| Introduction | p. 1 |
| Hooke's Law | p. 2 |
| Linear Solids with Memory | p. 9 |
| Sinusoidal Oscillations in Viscoelastic Material: Models of Viscoelasticity | p. 12 |
| Plasticity | p. 14 |
| Vibrations | p. 15 |
| Prototype of Wave Dynamics | p. 18 |
| Biomechanics | p. 22 |
| Historical Remarks | p. 25 |
| Tensor Analysis | p. 30 |
| Notation and Summation Convention | p. 30 |
| Coordinate Transformation | p. 33 |
| Euclidean Metric Tensor | p. 34 |
| Scalars, Contravariant Vectors, Covariant Vectors | p. 38 |
| Tensor Fields of Higher Rank | p. 39 |
| Some Important Special Tensors | p. 40 |
| The Significance of Tensor Characteristics | p. 42 |
| Rectangular Cartesian Tensors | p. 43 |
| Contraction | p. 44 |
| Quotient Rule | p. 45 |
| Partial Derivatives in Cartesian Coordinates | p. 46 |
| Covariant Differentiation of Vector Fields | p. 48 |
| Tensor Equations | p. 49 |
| Geometric Interpretation of Tensor Components | p. 52 |
| Geometric Interpretation of Covariant Derivatives | p. 58 |
| Physical Components of a Vector | p. 60 |
| Stress Tensor | p. 66 |
| Stresses | p. 66 |
| Laws of Motion | p. 69 |
| Cauchy's Formula | p. 71 |
| Equations of Equilibrium | p. 73 |
| Transformation of Coordinates | p. 78 |
| Plane State of Stress | p. 79 |
| Principal Stresses | p. 82 |
| Shearing Stresses | p. 85 |
| Mohr's Circles | p. 86 |
| Stress Deviations | p. 87 |
| Octahedral Shearing Stress | p. 88 |
| Stress Tensor in General Coordinates | p. 90 |
| Physical Components of a Stress Tensor in General Coordinates | p. 94 |
| Equations of Equilibrium in Curvilinear Coordinates | p. 95 |
| Analysis of Strain | p. 97 |
| Deformation | p. 97 |
| Strain Tensors in Rectangular Cartesian Coordinates | p. 100 |
| Geometric Interpretation of Infinitesimal Strain Components | p. 103 |
| Rotation | p. 104 |
| Finite Strain Components | p. 106 |
| Compatibility of Strain Components | p. 108 |
| Multiply Connected Regions | p. 113 |
| Multivalued Displacements | p. 117 |
| Properties of the Strain Tensor | p. 118 |
| Physical Components | p. 121 |
| Example--Spherical Coordinates | p. 123 |
| Example--Cylindrical Polar Coordinates | p. 125 |
| Conservation Laws | p. 127 |
| Gauss' Theorem | p. 127 |
| Material and Spatial Descriptions of Changing Configurations | p. 128 |
| Material Derivative of Volume Integral | p. 131 |
| The Equation of Continuity | p. 133 |
| Equations of Motion | p. 134 |
| Moment of Momentum | p. 135 |
| Other Field Equations | p. 136 |
| Elastic and Plastic Behavior of Materials | p. 138 |
| Generalized Hooke's Law | p. 138 |
| Stress-Strain Relationship for Isotropic Elastic Materials | p. 140 |
| Ideal Plastic Solids | p. 143 |
| Some Experimental Information | p. 146 |
| A Basic Assumption of the Mathematical Theory of Plasticity | p. 150 |
| Loading and Unloading Criteria | p. 156 |
| Isotropic Stress Theories of Yield Function | p. 157 |
| Further Examples of Yield Functions | p. 159 |
| Work Hardening--Drucker's Hypothesis and Definition | p. 166 |
| Ideal Plasticity | p. 167 |
| Flow Rule for Work-Hardening Materials | p. 171 |
| Subsequent Loading Surfaces--Isotropic and Kinematic Hardening Rules | p. 177 |
| Mroz's, Dafalias and Popov's, and Valanis' Plasticity Theories | p. 189 |
| Strain Space Formulations | p. 195 |
| Finite Deformation | p. 199 |
| Plastic Deformation of Crystals | p. 200 |
| Linearized Theory of Elasticity | p. 203 |
| Basic Equations of Elasticity for Homogeneous Isotropic Bodies | p. 203 |
| Equilibrium of an Elastic Body Under Zero Body Force | p. 206 |
| Boundary Value Problems | p. 207 |
| Equilibrium and Uniqueness of Solutions | p. 210 |
| Saint Venant's Theory of Torsion | p. 213 |
| Soap Film Analogy | p. 222 |
| Bending of Beams | p. 224 |
| Plane Elastic Waves | p. 229 |
| Rayleigh Surface Wave | p. 231 |
| Love Wave | p. 235 |
| Solutions of Problems in Linearized Theory of Elasticity by Potentials | p. 238 |
| Scalar and Vector Potentials for Displacement Vector Fields | p. 238 |
| Equations of Motion in Terms of Displacement Potentials | p. 241 |
| Strain Potential | p. 243 |
| Galerkin Vector | p. 246 |
