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| Preface | |
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| Mathematical Preliminaries | |
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| Vectors and Tensors | |
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| Vector Algebra | |
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| Coordinate Transformation: Rotation of Axes | |
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| Second-Rank Tensors | |
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| Symmetric and Antisymmetric Tensors | |
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| Prelude to Invariants of Tensors | |
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| Inverse of a Tensor | |
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| Additional Proofs | |
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| Additional Lemmas for Vectors | |
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| Coordinate Transformation of Tensors | |
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| Some Identities with Indices | |
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| Tensor Product | |
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| Orthonormal Basis | |
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| Eigenvectors and Eigenvalues | |
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| Symmetric Tensors | |
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| Positive Definiteness of a Tensor | |
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| Antisymmetric Tensors | |
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| Orthogonal Tensors | |
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| Polar Decomposition Theorem | |
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| Polar Decomposition: Physical Approach | |
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| The Cayley-Hamilton Theorem | |
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| Additional Lemmas for Tensors | |
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| Identities and Relations Involving [down triangle, open] Operator | |
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| Suggested Reading | |
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| Basic Integral Theorems | |
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| Gauss and Stokes's Theorems | |
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| Vector and Tensor Fields: Physical Approach | |
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| Surface Integrals: Gauss Law | |
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| Evaluating Surface Integrals | |
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| The Divergence | |
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| Divergence Theorem: Relation of Surface to Volume Integrals | |
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| More on Divergence Theorem | |
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| Suggested Reading | |
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| Fourier Series and Fourier Integrals | |
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| Fourier Series | |
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| Double Fourier Series | |
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| Integral Transforms | |
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| Dirichlet's Conditions | |
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| Integral Theorems | |
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| Convolution Integrals | |
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| Fourier Transforms of Derivatives of f(x) | |
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| Fourier Integrals as Limiting Cases of Fourier Series | |
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| Dirac Delta Function | |
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| Suggested Reading | |
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| Continuum Mechanics | |
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| Kinematics of Continuum | |
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| Preliminaries | |
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| Uniaxial Strain | |
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| Deformation Gradient | |
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| Strain Tensor | |
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| Stretch and Normal Strains | |
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| Angle Change and Shear Strains | |
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| Infinitesimal Strains | |
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| Principal Stretches | |
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| Eigenvectors and Eigenvalues of Deformation Tensors | |
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| Volume Changes | |
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| Area Changes | |
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| Area Changes: Alternative Approach | |
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| Simple Shear of a Thick Plate with a Central Hole | |
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| Finite vs. Small Deformations | |
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| Reference vs. Current Configuration | |
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| Material Derivatives and Velocity | |
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| Velocity Gradient | |
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| Deformation Rate and Spin | |
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| Rate of Stretching and Shearing | |
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| Material Derivatives of Strain Tensors: E vs. D | |
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| Rate of F in Terms of Principal Stretches | |
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| Additional Connections Between Current and Reference State Representations | |
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| Transport Formulae | |
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| Material Derivatives of Volume, Area, and Surface Integrals: Transport Formulae Revisited | |
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| Analysis of Simple Shearing | |
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| Examples of Particle and Plane Motion | |
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| Rigid Body Motions | |
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| Behavior under Superposed Rotation | |
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| Suggested Reading | |
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| Kinetics of Continuum | |
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| Traction Vector and Stress Tensor | |
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| Equations of Equilibrium | |
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| Balance of Angular Momentum: Symmetry of [sigma] | |
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| Principal Values of Cauchy Stress | |
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| Maximum Shear Stresses | |
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| Nominal Stress | |
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| Equilibrium in the Reference State | |
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| Work Conjugate Connections | |
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| Stress Deviator | |
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| Frame Indifference | |
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| Continuity Equation and Equations of Motion | |
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| Stress Power | |
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| The Principle of Virtual Work | |
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| Generalized Clapeyron's Formula | |
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| Suggested Reading | |
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| Thermodynamics of Continuum | |
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| First Law of Thermodynamics: Energy Equation | |
