Continuum Mechanics for Engineers

G. Thomas Mase0-8493-1855-6

The second edition of this popular text continues to provide a solid, fundamental introduction to the mathematics, laws, and applications of continuum mechanics. With the addition of three new chapters and eight new sections to existing chapters, the authors now provide even better coverage of continuum mechanics basics and focus even more attention on its applications.Beginning with the basic mathematical tools needed-including matrix methods and the algebra and calculus of Cartesian tensors-the authors develop the principles of stress, strain, and motion and derive the fundamental physical laws relating to continuity, energy, and momentum. With this basis established, they move to their expanded treatment of applications, including linear and nonlinear elasticity, fluids, and linear viscoelasticityMastering the contents of Continuum Mechanics: Second Edition provides the reader with the foundation necessary to be a skilled user of today’s advanced design tools, such as sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships. With its ample illustrations and exercises, it offers the ideal self-study vehicle for practicing engineers and an excellent introductory text for advanced engineering students.

---

Table of contents :
CONTINUUM MECHANICS for ENGINEERS……Page 2
Preface to Second Edition……Page 5
Preface to the First Edition……Page 7
Authors……Page 9
Nomenclature……Page 10
Contents……Page 13
1.1 The Continuum Concept……Page 16
1.2 Continuum Mechanics……Page 17
2.1 Scalars, Vectors, and Cartesian Tensors……Page 18
2.2 Tensor Algebra in Symbolic Notation — Summation Convention……Page 19
Solution:……Page 21
KRONECKER DELTA……Page 22
PERMUTATION SYMBOL……Page 23
IDENTITY………….Page 24
Example 2.2-2……Page 26
Solution……Page 27
2.3 Indicial Notation……Page 28
Example 2.3-1……Page 29
Solution……Page 30
2.4 Matrices and Determinants……Page 31
Solution……Page 32
Solution……Page 33
Solution……Page 35
Solution……Page 36
2.5 Transformations of Cartesian Tensors……Page 37
Example 2.5-2……Page 42
2.6 Principal Values and Principal Directions of Symmetric Second-Order Tensors……Page 43
Solution……Page 46
Example 2.6-2……Page 47
Solution……Page 48
2.7 Tensor Fields, Tensor Calculus……Page 49
2.8 Integral Theorems of Gauss and Stokes……Page 51
Problems……Page 52
3.1 Body and Surface Forces, Mass Density……Page 62
3.2 Cauchy Stress Principle……Page 63
3.3 The Stress Tensor……Page 66
Stress Tensor……Page 69
Solution……Page 71
3.4 Force and Moment Equilibrium, Stress Tensor Symmetry……Page 72
3.5 Stress Transformation Laws……Page 74
Solution……Page 75
Solution……Page 76
3.6 Principal Stresses, Principal Stress Directions……Page 77
Solution……Page 83
3.7 Maximum and Minimum Stress Values……Page 85
3.8 Mohr’s Circles For Stress……Page 88
Solution……Page 93
3.9 Plane Stress……Page 95
Example 3.9-1……Page 99
3.10 Deviator and Spherical Stress States……Page 100
3.11 Octahedral Shear Stress……Page 102
Problems……Page 104
4.1 Particles, Configurations, Deformation, and Motion……Page 117
4.2 Material and Spatial Coordinates……Page 118
Solution……Page 122
4.3 Lagrangian and Eulerian Descriptions……Page 123
Solution……Page 124
4.4 The Displacement Field……Page 125
Solution……Page 126
4.5 The Material Derivative……Page 127
Solution……Page 128
Solution……Page 129
4.6 Deformation Gradients, Finite Strain Tensors……Page 130
Solution……Page 134
4.7 Infinitesimal Deformation Theory……Page 136
Solution……Page 143
4.8 Stretch Ratios……Page 145
Solution……Page 148
Solution……Page 149
4.9 Rotation Tensor, Stretch Tensors……Page 150
Solution……Page 152
4.10 Velocity Gradient, Rate of Deformation, Vorticity……Page 154
4.11 Material Derivative of Line Elements, Areas, Volumes……Page 160
Problems……Page 163
5.1 Balance Laws, Field Equations, Constitutive Equations……Page 182
5.2 Material Derivatives of Line, Surface, and Volume Integrals……Page 183
5.3 Conservation of Mass, Continuity Equation……Page 185
Solution……Page 187
5.4 Linear Momentum Principle, Equations of Motion……Page 188
5.5 The Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion……Page 189
5.6 Moment of Momentum (Angular Momentum) Principle……Page 194
5.7 Law of Conservation of Energy, The Energy Equation……Page 195
5.8 Entropy and the Clausius-Duhem Equation……Page 199
5.9 Restrictions on Elastic Materials by the Second Law of Thermodynamics……Page 203
5.10 Invariance……Page 207
Solution……Page 210
5.11 Restrictions on Constitutive Equations from Invariance……Page 217
5.12 Constitutive Equations……Page 220
Problems……Page 223
6.1 Elasticity, Hooke’s Law, Strain Energy……Page 231
6.2 Hooke’s Law for Isotropic Media, Elastic Constants……Page 236
Solution……Page 237
6.3 Elastic Symmetry; Hooke’s Law for Anisotropic Media……Page 242
6.4 Isotropic Elastostatics and Elastodynamics, Superposition Principle……Page 247
6.5 Plane Elasticity……Page 250
6.6 Linear Thermoelasticity……Page 254
6.7 Airy Stress Function……Page 256
Solution……Page 257
Example 6.7-2……Page 258
Solution……Page 259
Solution……Page 262
Example 6.7-4……Page 264
Solution……Page 265
Solution……Page 266
6.8 Torsion……Page 268
Solution……Page 274
6.9 Three-Dimensional Elasticity……Page 276
Solution……Page 280
Problems……Page 285
7.1 Viscous Stress Tensor, Stokesian, and Newtonian Fluids……Page 296
7.2 Basic Equationsof Viscous Flow, Navier-Stokes Equations……Page 299
7.3 Specialized Fluids……Page 301
7.4 Steady Flow, Irrotational Flow, Potential Flow……Page 302
Example 7.41……Page 303
Solution……Page 304
7.5 The Bernoulli Equation, Kelvin’s Theorem……Page 306
Problems……Page 307
8.1 Molecular Approach to Rubber Elasticity……Page 311
8.2 A Strain Energy Theory for Nonlinear Elasticity……Page 319
8.3 Specific Forms of the Strain Energy……Page 324
8.4 Exact Solution for an Incompressible, Neo-Hookean Material……Page 326
Problems……Page 334
9.1 Introduction……Page 339
9.2 Viscoelastic Constitutive Equations in Linear Differential Operator Form……Page 340
9.3 One-Dimensional Theory, Mechanical Models……Page 342
9.4 Creep and Relaxation……Page 346
9.5 Superposition Principle, Hereditary Integrals……Page 352
9.6 Harmonic Loadings, Complex Modulus, and Complex Compliance……Page 354
9.7 Three-Dimensional Problems, The Correspondence Principle……Page 360
Solution……Page 363
Solution……Page 366
References……Page 367
Problems……Page 368