| Equivalent Galerkin Vectors | p. 249 |
| Example--Vertical Load on the Horizontal Surface of a Semi-Infinite Solid | p. 250 |
| Love's Strain Function | p. 252 |
| Kelvin's Problem--A Single Force Acting in the Interior of an Infinite Solid | p. 254 |
| Perturbation of Elasticity Solutions by a Change of Poisson's Ratio | p. 259 |
| Boussinesq's Problem | p. 262 |
| On Biharmonic Functions | p. 263 |
| Neuber-Papkovich Representation | p. 268 |
| Other Methods of Solution of Elastostatic Problems | p. 270 |
| Reflection and Refraction of Plane P and S Waves | p. 270 |
| Lamb's Problem--Line Load Suddenly Applied on Elastic Half-Space | p. 273 |
| Two-Dimensional Problems in Linearized Theory of Elasticity | p. 280 |
| Plane State of Stress or Strain | p. 280 |
| Airy Stress Functions for Two-Dimensional Problems | p. 282 |
| Airy Stress Function in Polar Coordinates | p. 288 |
| General Case | p. 295 |
| Representation of Two-Dimensional Biharmonic Functions by Analytic Functions of a Complex Variable | p. 299 |
| Kolosoff-Muskhelishvili Method | p. 301 |
| Variational Calculus, Energy Theorems, Saint-Venant's Principle | p. 313 |
| Minimization of Functionals | p. 313 |
| Functional Involving Higher Derivatives of the Dependent Variable | p. 319 |
| Several Unknown Functions | p. 320 |
| Several Independent Variables | p. 323 |
| Subsidiary Conditions--Lagrangian Multipliers | p. 325 |
| Natural Boundary Conditions | p. 328 |
| Theorem of Minimum Potential Energy Under Small Variations of Displacements | p. 330 |
| Example of Application: Static Loading on a Beam--Natural and Rigid End Conditions | p. 335 |
| The Complementary Energy Theorem Under Small Variations of Stresses | p. 339 |
| Variational Functionals Frequently Used in Computational Mechanics | p. 346 |
| Saint-Venant's Principle | p. 355 |
| Saint-Venant's Principle-Boussinesq-Von Mises-Sternberg Formulation | p. 359 |
| Practical Applications of Saint-Venant's Principle | p. 362 |
| Extremum Principles for Plasticity | p. 365 |
| Limit Analysis | p. 369 |
| Hamilton's Principle, Wave Propagation, Applications of Generalized Coordinates | p. 379 |
| Hamilton's Principle | p. 379 |
| Example of Application--Equation of Vibration of a Beam | p. 383 |
| Group Velocity | p. 393 |
| Hopkinson's Experiment | p. 396 |
| Generalized Coordinates | p. 398 |
| Approximate Representation of Functions | p. 399 |
| Approximate Solution of Differential Equations | p. 402 |
| Direct Methods of Variational Calculus | p. 402 |
| Elasticity and Thermodynamics | p. 407 |
| The Laws of Thermodynamics | p. 407 |
| The Energy Equation | p. 412 |
| The Strain Energy Function | p. 414 |
| The Conditions of Thermodynamic Equilibrium | p. 416 |
| The Positive Definiteness of the Strain Energy Function | p. 418 |
| Thermodynamic Restrictions on the Stress-Strain Law of an Isotropic Elastic Material | p. 419 |
| Generalized Hooke's Law, Including the Effect of Thermal Expansion | p. 421 |
| Thermodynamic Functions for Isotropic Hookean Materials | p. 423 |
| Equations Connecting Thermal and Mechanical Properties of a Solid | p. 425 |
| Irreversible Thermodynamics and Viscoelasticity | p. 428 |
| Basic Assumptions | p. 428 |
| One-Dimensional Heat Conduction | p. 431 |
| Phenomenological Relations-Onsager Principle | p. 432 |
| Basic Equations of Thermomechanics | p. 436 |
| Equations of Evolution for a Linear Hereditary Material | p. 440 |
| Relaxation Modes | p. 444 |
| Normal Coordinates | p. 447 |
| Hidden Variables and the Force-Displacement Relationship | p. 450 |
| Anisotropic Linear Viscoelastic Materials | p. 454 |
| Thermoelasticity | p. 456 |
| Basic Equations | p. 456 |
| Thermal Effects Due to a Change of Strain; Kelvin's Formula | p. 459 |
| Ratio of Adiabatic to Isothermal Elastic Moduli | p. 459 |
| Uncoupled, Quasi-Static Thermoelastic Theory | p. 461 |
| Temperature Distribution | p. 462 |
| Thermal Stresses | p. 464 |
| Particular Integral: Goodier's Method | p. 466 |
| Plane Strain | p. 467 |
| An Example--Stresses in a Turbine Disk | p. 470 |
| Variational Principle for Uncoupled Thermoelasticity | p. 473 |
