Elements of Continuum Mechanics.

Cover -- Title -- Copyright -- Foreword -- Contents -- Preface -- Acknowledgments -- Chapter 1 Introduction -- 1.1 What is Mechanics? -- 1.2 Continuum Mechanics -- 1.3 An Example of an Ad-Hoc Approach -- Chapter 2 Mathematical Preliminaries -- 2.1 Summation Convention, Dummy Indices -- 2.2 Free Indices -- 2.3 Kronecker Delta -- 2.4 Index Notation -- 2.5 Permutation Symbol -- 2.6 Manipulations with the Indicial Notations -- 2.7 Translation and Rotation of Coordinate Axes -- 2.8 Tensors -- 2.9 The Divergence Theorem -- 2.10 Differentiation of Tensor Fields -- References -- Exercises -- Chapter 3 Kinematics -- 3.1 Description of Motion of a Continuum -- 3.2 Referential and Spatial Descriptions -- 3.3 Displacement Vector -- 3.4 Restrictions on Continuous Deformation of a Deformable Body -- 3.5 Material Derivative -- 3.6 Finding Acceleration of a Particle from a Given Velocity Field -- 3.7 Deformation Gradient -- 3.8 Strain Tensors -- 3.9 Principal Strains -- 3.10 Deformation of Areas and Volumes -- 3.11 Mass Density, Equation of Continuity -- 3.12 Rate of Deformation, Strain-Rate Tensor, Spin -- 3.13 Polar Decomposition -- 3.14 Infinitesimal Deformations -- 3.15 Infinitesimal Deformations Superimposed upon Finite Deformations -- 3.16 Volumetric and Deviatoric Strains -- 3.17 Transformation of Tensors Under a Change of Bases -- 3.18 Plane Strain Deformation -- Appendix A: Solution of a Cubic Equation -- References -- Exercises -- Chapter 4 The Balance Laws, Stress Tensors -- 4.1 Kinetics of a Continuous Media -- 4.2 Traction Boundary Conditions -- 4.3 The Nominal Stress Tensor -- 4.4 Transformation of Stress Tensors Under the Rotation of Axes -- 4.5 Principal Stresses -- Maximum Shear Stress -- 4.6 Relations Among Stress Tensors for Infinitesimal Deformations -- 4.7 Plane Stress -- 4.8 Deviatoric Stress, von-Mises Stress -- 4.9 Balance of Energy.

4.10 Entropy Inequality, The Clausius-Duhem Inequality -- 4.11 Summary of Equations Governing Deformations of a Body -- 4.12 Nonuniqueness of Solutions for Static Problems -- Appendix B: The Transport Theorem -- Exercises -- Chapter 5 Constitutive Relations -- 5.1 Introductory Remarks -- 5.2 Thermoelastic Material -- 5.3 Principle of Material Objectivity -- 5.4 Linear Constitutive Relations for Finite Deformations of a Thermoelastic Body -- 5.5 Isotropic Thermoelastic Materials -- 5.6 Comparison of Results from Four Linear Constitutive Relations in Isotropic Finite Elasticity -- 5.7 Transversely Isotropic Thermoelastic Materials -- 5.8 Orthotropic Thermoelastic Materials -- 5.9 Coincidence of Principal Axes of Stress and Strain in Isotropic Elastic Materials -- 5.10 Coincidence of Principal Axes of Stress and Strain in Transversely Isotropic Elastic Materials -- 5.11 Incompressible Elastic Materials -- 5.12 Comparison of Results from Constitutive Relations -- 5.13 Constitutive Relations for Infinitesimal Deformations of Elastic Materials -- 5.14 Constitutive Relations for Special Isotropic Nonlinear Elastic Materials -- 5.15 Infinitesimal Deformations Superimposed upon Finite Deformations of an Isotropic Elastic Body -- 5.16 Constitutive Relations for Plane Deformations of a Thermoelastic Body -- 5.17 Thermoviscoelastic Materials -- 5.18 Summary -- References -- Exercises -- Chapter 6 Torsion of a Circular Cylinder -- 6.1 Torsion of a Linear Elastic Circular Cylinder -- 6.2 Torsion of a Second-Order Elastic Circular Cylinder -- 6.3 Infinitesimal Twist of a Finitely Stretched Circular Cylinder -- 6.4 Finite Torsion of a Circular Cylinder -- Appendix C: A Uniqueness Theorem -- References -- Exercise -- Chapter 7 Fluid Flow -- 7.1 Steady Flow Between Two Parallel Plates -- 7.2 Steady Isothermal Flow of an Incompressible Fluid Down an Inclined Plane.

7.3 Steady Flow of an Incompressible Fluid in a Horizontal Circular Pipe -- Exercise -- Chapter 8 Bending of Beams -- 8.1 Bending of a Rectangular Beam -- 8.2 Bending of a Nonlinear Elastic Rectangular Beam -- 8.3 Airy Stress Function for Bending of a Beam -- Exercises -- Chapter 9 Wave Propagation -- 9.1 Singular Surface -- 9.2 Kinematics of a Singular Surface -- 9.3 Acceleration Waves in Linear Elasticity -- 9.4 Progressive Waves -- 9.5 Incompressible Linear Elastic Materials -- 9.6 Acceleration Waves in Nonlinear Elastic Bodies -- 9.7 Infinitesimal Deformations Superimposed upon Finite Deformations -- Exercises -- Chapter 10 Spherical and Cylindrical Pressure Vessels -- 10.1 Radial Expansion of a Spherical Pressure Vessel -- 10.2 Radial Expansion of an Incompressible Hookean Sphere with Shear Modulus a Function of Radius -- 10.3 Radial Expansion of a Cylindrical Pressure Vessel -- 10.4 Radial Expansion of an Inhomogeneous and Incompressible Hookean Cylinder -- 10.5 Finite Radial Expansion of a NeoHookean Cylinder -- Index -- A -- B -- C -- D -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Y.

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