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| Preface to the Third Edition |
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| Preface to the Second Edition |
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| Preface to the First Edition |
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| Acknowledgments |
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| Authors |
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| Nomenclature |
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1 | (4) |
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1 | (1) |
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2 | (1) |
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3 | (2) |
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5 | (48) |
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Scalars, Vectors and Cartesian Tensors |
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5 | (2) |
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Tensor Algebra in Symbolic Notation - Summation Convention |
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7 | (9) |
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9 | (1) |
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10 | (1) |
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10 | (1) |
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11 | (5) |
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16 | (3) |
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Matrices and Determinants |
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19 | (6) |
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Transformations of Cartesian Tensors |
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25 | (5) |
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Principal Values and Principal Directions |
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30 | (7) |
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Tensor Fields, Tensor Calculus |
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37 | (3) |
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Integral Theorems of Gauss and Stokes |
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40 | (13) |
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42 | (11) |
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53 | (50) |
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Body and Surface Forces, Mass Density |
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53 | (1) |
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54 | (2) |
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56 | (5) |
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Force and Moment Equilibrium; Stress Tensor Symmetry |
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61 | (2) |
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Stress Transformation Laws |
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63 | (3) |
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Principal Stresses; Principal Stress Directions |
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66 | (5) |
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Maximum and Minimum Stress Values |
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71 | (3) |
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Mohr's Circles for Stress |
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74 | (6) |
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80 | (5) |
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Deviator and Spherical Stress States |
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85 | (2) |
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87 | (16) |
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90 | (13) |
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Kinematics of Deformation and Motion |
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103 | (64) |
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Particles, Configurations, Deformations and Motion |
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103 | (1) |
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Material and Spatial Coordinates |
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104 | (4) |
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Langrangian and Eulerian Descriptions |
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108 | (2) |
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110 | (1) |
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111 | (5) |
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Deformation Gradients, Finite Strain Tensors |
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116 | (4) |
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Infinitesimal Deformation Theory |
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120 | (8) |
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128 | (3) |
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131 | (3) |
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Rotation Tensor, Stretch Tensors |
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134 | (3) |
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Velocity Gradient, Rate of Deformation, Vorticity |
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137 | (6) |
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Material Derivative of Line Elements, Areas, Volumes |
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143 | (24) |
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147 | (20) |
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Fundamental Laws and Equations |
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167 | (44) |
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Material Derivatives of Line, Surface and Volume Integrals |
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167 | (2) |
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Conservation of Mass, Continuity Equation |
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169 | (2) |
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Linear Momentum Principle, Equations of Motion |
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171 | (1) |
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Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion |
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172 | (4) |
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Moment of Momentum (Angular Momentum) Principle |
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176 | (1) |
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Law of Conservation of Energy, The Energy Equation |
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177 | (2) |
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Entropy and the Clausius-Duhem Equation |
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179 | (3) |
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182 | (4) |
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Restrictions on Elastic Materials by the Second Law of Thermodynamics |
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186 | (3) |
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189 | (7) |
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Restrictions on Constitutive Equations from Invariance |
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196 | (2) |
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198 | (13) |
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201 | (1) |
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202 | (9) |
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211 | (60) |
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Elasticity, Hooke's Law, Strain Energy |
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211 | (3) |
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Hooke's Law for Isotropic Media, Elastic Constants |
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214 | (5) |
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Elastic Symmetry; Hooke's Law for Anisotropic Media |
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219 | (4) |
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Isotropic Elastostatics and Elastodynamics, Superposition Principle |
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223 | (3) |
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226 | (12) |
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227 | (1) |
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228 | (6) |
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234 | (2) |
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236 | (2) |
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238 | (4) |
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242 | (10) |
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252 | (1) |
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Three-Dimensional Elasticity |
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253 | (18) |
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260 | (11) |
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271 | (14) |
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Viscous Stress Tensor, Stokesian, and Newtonian Fluids |
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271 | (2) |
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Basic Equations of Viscous Flow, Navier-Stokes Equations |
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273 | (2) |
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275 | (1) |
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Steady Flow, Irrotational Flow, Potential Flow |
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276 | (4) |
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The Bernoulli Equation, Kelvin's Theorem |
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280 | (5) |
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282 | (3) |
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285 | (24) |
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Molecular Approach to Rubber Elasticity |
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287 | (5) |
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A Strain Energy Theory for Nonlinear Elasticity |
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292 | (4) |
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Specific Forms of the Strain Energy |
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296 | (1) |
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Exact Solution for an Incompressible, Neo-Hookean Material |
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297 | (12) |
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302 | (2) |
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304 | (5) |
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309 | (34) |
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Viscoelastic Constitutive Equations in Linear Differential Operator Form |
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309 | (2) |
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One-Dimensional Theory, Mechanical Models |
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311 | (4) |
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315 | (3) |
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Superposition Principle, Hereditary Integrals |
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318 | (2) |
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Harmonic Loadings, Complex Modulus, and Complex Compliance |
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320 | (4) |
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Three-Dimensional Problems, The Correspondence Principle |
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324 | (19) |
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330 | (1) |
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331 | (12) |
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Appendix A: General Tensors |
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343 | (18) |
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A.1 Representation of Vectors in General Bases |
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343 | (2) |
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A.2 The Dot Product and the Reciprocal Basis |
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345 | (1) |
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A.3 Components of a Tensor |
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346 | (2) |
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A.4 Determination of the Base Vectors |
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348 | (2) |
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A.5 Derivatives of Vectors |
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350 | (3) |
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A.5.1 Time Derivative of a Vector |
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350 | (1) |
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A.5.2 Covariant Derivative of a Vector |
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351 | (2) |
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353 | (2) |
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A.6.1 Types of Christoffel Symbols |
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353 | (1) |
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A.6.2 Calculation of the Christoffel Symbols |
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354 | (1) |
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A.7 Covariant Derivatives of Tensors |
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355 | (1) |
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A.8 General Tensor Equations |
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356 | (2) |
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A.9 General Tensors and Physical Components |
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358 | (3) |
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360 | (1) |
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Appendix B: Viscoelastic Creep and Relaxation |
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361 | (4) |
| Index |
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365 | |