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| Second Law of Thermodynamics: Clausius-Duhem Inequality | |
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| Reversible Thermodynamics | |
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| Thermodynamic Relationships with p, V, T, and s | |
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| Theoretical Calculations of Heat Capacity | |
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| Third Law of Thermodynamics | |
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| Irreversible Thermodynamics | |
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| Gibbs Conditions of Thermodynamic Equilibrium | |
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| Linear Thermoelasticity | |
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| Thermodynamic Potentials in Linear Thermoelasticity | |
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| Uniaxial Loading and Thermoelastic Effect | |
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| Thermodynamics of Open Systems: Chemical Potentials | |
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| Gibbs-Duhem Equation | |
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| Chemical Potentials for Binary Systems | |
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| Configurational Entropy | |
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| Ideal Solutions | |
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| Regular Solutions for Binary Alloys | |
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| Suggested Reading | |
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| Nonlinear Elasticity | |
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| Green Elasticity | |
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| Isotropic Green Elasticity | |
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| Constitutive Equations in Terms of B | |
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| Constitutive Equations in Terms of Principal Stretches | |
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| Incompressible Isotropic Elastic Materials | |
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| Elastic Moduli Tensors | |
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| Instantaneous Elastic Moduli | |
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| Elastic Pseudomoduli | |
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| Elastic Moduli of Isotropic Elasticity | |
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| Elastic Moduli in Terms of Principal Stretches | |
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| Suggested Reading | |
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| Linear Elasticity | |
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| Governing Equations of Linear Elasticity | |
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| Elementary Theory of Isotropic Linear Elasticity | |
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| Elastic Energy in Linear Elasticity | |
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| Restrictions on the Elastic Constants | |
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| Compatibility Relations | |
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| Compatibility Conditions: Cesaro Integrals | |
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| Beltrami-Michell Compatibility Equations | |
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| Navier Equations of Motion | |
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| Uniqueness of Solution to Linear Elastic Boundary Value Problem | |
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| Potential Energy and Variational Principle | |
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| Betti's Theorem of Linear Elasticity | |
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| Plane Strain | |
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| Governing Equations of Plane Elasticity | |
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| Thermal Distortion of a Simple Beam | |
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| Suggested Reading | |
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| Elastic Beam Problems | |
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| A Simple 2D Beam Problem | |
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| Polynomial Solutions to [down triangle, open superscript 4 phi] = 0 | |
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| A Simple Beam Problem Continued | |
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| Beam Problems with Body Force Potentials | |
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| Beam under Fourier Loading | |
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| Complete Boundary Value Problems for Beams | |
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| Suggested Reading | |
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| Solutions in Polar Coordinates | |
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| Polar Components of Stress and Strain | |
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| Plate with Circular Hole | |
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| Degenerate Cases of Solution in Polar Coordinates | |
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| Curved Beams: Plane Stress | |
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| Axisymmetric Deformations | |
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| Suggested Reading | |
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| Torsion and Bending of Prismatic Rods | |
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| Torsion of Prismatic Rods | |
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| Elastic Energy of Torsion | |
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| Torsion of a Rod with Rectangular Cross Section | |
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| Torsion of a Rod with Elliptical Cross Section | |
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| Torsion of a Rod with Multiply Connected Cross Sections | |
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| Bending of a Cantilever | |
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| Elliptical Cross Section | |
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| Suggested Reading | |
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| Semi-Infinite Media | |
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| Fourier Transform of Biharmonic Equation | |
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| Loading on a Half-Plane | |
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| Half-Plane Loading: Special Case | |
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| Symmetric Half-Plane Loading | |
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| Half-Plane Loading: Alternative Approach | |
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| Additional Half-Plane Solutions | |
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| Infinite Strip | |
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| Suggested Reading | |
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| Isotropic 3D Solutions | |
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| Displacement-Based Equations of Equilibrium | |
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| Boussinesq-Papkovitch Solutions | |
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| Spherically Symmetrical Geometries | |
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| Pressurized Sphere: Stress-Based Solution | |
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| Spherical Indentation | |
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| Point Forces on Elastic Half-Space | |
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| Suggested Reading | |
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| Anisotropic 3D Solutions | |
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| Point Force | |
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| Green's Function | |
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| Isotropic Green's Function | |
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| Suggested Reading | |
