| Introduction to Continuum Thermomechanics | |
| Mathematical Fundamentals | p. 1 |
| Notation | p. 1 |
| Cartesian Tensors | p. 3 |
| Vector and Tensor Calculus | p. 6 |
| Curvilinear Coordinates | p. 9 |
| Continuum Deformation | p. 14 |
| Displacement | p. 14 |
| Strain | p. 15 |
| Principal Strains | p. 21 |
| Compatibility Conditions | p. 23 |
| Mechanics of Continuous Bodies | p. 26 |
| Introduction | p. 26 |
| Stress | p. 29 |
| Mohr's Circle | p. 33 |
| Plane Stress | p. 35 |
| Boundary-Value Problems | p. 36 |
| Constitutive Relations: Elastic | p. 44 |
| Energy and Thermoelasticity | p. 44 |
| Linear Elasticity | p. 49 |
| Energy Principles | p. 54 |
| Constitutive Relations: Inelastic | p. 59 |
| Inelasticity | p. 59 |
| Linear Viscoelasticity | p. 61 |
| Internal Variables: General Theory | p. 65 |
| Flow Law and Flow Potential | p. 69 |
| The Physics of Plasticity | |
| Phenomenology of Plastic Deformation | p. 75 |
| Experimental Stress-Strain Relations | p. 76 |
| Plastic Deformation | p. 80 |
| Temperature and Rate Dependence | p. 85 |
| Crystal Plasticity | p. 89 |
| Crystals and Slip | p. 89 |
| Dislocations and Crystal Plasticity | p. 94 |
| Dislocation Models of Plastic Phenomena | p. 100 |
| Plasticity of Soils, Rocks and Concrete | p. 103 |
| Plasticity of Soil | p. 104 |
| "Plasticity" of Rock and Concrete | p. 108 |
| Constitutive Theory | |
| Viscoplasticity | p. 111 |
| Internal-Variable Theory of Viscoplasticity | p. 111 |
| Transition to Rate-Independent Plasticity | p. 116 |
| Viscoplasticity Without a Yield Surface | p. 118 |
| Rate-Independent Plasticity | p. 122 |
| Flow Rule and Work-Hardening | p. 122 |
| Maximum-Dissipation Postulate and Normality | p. 127 |
| Strain-Space Plasticity | p. 130 |
| Yield Criteria, Flow Rules and Hardening Rules | p. 135 |
| Introduction | p. 135 |
| Yield Criteria Independent of the Mean Stress | p. 137 |
| Yield Criteria Dependent on the Mean Stress | p. 141 |
| Yield Criteria Under Special States of Stress or Deformation | p. 144 |
| Hardening Rules | p. 146 |
| Uniqueness and Extremum Theorems | p. 152 |
| Uniqueness Theorems | p. 152 |
| Extremum and Variational Principles | p. 154 |
| Rigid-Plastic Materials | p. 159 |
| Limit-Analysis and Shakedown Theorems | p. 162 |
| Standard Limit-Analysis Theorems | p. 162 |
| Nonstandard Limit-Analysis Theorems | p. 168 |
| Shakedown Theorems | p. 170 |
| Problems in Contained Plastic Deformation | |
| Elementary Problems | p. 177 |
| Introduction: Statically Determinate Problems | p. 177 |
| Thin-Walled Circular Tube in Torsion and Extension | p. 178 |
| Thin-Walled Cylinder Under Pressure and Axial Force | p. 181 |
| Statically Indeterminate Problems | p. 184 |
| Elastic-Plastic Torsion | p. 189 |
| The Torsion Problem | p. 189 |
| Elastic Torsion | p. 191 |
| Plastic Torsion | p. 194 |
| The Thick-Walled Hollow Sphere and Cylinder | p. 205 |
| Elastic Hollow Sphere Under Internal and External Pressure | p. 206 |
| Elastic-Plastic Hollow Sphere Under Internal Pressure | p. 208 |
