Continuum Mechanics for Engineers

Cover\r......Page 1
Title\r......Page 2
Copyright......Page 3
Preface to Second Edition......Page 4
Preface to the First Edition......Page 6
Authors......Page 8
Nomenclature......Page 9
Contents......Page 12
1.1 The Continuum Concept......Page 15
1.2 Continuum Mechanics......Page 16
2.1 Scalars, Vectors, and Cartesian Tensors......Page 17
2.2 Tensor Algebra in Symbolic Notation — Summation Convention......Page 18
Solution:......Page 20
KRONECKER DELTA......Page 21
PERMUTATION SYMBOL......Page 22
IDENTITY.............Page 23
Example 2.2-2......Page 25
Solution......Page 26
2.3 Indicial Notation......Page 27
Example 2.3-1......Page 28
Solution......Page 29
2.4 Matrices and Determinants......Page 30
Solution......Page 31
Solution......Page 32
Solution......Page 34
Solution......Page 35
2.5 Transformations of Cartesian Tensors......Page 36
Example 2.5-2......Page 41
2.6 Principal Values and Principal Directions of Symmetric Second-Order Tensors......Page 42
Solution......Page 45
Example 2.6-2......Page 46
Solution......Page 47
2.7 Tensor Fields, Tensor Calculus......Page 48
2.8 Integral Theorems of Gauss and Stokes......Page 50
Problems......Page 51
3.1 Body and Surface Forces, Mass Density......Page 61
3.2 Cauchy Stress Principle......Page 62
3.3 The Stress Tensor......Page 65
Stress Tensor......Page 68
Solution......Page 70
3.4 Force and Moment Equilibrium, Stress Tensor Symmetry......Page 71
3.5 Stress Transformation Laws......Page 73
Solution......Page 74
Solution......Page 75
3.6 Principal Stresses, Principal Stress Directions......Page 76
Solution......Page 82
3.7 Maximum and Minimum Stress Values......Page 84
3.8 Mohr’s Circles For Stress......Page 87
Solution......Page 92
3.9 Plane Stress......Page 94
Example 3.9-1......Page 98
3.10 Deviator and Spherical Stress States......Page 99
3.11 Octahedral Shear Stress......Page 101
Problems......Page 103
4.1 Particles, Configurations, Deformation, and Motion......Page 116
4.2 Material and Spatial Coordinates......Page 117
Solution......Page 121
4.3 Lagrangian and Eulerian Descriptions......Page 122
Solution......Page 123
4.4 The Displacement Field......Page 124
Solution......Page 125
4.5 The Material Derivative......Page 126
Solution......Page 127
Solution......Page 128
4.6 Deformation Gradients, Finite Strain Tensors......Page 129
Solution......Page 133
4.7 Infinitesimal Deformation Theory......Page 135
Solution......Page 142
4.8 Stretch Ratios......Page 144
Solution......Page 147
Solution......Page 148
4.9 Rotation Tensor, Stretch Tensors......Page 149
Solution......Page 151
4.10 Velocity Gradient, Rate of Deformation, Vorticity......Page 153
4.11 Material Derivative of Line Elements, Areas, Volumes......Page 159
Problems......Page 162
5.1 Balance Laws, Field Equations, Constitutive Equations......Page 181
5.2 Material Derivatives of Line, Surface, and Volume Integrals......Page 182
5.3 Conservation of Mass, Continuity Equation......Page 184
Solution......Page 186
5.4 Linear Momentum Principle, Equations of Motion......Page 187
5.5 The Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion......Page 188
5.6 Moment of Momentum (Angular Momentum) Principle......Page 193
5.7 Law of Conservation of Energy, The Energy Equation......Page 194
5.8 Entropy and the Clausius-Duhem Equation......Page 198
5.9 Restrictions on Elastic Materials by the Second Law of Thermodynamics......Page 202
5.10 Invariance......Page 206
Solution......Page 209
5.11 Restrictions on Constitutive Equations from Invariance......Page 216
5.12 Constitutive Equations......Page 219
Problems......Page 222
6.1 Elasticity, Hooke’s Law, Strain Energy......Page 230
6.2 Hooke’s Law for Isotropic Media, Elastic Constants......Page 235
Solution......Page 236
6.3 Elastic Symmetry; Hooke’s Law for Anisotropic Media......Page 241
6.4 Isotropic Elastostatics and Elastodynamics, Superposition Principle......Page 246
6.5 Plane Elasticity......Page 249
6.6 Linear Thermoelasticity......Page 253
6.7 Airy Stress Function......Page 255
Solution......Page 256
Example 6.7-2......Page 257
Solution......Page 258
Solution......Page 261
Example 6.7-4......Page 263
Solution......Page 264
Solution......Page 265
6.8 Torsion......Page 267
Solution......Page 273
6.9 Three-Dimensional Elasticity......Page 275
Solution......Page 279
Problems......Page 284
7.1 Viscous Stress Tensor, Stokesian, and Newtonian Fluids......Page 295
7.2 Basic Equationsof Viscous Flow, Navier-Stokes Equations......Page 298
7.3 Specialized Fluids......Page 300
7.4 Steady Flow, Irrotational Flow, Potential Flow......Page 301
Example 7.41......Page 302
Solution......Page 303
7.5 The Bernoulli Equation, Kelvin’s Theorem......Page 305
Problems......Page 306
8.1 Molecular Approach to Rubber Elasticity......Page 310
8.2 A Strain Energy Theory for Nonlinear Elasticity......Page 318
8.3 Specific Forms of the Strain Energy......Page 323
8.4 Exact Solution for an Incompressible, Neo-Hookean Material......Page 325
Problems......Page 333
9.1 Introduction......Page 338
9.2 Viscoelastic Constitutive Equations in Linear Differential Operator Form......Page 339
9.3 One-Dimensional Theory, Mechanical Models......Page 341
9.4 Creep and Relaxation......Page 345
9.5 Superposition Principle, Hereditary Integrals......Page 351
9.6 Harmonic Loadings, Complex Modulus, and Complex Compliance......Page 353
9.7 Three-Dimensional Problems, The Correspondence Principle......Page 359
Solution......Page 362
Solution......Page 365
References......Page 366
Problems......Page 367