussinesq's Fundamental Solution -- 4.4.3.1.Love's and Lame's Strain Potential Methods -- 4.4.3.2.Papkovitch-Neuber Potential Method -- 4.4.4.Cerruti's Fundamental Solution -- 4.4.5.Mindlin's Fundamental Solution in Half-space -- 4.4.6.Lorentz's Fundamental Solution -- 4.4.7.Melan's Fundamental Solution -- 4.5.Harmonic Functions and Indirect Method -- 4.6.Harmonic Functions in Spherical Coordinates -- 4.7.Harmonic Functions in Cylindrical Coordinates -- 4.8.Biharmonic Functions -- 4.9.Muki's Formulation in Cylindrical Coordinates -- 4.9.1.Muki's Vector Potentials -- 4.9.2.Method of Solution by Hankel Transform --

Contents note continued: 4.9.3.Boussinesq Solution by Hankel Transform -- 4.10.Summary and Further Reading -- 4.10.1.Summary -- 4.10.2.Further Reading -- 4.10.2.1.General Method of Solutions for 3-D Elasticity -- 4.10.2.2.Integral Transform in Solving 3-D Problems -- 4.10.2.3.General Method of Solutions for Circular Cylinders -- 4.10.2.4.General Method of Solutions for Spheres -- 4.11.Problems -- ch. 5 Plasticity and Its Applications -- 5.1.Introduction -- 5.2.Flow Theory and Deformation Theory -- 5.3.Yield Function and Plastic Potential -- 5.4.Elasto-plastic Constitutive Model -- 5.5.Rudnicki-Rice (1975) Model -- 5.6.Drucker's Postulate, PMPR, and Il'iushin's Postulate -- 5.7.Yield Vertex -- 5.8.Mohr-Coulomb Model -- 5.9.Lode Angle or Parameter -- 5.10.Yield Criteria on the π-Plane -- 5.11.Other Soil Yield Models -- 5.12.Cap Models -- 5.13.Physical Meaning of Cam-Clay Model -- 5.14.Modified Cam-Clay -- 5.15.A Cam-clay Model for Finite Strain --

Contents note continued: 5.16.Plasticity by Internal Variables -- 5.17.Viscoplasticity -- 5.17.1.One-dimensional Modeling -- 5.17.2.Three-dimensional Models -- 5.17.3.Consistency Condition for Perzyna Model -- 5.17.4.Consistency Model of Wang et al. (1997) -- 5.17.5.Adachi-Oka (1984) Model -- 5.18.Summary and Further Reading -- 5.19.Problems -- ch. 6 Fracture Mechanics and Its Applications -- 6.1.Introduction -- 6.2.Stress Concentration at a Elliptical Hole -- 6.3.Stress Concentration at a Tensile Crack -- 6.4.Stress Field near a Shear Crack -- 6.5.The General Stress and Displacement Field for Mode I Cracks -- 6.6.The General Stress and Displacement Field for Mode II Cracks -- 6.7.The General Stress and Displacement Field for Mode III Cracks -- 6.8.The Energy Release Rate at Crack Tips -- 6.9.Fracture Toughness for Rocks -- 6.10.J-integral and the Energy Release Rate -- 6.11.Westergaard Stress Function and Superposition -- 6.12.Growth of Slip Surface in Slopes --

Contents note continued: 6.13.Energy Release Rate for Earthquake -- 6.14.Wing Crack Model under Compressions -- 6.15.Bazant's Size Effect Law via J-integral -- 6.16.Continuum Damage Mechanics -- 6.17.Solids Containing Microcracks -- 6.17.1.Compliance Change due to a Single Crack -- 6.17.2.Effective Compliance for Cracked Bodies -- 6.17.3.Non-interacting Result for Planar Transverse Isotropy -- 6.17.4.Planar Transverse Isotropy by Self-consistent Method -- 6.17.5.Planar Transverse Isotropy by Differential Scheme -- 6.17.6.Non-interacting Result for Cylindrical Transverse Isotropy -- 6.17.7.Non-interacting Result for Isotropically Cracked Solids -- 6.18.Rudnicki-Chau (1996) Multiaxial Microcrack Model -- 6.19.Summary and Further Reading -- 6.20.Problems -- ch. 7 Viscoelasticty and Its Applications -- 7.1.Introduction -- 7.2.Boltzmann's Integral Form of Stress and Strain -- 7.3.Stieltjes Convolution Notation -- 7.4.Stress-Strain Relation in Differential Equation Form --

Contents note continued: 7.4.1.Maxwell Model -- 7.4.2.Kelvin-Voigt Model -- 7.4.3.Three-Parameter Models -- 7.4.4.Generalized Maxwell and Kelvin Models -- 7.5.Stress-strain Relation in Laplace Transform Space -- 7.5.1.Viscoelastic Solids with Elastic Bulk Modulus -- 7.5.2.Maxwell Solids -- 7.5.3.Kelvin-Voigt Solids -- 7.5.4.Standard Linear Solid and Three-Parameter Models -- 7.6.Correspondence Principle -- 7.6.1.Boussinesq Problem for Maxwell Half-space -- 7.6.2.Boussinesq Problem for Kelvin-Voigt Half-space -- 7.6.3.Boussinesq Problem for Three-Parameter Model A -- 7.7.Creeping and Relaxation Tests -- 7.7.1.Maxwell Material -- 7.7.1.1.Creeping Test -- 7.7.1.2.Relaxation Test -- 7.7.2.Kelvin-Voigt Material -- 7.7.2.1.Creeping Test -- 7.7.2.2.Relaxation Test -- 7.7.3.Three-parameter Model A or Standard Linear Solid -- 7.7.3.1.Creeping Test -- 7.7.3.2.Relaxation Test -- 7.7.3.3.Relaxation Test in Compression -- 7.8.Calibration of the Viscoelastic Model --