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| Plane Contact Problems | |
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| Wedge Problem | |
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| Distributed Contact Forces | |
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| Displacement-Based Contact: Rigid Flat Punch | |
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| Suggested Reading | |
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| Deformation of Plates | |
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| Stresses and Strains of Bent Plates | |
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| Energy of Bent Plates | |
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| Equilibrium Equations for a Plate | |
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| Shear Forces and Bending and Twisting Moments | |
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| Examples of Plate Deformation | |
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| Rectangular Plates | |
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| Suggested Reading | |
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| Micromechanics | |
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| Dislocations and Cracks: Elementary Treatment | |
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| Dislocations | |
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| Tensile Cracks | |
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| Suggested Reading | |
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| Dislocations in Anisotropic Media | |
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| Dislocation Character and Geometry | |
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| Dislocations in Isotropic Media | |
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| Planar Geometric Theorem | |
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| Applications of the Planar Geometric Theorem | |
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| A 3D Geometrical Theorem | |
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| Suggested Reading | |
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| Cracks in Anisotropic Media | |
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| Dislocation Mechanics: Reviewed | |
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| Freely Slipping Crack | |
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| Crack Extension Force | |
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| Crack Faces Loaded by Tractions | |
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| Stress Intensity Factors and Crack Extension Force | |
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| Crack Tip Opening Displacement | |
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| Dislocation Energy Factor Matrix | |
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| Inversion of a Singular Integral Equation | |
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| 2D Anisotropic Elasticity - Stroh Formalism | |
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| Suggested Reading | |
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| The Inclusion Problem | |
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| The Problem | |
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| Eshelby's Solution Setup | |
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| Calculation of the Constrained Fields: u[superscript c], e[superscript c], and [sigma superscript c] | |
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| Components of the Eshelby Tensor for Ellipsoidal Inclusion | |
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| Elastic Energy of an Inclusion | |
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| Inhomogeneous Inclusion: Uniform Transformation Strain | |
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| Nonuniform Transformation Strain Inclusion Problem | |
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| Inclusions in Isotropic Media | |
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| Suggested Reading | |
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| Forces and Energy in Elastic Systems | |
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| Free Energy and Mechanical Potential Energy | |
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| Forces of Translation | |
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| Interaction Between Defects and Loading Mechanisms | |
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| Elastic Energy of a Dislocation | |
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| In-Plane Stresses of Straight Dislocation Lines | |
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| Chemical Potential | |
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| Applications of the J Integral | |
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| Suggested Reading | |
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| Micropolar Elasticity | |
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| Introduction | |
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| Basic Equations of Couple-Stress Elasticity | |
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| Displacement Equations of Equilibrium | |
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| Correspondence Theorem of Couple-Stress Elasticity | |
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| Plane Strain Problems of Couple-Stress Elasticity | |
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| Edge Dislocation in Couple-Stress Elasticity | |
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| Edge Dislocation in a Hollow Cylinder | |
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| Governing Equations for Antiplane Strain | |
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| Antiplane Shear of Circular Annulus | |
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| Screw Dislocation in Couple-Stress Elasticity | |
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| Configurational Forces in Couple-Stress Elasticity | |
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| Energy-Momentum Tensor of a Couple-Stress Field | |
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| Basic Equations of Micropolar Elasticity | |
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| Noether's Theorem of Micropolar Elasticity | |
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| Conservation Integrals in Micropolar Elasticity | |
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| Conservation Laws for Plane Strain Micropolar Elasticity | |
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| M Integral of Micropolar Elasticity | |
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| Suggested Reading | |
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| Thin Films and Interfaces | |
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| Dislocations in Bimaterials | |
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| Introduction | |
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| Screw Dislocation Near a Bimaterial Interface | |
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| Edge Dislocation (b[subscript x]) Near a Bimaterial Interface | |
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| Edge Dislocation (b[subscript y]) Near a Bimaterial Interface | |
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| Strain Energy of a Dislocation Near a Bimaterial Interface | |
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| Suggested Reading | |
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| Strain Relaxation in Thin Films | |
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| Dislocation Array Beneath the Free Surface | |
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| Energy of a Dislocation Array | |
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| Strained-Layer Epitaxy | |
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| Conditions for Dislocation Array Formation | |
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| Frank and van der Merwe Energy Criterion | |
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| Gradual Strain Relaxation | |
