Front Cover -- Introduction to Continuum Mechanics -- Copyright Page -- Table of Contents -- Preface to the Fourth Edition -- Chapter 1: Introduction -- 1.1 Introduction -- 1.2 What is Continuum Mechanics? -- Chapter 2: Tensors -- Part A: Indicial Notation -- 2.1 Summation Convention, Dummy Indices -- 2.2 Free Indices -- 2.3 The Kronecker Delta -- 2.4 The Permutation Symbol -- 2.5 Indicial Notation Manipulations -- Problems For Part A -- Part B: Tensors -- 2.6 Tensor: A Linear Transformation -- 2.7 Components of a Tensor -- 2.8 Components of a Transformed Vector -- 2.9 Sum of Tensors -- 2.10 Product of Two Tensors -- 2.11 Transpose of A Tensor -- 2.12 Dyadic Product of Vectors -- 2.13 Trace of A Tensor -- 2.14 Identity Tensor and Tensor Inverse -- 2.15 Orthogonal Tensors -- 2.16 Transformation Matrix Between Two Rectangular Cartesian Coordinate Systems -- 2.17 Transformation Law for Cartesian Components of A Vector -- 2.18 Transformation Law for Cartesian Components of a Tensor -- 2.19 Defining Tensor by Transformation Laws -- 2.20 Symmetric and Antisymmetric Tensors -- 2.21 The Dual Vector of an Antisymmetric Tensor -- 2.22 Eigenvalues and Eigenvectors of a Tensor -- 2.23 Principal Values and Principal Directions of Real Symmetric Tensors -- 2.24 Matrix of a Tensor with Respect to Principal Directions -- 2.25 Principal Scalar Invariants of a Tensor -- Problems for Part B -- Part C: Tensor Calculus -- 2.26 Tensor-Valued Functions of a Scalar -- 2.27 Scalar Field and Gradient of a Scalar Function -- 2.28 Vector Field and Gradient of a Vector Function -- 2.29 Divergence of a Vector Field and Divergence of a Tensor Field -- 2.30 Curl of a Vector Field -- 2.31 Laplacian of a Scalar Field -- 2.32 Laplacian of a Vector Field -- Problems for Part C -- Part D: Curvilinear Coordinates -- 2.33 Polar Coordinates -- 2.34 Cylindrical Coordinates.

2.35 Spherical Coordinates -- Problems for Part D -- Chapter 3: Kinematics of a Continuum -- 3.1 Description of Motions of a Continuum -- 3.2 Material Description and Spatial Description -- 3.3 Material Derivative -- 3.4 Acceleration of a Particle -- 3.5 Displacement Field -- 3.6 Kinematic Equation for Rigid Body Motion -- 3.7 Infinitesimal Deformation -- 3.8 Geometrical Meaning of the Components of the Infinitesimal Strain Tensor -- 3.9 Principal Strain -- 3.10 Dilatation -- 3.11 The Infinitesimal Rotation Tensor -- 3.12 Time Rate of Change of a Material Element -- 3.13 The Rate of Deformation Tensor -- 3.14 The Spin Tensor and the Angular Velocity Vector -- 3.15 Equation of Conservation of Mass -- 3.16 Compatibility Conditions for Infinitesimal Strain Components -- 3.17 Compatibility Condition for Rate of Deformation Components -- 3.18 Deformation Gradient -- 3.19 Local Rigid Body Motion -- 3.20 Finite Deformation -- 3.21 Polar Decomposition Theorem -- 3.22 Calculation of Stretch and Rotation Tensors from the Deformation Gradient -- 3.23 Right Cauchy-Green Deformation Tensor -- 3.24 Lagrangian Strain Tensor -- 3.25 Left Cauchy-Green Deformation Tensor -- 3.26 Eulerian Strain Tensor -- 3.27 Change of Area Due to Deformation -- 3.28 Change of Volume Due to Deformation -- 3.29 Components of Deformation Tensors in Other Coordinates -- 3.30 Current Configuration as the Reference Configuration -- Appendix 3.1: Necessary and Sufficient Conditions for Strain Compatibility -- Appendix 3.2: Positive Definite Symmetric Tensors -- Appendix 3.3: The Positive Definite Root of U2 = D -- Problems for Chapter 3 -- Chapter 4: Stress and Integral Formulations of General Principles -- 4.1 Stress Vector -- 4.2 Stress Tensor -- 4.3 Components of Stress Tensor -- 4.4 Symmetry of Stress Tensor: Principle of Moment of Momentum -- 4.5 Principal Stresses.

4.6 Maximum Shearing Stresses -- 4.7 Equations of Motion: Principle of Linear Momentum -- 4.8 Equations of Motion in Cylindrical and Spherical Coordinates -- 4.9 Boundary Condition for the Stress Tensor -- 4.10 Piola Kirchhoff Stress Tensors -- 4.11 Equations of Motion Written with Respect to the Reference Configuration -- 4.12 Stress Power -- 4.13 Stress Power in Terms of the Piola-Kirchhoff Stress Tensors -- 4.14 Rate of Heat Flow into a Differential Element by Conduction -- 4.15 Energy Equation -- 4.16 Entropy Inequality -- 4.17 Entropy Inequality in Terms of the Helmholtz Energy Function -- 4.18 Integral Formulations of the General Principles of Mechanics -- Appendix 4.1: Determination of Maximum Shearing Stress and the Planes on Which It Acts -- Problems for Chapter 4 -- Chapter 5: The Elastic Solid -- 5.1 Mechanical Properties -- 5.2 Linearly Elastic Solid -- Part A: Isotropic Linearly Elastic Solid -- 5.3 Isotropic Linearly Elastic Solid -- 5.4 Young's Modulus, Poisson's Ratio, Shear Modulus, and Bulk Modulus -- 5.5 Equations of the Infinitesimal Theory of Elasticity -- 5.6 Navier Equations of Motion for Elastic Medium -- 5.7 Navier Equations in Cylindrical and Spherical Coordinates -- 5.8 Principle of Superposition -- A.1 Plane Elastic Waves -- 5.9 Plane Irrotational Waves -- 5.10 Plane Equivoluminal Waves -- 5.11 Reflection of Plane Elastic Waves -- 5.12 Vibration of an Infinite Plate -- A.2 Simple Extension, Torsion, and Pure Bending -- 5.13 Simple Extension -- 5.14 Torsion of a Circular Cylinder -- 5.15 Torsion of a Noncircular Cylinder: St. Venant's Problem -- 5.16 Torsion of Elliptical Bar -- 5.17 Prandtl's Formulation of the Torsion Problem -- 5.18 Torsion of a Rectangular Bar -- 5.19 Pure Bending of a Beam -- A.3 Plane Stress and Plane Strain Solutions -- 5.20 Plane Strain Solutions -- 5.21 Rectangular Beam Bent by End Couples.