Contents note continued: 7.9.Viscoelastic Crack Models for Steam Injection -- 7.9.1.Superposition of Auxiliary Problems I and II -- 7.9.2.Center of Dilatation in Two-dimensional Bimaterial -- 7.9.3.Stress Intensity Factor of Auxiliary Problem II -- 7.9.4.Inverse Laplace Transform -- 7.9.5.Numerical Results -- 7.10.Summary and Further Reading -- 7.11.Problems -- ch. 8 Linear Elastic Fluid-Infiltrated Solids and Poroelasticity -- 8.1.Introduction -- 8.2.Biot's Theory of Poroelasticity -- 8.2.1.McNamee and Gibson Cylindrical Form -- 8.2.2.Rice-Cleary (1976) Linearized Constitutive Relation -- 8.2.3.Rudnicki (1986) Constitutive Relation -- 8.2.4.Rudnicki's (1985) Anisotropic Diffusive Solids -- 8.3.Biot-Verruijt Displacement Function -- 8.4.McNamee-Gibson-Verruijt Displacement Function -- 8.5.Schiffman-Fungaroli-Verruijt Displacement Function -- 8.6.Schiffman-Fungaroli Displacement Function -- 8.7.Laplace-Hankel Transform Technique --

Contents note continued: 8.8.Point Forces and Point Fluid Source in Half-space -- 8.8.1.Vertical Point Force Solution -- 8.8.2.Horizontal Point Force Solution -- 8.8.3.Fluid Point Source Solution -- 8.9.Cleary's Fundamental Solution of Point Forces in Full Space -- 8.9.1.Canonical Representation of Point Force Solution -- 8.9.2.Determination of Evolution Functions -- 8.9.3.Determination of Unknown Constant F[∞] -- 8.9.4.Final Solutions -- 8.10.Rudnicki's Fundamental Solutions in Full Space -- 8.10.1.Impulsive Fluid Source -- 8.10.2.Canonical Form of Displacement Solution -- 8.10.3.Error Function Representation -- 8.10.4.Suddenly Applied Fluid Mass Source -- 8.10.5.Equivalence of Fluid Mass Dipole and Body Force -- 8.10.6.Fluid Mass Dipoles -- 8.10.7.Point Force Solution by Rudnicki (1986) -- 8.11.Thermoelasticity vs. Poroelasticity -- 8.12.Summary and Further Reading -- 8.12.1.Summary -- 8.12.2.Further Reading -- 8.13.Problems -- ch. 9 Dynamics and Waves in Geomaterials --

Contents note continued: 9.1.Introduction -- 9.2.Seismic Waves -- 9.3.Waves in Infinite Elastic Isotropic Solids -- 9.4.Helmholtz Theorem and Wave Speeds -- 9.5.Rayleigh Waves -- 9.5.1.Characteristics Equation for Rayleigh Wave Speed -- 9.5.2.Rayleigh Wave in Solids Satisfying Poisson Condition -- 9.5.3.Segel (1977) Method for Arbitrary Poisson's Ratio -- 9.6.Love Waves -- 9.6.1.Non-existence of SH-wave in Homogeneous Half-space -- 9.6.2.Love Waves in an Elastic Layer on a Half-space -- 9.6.3.Dispersion Characteristics of Love Waves -- 9.7.Stoneley Waves -- 9.8.Elastic-plastic Waves -- 9.8.1.Acceleration Waves in Solids -- 9.8.2.Shear Banding as Stationary Acceleration Wave -- 9.8.3.Acoustic Tensor for Geomaterials -- 9.8.4.Wave Speed Analysis -- 9.9.Waves in Viscoelastic Solids -- 9.9.1.Complex Moduli -- 9.9.2.Longitudinal and Transverse Waves Speeds -- 9.10.Dynamic Fracture Mechanics -- 9.10.1.Dynamic Solutions for a Stationary Crack --

Contents note continued: 9.10.2.Asymptotic Fields near a Moving Crack-tip -- 9.10.3.Dynamic Energy Release Rate -- 9.10.4.Dynamic Fracture Toughness -- 9.11.Vibrations and Soil Dynamics -- 9.12.Summary and Further Reading -- 9.12.1.Summary -- 9.12.2.Further Reading -- 9.12.2.1.Waves in Solids and Elastodynamics -- 9.12.2.2.Seismic Waves on Earth -- 9.12.2.3.Waves in Porous Media -- 9.12.2.4.Dynamic Fracture Mechanics -- 9.12.2.5.Dynamic Fragmentation -- 9.13.Problems -- Appendices -- Appendix A Nanson Formula -- Appendix B Laplace Transform -- Appendix C Legendre Transform and Work Increments.