| Thermal Stresses in an Elastic-Plastic Hollow Sphere | p. 213 |
| Hollow Cylinder: Elastic Solution and Initial Yield Pressure | p. 216 |
| Elastic-Plastic Hollow Cylinder | p. 220 |
| Elastic-Plastic Bending | p. 229 |
| Pure Bending of Prismatic Beams | p. 229 |
| Rectangular Beams Under Transverse Loads | p. 239 |
| Plane-Strain Pure Bending of Wide Beams or Plates | p. 245 |
| Numerical Methods | p. 250 |
| Integration of Rate Equations | p. 251 |
| The Finite-Element Method | p. 256 |
| Finite-Element Methods for Nonlinear Continua | p. 262 |
| Problems in Plastic Flow and Collapse I: Theories and "Exact" Solutions | |
| Introduction | p. 275 |
| Plane Problems | p. 276 |
| Slip-Line Theory | p. 277 |
| Simple Slip-Line Fields | p. 287 |
| Metal-Forming Problems | p. 291 |
| Collapse of Circular Plates | p. 298 |
| Introduction to Plate Theory | p. 299 |
| Elastic Plates | p. 303 |
| Yielding of Plates | p. 308 |
| Plastic Buckling | p. 313 |
| Introduction to Stability Theory | p. 314 |
| Theories of the Effective Modulus | p. 319 |
| Plastic Buckling of Plates and Shells | p. 326 |
| Problems in Plastic Flow and Collapse II: Applications of Limit Analysis | |
| Introduction | p. 337 |
| Limit Analysis of Plane Problems | p. 338 |
| Blocks and Slabs with Grooves or Cutouts | p. 338 |
| Problems in Bending | p. 341 |
| Problems in Soil Mechanics | p. 347 |
| Beams Under Combined Stresses | p. 355 |
| Generalized Stress | p. 355 |
| Extension and Bending | p. 358 |
| Combined Extension, Bending and Torsion | p. 364 |
| Bending and Shear | p. 369 |
| Limit Analysis of Trusses, Beams and Frames | p. 374 |
| Trusses | p. 374 |
| Beams | p. 380 |
| Limit Analysis of Frames | p. 385 |
| Limit Design of Frames | p. 390 |
| Limit Analysis of Plates and Shells | p. 398 |
| Limit Analysis of Plates | p. 398 |
| Limit Analysis of Shells: Theory | p. 404 |
| Limit Analysis of Shells: Examples | p. 407 |
| Dynamic Problems | |
| Dynamic Loading of Structures | p. 417 |
| Introduction | p. 417 |
| Dynamic Loading of Beams | p. 419 |
| Dynamic Loading of Plates and Shells | p. 425 |
| One-Dimensional Plastic Waves | p. 434 |
| Theory of One-Dimensional Waves | p. 434 |
| Waves in Elastic-Plastic bars | p. 438 |
| Rate Dependence | p. 446 |
| Application of the Method of Characteristics | p. 448 |
| Three-Dimensional Waves | p. 452 |
| Theory of Acceleration Waves | p. 453 |
| Special Cases | p. 459 |
| Large-Deformation Plasticity | |
| Large-Deformation Continuum Mechanics | p. 465 |
| Continuum Deformation | p. 465 |
| Continuum Mechanics and Objectivity | p. 473 |
| Large-Deformation Constitutive Theory | p. 478 |
| Thermoelasticity | p. 478 |
| Inelasticity: Kinematics | p. 480 |
| Inelasticity: Thermomechanics | p. 485 |
| Yield Condition and Flow Rule | p. 487 |
| Numerical Methods in Large-Deformation Plasticity | p. 491 |
| Rate-Based Formulations | p. 492 |
| "Hyperelastic" Numerical Methods | p. 496 |
| References | p. 501 |
| Index | p. 517 |
| Table of Contents provided by Ingram. All Rights Reserved. |