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| Stability of Array Configurations | |
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| Stronger Stability Criteria | |
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| Further Stability Bounds | |
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| Suggested Reading | |
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| Stability of Planar Interfaces | |
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| Stressed Surface Problem | |
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| Chemical Potential | |
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| Surface Diffusion and Interface Stability | |
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| Volume Diffusion and Interface Stability | |
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| 2D Surface Profiles and Surface Stability | |
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| Asymptotic Stresses for 1D Surface Profiles | |
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| Suggested Reading | |
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| Plasticity and Viscoplasticity | |
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| Phenomenological Plasticity | |
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| Yield Criteria for Multiaxial Stress States | |
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| Von Mises Yield Criterion | |
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| Tresca Yield Criterion | |
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| Mohr-Coulomb Yield Criterion | |
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| Gurson Yield Criterion for Porous Metals | |
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| Anisotropic Yield Criteria | |
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| Elastic-Plastic Constitutive Equations | |
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| Isotropic Hardening | |
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| Kinematic Hardening | |
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| Constitutive Equations for Pressure-Dependent Plasticity | |
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| Nonassociative Plasticity | |
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| Plastic Potential for Geomaterials | |
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| Rate-Dependent Plasticity | |
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| Deformation Theory of Plasticity | |
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| J[subscript 2] Corner Theory | |
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| Rate-Dependent Flow Theory | |
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| Elastic and Plastic Constitutive Contributions | |
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| A Rate Tangent Integration | |
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| Plastic Void Growth | |
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| Suggested Reading | |
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| Micromechanics of Crystallographic Slip | |
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| Early Observations | |
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| Dislocations | |
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| Other Strengthening Mechanisms | |
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| Measurements of Latent Hardening | |
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| Observations of Slip in Single Crystals and Polycrystals at Modest Strains | |
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| Deformation Mechanisms in Nanocrystalline Grains | |
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| Suggested Reading | |
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| Crystal Plasticity | |
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| Basic Kinematics | |
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| Stress and Stress Rates | |
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| Convected Elasticity | |
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| Rate-Dependent Slip | |
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| Crystalline Component Forms | |
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| Suggested Reading | |
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| The Nature of Crystalline Deformation: Localized Plastic Deformation | |
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| Perspectives on Nonuniform and Localized Plastic Flow | |
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| Localized Deformation in Single Slip | |
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| Localization in Multiple Slip | |
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| Numerical Results for Crystalline Deformation | |
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| Suggested Reading | |
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| Polycrystal Plasticity | |
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| Perspectives on Polycrystalline Modeling and Texture Development | |
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| Polycrystal Model | |
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| Extended Taylor Model | |
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| Model Calculational Procedure | |
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| Deformation Theories and Path-Dependent Response | |
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| Suggested Reading | |
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| Laminate Plasticity | |
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| Laminate Model | |
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| Additional Kinematical Perspective | |
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| Final Constitutive Forms | |
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| Suggested Reading | |
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| Biomechanics | |
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| Mechanics of a Growing Mass | |
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| Introduction | |
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| Continuity Equation | |
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| Reynolds Transport Theorem | |
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| Momentum Principles | |
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| Energy Equation | |
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| Entropy Equation | |
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| General Constitutive Framework | |
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| Multiplicative Decomposition of Deformation Gradient | |
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| Density Expressions | |
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| Elastic Stress Response | |
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| Partition of the Rate of Deformation | |
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| Elastic Moduli Tensor | |
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| Elastic Strain Energy Representation | |
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| Evolution Equation for Stretch Ratio | |
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| Suggested Reading | |
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| Constitutive Relations for Membranes | |
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| Biological Membranes | |
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| Membrane Kinematics | |
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| Constitutive Laws for Membranes | |
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| Limited Area Compressibility | |
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| Simple Triangular Networks | |
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| Suggested Reading | |
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| Solved Problems | |
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| Solved Problems for Chapters 1-33 | |
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| Bibliography | |
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| Index | |