| Variational Principle for Heat Conduction | p. 474 |
| Coupled Thermoelasticity | p. 478 |
| Lagrangian Equations for Heat Conduction and Thermoelasticity | p. 481 |
| Viscoelasticity | p. 487 |
| Viscoelastic Material | p. 487 |
| Stress-Strain Relations in Differential Equation Form | p. 491 |
| Boundary-Value Problems and Integral Transformations | p. 497 |
| Waves in an Infinite Medium | p. 500 |
| Quasi-Static Problems | p. 503 |
| Reciprocity Relations | p. 507 |
| Large Deformation | p. 514 |
| Coordinate Systems and Tensor Notation | p. 514 |
| Deformation Gradient | p. 521 |
| Strains | p. 525 |
| Right and Left Stretch Strain and Rotation Tensors | p. 526 |
| Strain Rates | p. 528 |
| Material Derivatives of Line, Area, and Volume Elements | p. 529 |
| Stresses | p. 532 |
| Example: Combined Tension and Torsion Loads | p. 539 |
| Objectivity | p. 543 |
| Equations of Motion | p. 548 |
| Constitutive Equations of Thermoelastic Bodies | p. 550 |
| More Examples | p. 557 |
| Variational Principles for Finite Elasticity: Compressible Materials | p. 562 |
| Variational Principles for Finite Elasticity: Nearly Incompressible or Incompressible Materials | p. 568 |
| Small Deflection of Thin Plates | p. 573 |
| Large Deflection of Plates | p. 581 |
| Incremental Approach to Solving Some Nonlinear Problems | p. 587 |
| Updated Lagrangian Description | p. 587 |
| Linearized Rates of Deformation | p. 590 |
| Linearized Rates of Stress Measures | p. 593 |
| Incremental Equations of Motion | p. 597 |
| Constitutive Laws | p. 598 |
| Incremental Variational Principles in Terms of T | p. 604 |
| Incremental Variational Principles in Terms of r | p. 610 |
| Incompressible and Nearly Incompressible Materials | p. 612 |
| Updated Solution | p. 617 |
| Incremental Loads | p. 620 |
| Infinitesimal Strain Theory | p. 622 |
| Finite Element Methods | p. 624 |
| Basic Approach | p. 626 |
| One Dimensional Problems Governed by a Second Order Differential Equation | p. 629 |
| Shape Functions and Element Matrices for Higher Order Ordinary Differential Equations | p. 638 |
| Assembling and Constraining Global Matrices | p. 643 |
| Equation Solving | p. 651 |
| Two Dimensional Problems by One-Dimensional Elements | p. 655 |
| General Finite Element Formulation | p. 657 |
| Convergence | p. 664 |
| Two-Dimensional Shape Functions | p. 665 |
| Element Matrices for a Second-Order Elliptical Equation | p. 672 |
| Coordinate Transformation | p. 676 |
| Triangular Elements with Curved Sides | p. 679 |
| Quadrilateral Elements | p. 682 |
| Plane Elasticity | p. 690 |
| Three-Dimensional Shape Functions | p. 702 |
| Three Dimensional Elasticity | p. 708 |
| Dynamic Problems of Elastic Solids | p. 714 |
| Numerical Integration | p. 726 |
| Patch Tests | p. 731 |
| Locking-Free Elements | p. 735 |
| Spurious Modes in Reduced Integration | p. 750 |
| Perspective | p. 754 |
| Mixed and Hybrid Formulations | p. 756 |
| Mixed Formulations | p. 756 |
| Hybrid Formulations | p. 760 |
| Hybrid Singular Elements (Super-Elements) | p. 767 |
| Elements for Heterogeneous Materials | p. 782 |
| Elements for Infinite Domain | p. 782 |
| Incompressible or Nearly Incompressible Elasticity | p. 788 |
| Finite Element Methods for Plates and Shells | p. 795 |
| Linearized Bending Theory of Thin Plates | p. 795 |
| Reissner-Mindlin Plates | p. 805 |
| Mixed Functionals for Reissner Plate Theory | p. 813 |
| Hybrid Formulations for Plates | p. 819 |
| Shell as an Assembly of Plate Elements | p. 822 |
| General Shell Elements | p. 832 |
| Locking and Stabilization in Shell Applications | p. 843 |
| Finite Element Modeling of Nonlinear Elasticity, Viscoelasticity, Plasticity, Viscoplasticity and Creep | p. 848 |
| Updated Lagrangian Solution for Large Deformation | p. 849 |
| Incremental Solution | p. 852 |
| Dynamic Solution | p. 854 |
| Newton-Raphson Iteration Method | p. 855 |
| Viscoelasticity | p. 857 |
| Plasticity | p. 859 |
| Viscoplasticity | p. 869 |
| Creep | p. 870 |
| Bibliography | p. 873 |
| Author Index | p. 909 |
| Subject Index | p. 919 |
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