5.22 Plane Stress Problem -- 5.23 Cantilever Beam with End Load -- 5.24 Simply Supported Beam Under Uniform Load -- 5.25 Slender Bar Under Concentrated Forces and St. Venant's Principle -- 5.26 Conversion for Strains Between Plane Strain and Plane Stress Solutions -- 5.27 Two-Dimensional Problems in Polar Coordinates -- 5.28 Stress Distribution Symmetrical About an Axis -- 5.29 Displacements for Symmetrical Stress Distribution in Plane Stress Solution -- 5.30 Thick-Walled Circular Cylinder Under Internal and External Pressure -- 5.31 Pure Bending of a Curved Beam -- 5.32 Initial Stress in a Welded Ring -- 5.33 Airy Stress Function phivf(r)cosntheta and phivf(r)sinntheta -- 5.34 Stress Concentration Due to a Small Circular Hole in a Plate Under Tension -- 5.35 Stress Concentration Due to a Small Circular Hole in a Plate Under Pure Shear -- 5.36 Simple Radial Distribution of Stresses in a Wedge Loaded at the Apex -- 5.37 Concentrated Line Load on a 2-D Half-Space: the Flamont Problem -- A.4 Elastostatic Problems Solved with Potential Functions -- 5.38 Fundamental Potential Functions for Elastostatic Problems -- 5.39 Kelvin Problem: Concentrated Force at the Interior of an Infinite Elastic Space -- 5.40 Boussinesq Problem: Normal Concentrated Load on an Elastic Half-Space -- 5.41 Distributive Normal Load On The Surface Of An Elastic Half-Space -- 5.42 Hollow Sphere Subjected to Uniform Internal and External Pressure -- 5.43 Spherical Hole in a Tensile Field -- 5.44 Indentation by a Rigid Flat-Ended Smooth Indenter on an Elastic Half-Space -- 5.45 Indentation by a Smooth Rigid Sphere on an Elastic Half-Space -- Appendix 5A.1: Solution of the Integral Equation in Section 5.45 -- Problems for Chapter 5, Part A, Sections 5.1-5.8 -- Problems for Chapter 5, Part A, Sections 5.9-5.12 (A.1) -- Problems for Chapter 5, Part A, Sections 5.13-5.19 (A.2).

Problems for Chapter 5, Part A, Sections 5.20-5.37 (A.3) -- Problems for Chapter 5, Part A, Sections 5.38-5.46 (A.4) -- Part B: Anisotropic Linearly Elastic Solid -- 5.46 Constitutive Equations for an Anisotropic Linearly Elastic Solid -- 5.47 Plane of Material Symmetry -- 5.48 Constitutive Equation for a Monoclinic Linearly Elastic Solid -- 5.49 Constitutive Equation for an Orthotropic Linearly Elastic Solid -- 5.50 Constitutive Equation for a Transversely Isotropic Linearly Elastic Material -- 5.51 Constitutive Equation for an Isotropic Linearly Elastic Solid -- 5.52 Engineering Constants for an Isotropic Linearly Elastic Solid -- 5.53 Engineering Constants for a Transversely Isotropic Linearly Elastic Solid -- 5.54 Engineering Constants for an Orthotropic Linearly Elastic Solid -- 5.55 Engineering Constants for a Monoclinic Linearly Elastic Solid -- Problems for Part B -- Part C: Isotropic Elastic Solid Under Large Deformation -- 5.56 Change of Frame -- 5.57 Constitutive Equation for an Elastic Medium Under Large Deformation -- 5.58 Constitutive Equation for an Isotropic Elastic Medium -- 5.59 Simple Extension of an Incompressible Isotropic Elastic Solid -- 5.60 Simple Shear of an Incompressible Isotropic Elastic Rectangular Block -- 5.61 Bending of an Incompressible Isotropic Rectangular Bar -- 5.62 Torsion and Tension of an Incompressible Isotropic Solid Cylinder -- Appendix 5C.1: Representation of Isotropic Tensor-Valued Functions -- Problems for Part C -- Chapter 6: Newtonian Viscous Fluid -- 6.1 Fluids -- 6.2 Compressible and Incompressible Fluids -- 6.3 Equations of Hydrostatics -- 6.4 Newtonian Fluids -- 6.5 Interpretation of lambda and mu -- 6.6 Incompressible Newtonian Fluid -- 6.7 Navier-Stokes Equations for Incompressible Fluids -- 6.8 Navier-Stokes Equations for Incompressible Fluids in Cylindrical and Spherical Coordinates.

6.9 Boundary Conditions.