| |
| |
| |
| Introduction to Continuum Thermomechanics | |
| |
| |
| |
| Mathematical Fundamentals | |
| |
| |
| |
| Notation | |
| |
| |
| |
| Cartesian Tensors | |
| |
| |
| |
| Vector and Tensor Calculus | |
| |
| |
| |
| Curvilinear Coordinates | |
| |
| |
| |
| Continuum Deformation | |
| |
| |
| |
| Displacement | |
| |
| |
| |
| Strain | |
| |
| |
| |
| Principal Strains | |
| |
| |
| |
| Compatibility Conditions | |
| |
| |
| |
| Mechanics of Continuous Bodies | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Stress | |
| |
| |
| |
| Mohr's Circle | |
| |
| |
| |
| Plane Stress | |
| |
| |
| |
| Boundary-Value Problems | |
| |
| |
| |
| Constitutive Relations: Elastic | |
| |
| |
| |
| Energy and Thermoelasticity | |
| |
| |
| |
| Linear Elasticity | |
| |
| |
| |
| Energy Principles | |
| |
| |
| |
| Constitutive Relations: Inelastic | |
| |
| |
| |
| Inelasticity | |
| |
| |
| |
| Linear Viscoelasticity | |
| |
| |
| |
| Internal Variables: General Theory | |
| |
| |
| |
| Flow Law and Flow Potential | |
| |
| |
| |
| The Physics of Plasticity | |
| |
| |
| |
| Phenomenology of Plastic Deformation | |
| |
| |
| |
| Experimental Stress-Strain Relations | |
| |
| |
| |
| Plastic Deformation | |
| |
| |
| |
| Temperature and Rate Dependence | |
| |
| |
| |
| Crystal Plasticity | |
| |
| |
| |
| Crystals and Slip | |
| |
| |
| |
| Dislocations and Crystal Plasticity | |
| |
| |
| |
| Dislocation Models of Plastic Phenomena | |
| |
| |
| |
| Plasticity of Soils, Rocks and Concrete | |
| |
| |
| |
| Plasticity of Soil | |
| |
| |
| |
| "Plasticity" of Rock and Concrete | |
| |
| |
| |
| Constitutive Theory | |
| |
| |
| |
| Viscoplasticity | |
| |
| |
| |
| Internal-Variable Theory of Viscoplasticity | |
| |
| |
| |
| Transition to Rate-Independent Plasticity | |
| |
| |
| |
| Viscoplasticity Without a Yield Surface | |
| |
| |
| |
| Rate-Independent Plasticity | |
| |
| |
| |
| Flow Rule and Work-Hardening | |
| |
| |
| |
| Maximum-Dissipation Postulate and Normality | |
| |
| |
| |
| Strain-Space Plasticity | |
| |
| |
| |
| Yield Criteria, Flow Rules and Hardening Rules | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Yield Criteria Independent of the Mean Stress | |
| |
| |
| |
| Yield Criteria Dependent on the Mean Stress | |
| |
| |
| |
| Yield Criteria Under Special States of Stress or Deformation | |
| |
| |
| |
| Hardening Rules | |
| |
| |
| |
| Uniqueness and Extremum Theorems | |
| |
| |
| |
| Uniqueness Theorems | |
| |
| |
| |
| Extremum and Variational Principles | |
| |
| |
| |
| Rigid-Plastic Materials | |
| |
| |
| |
| Limit-Analysis and Shakedown Theorems | |
| |
| |
| |
| Standard Limit-Analysis Theorems | |
| |
| |
| |
| Nonstandard Limit-Analysis Theorems | |
| |
| |
| |
| Shakedown Theorems | |
| |
| |
| |
| Problems in Contained Plastic Deformation | |
| |
| |
| |
| Elementary Problems | |
| |
| |
| |
| Introduction: Statically Determinate Problems | |
| |
| |
| |
| Thin-Walled Circular Tube in Torsion and Extension | |
| |
| |
| |
| Thin-Walled Cylinder Under Pressure and Axial Force | |
| |
| |
| |
| Statically Indeterminate Problems | |
| |
| |
| |
| Elastic-Plastic Torsion | |
| |
| |
| |
| The Torsion Problem | |
| |
| |
| |
| Elastic Torsion | |
| |
| |
| |
| Plastic Torsion | |
| |
| |
| |
| The Thick-Walled Hollow Sphere and Cylinder | |
| |
| |
| |
| Elastic Hollow Sphere Under Internal and External Pressure | |
| |
| |
| |
| Elastic-Plastic Hollow Sphere Under Internal Pressure | |
| |
| |
| |
| Thermal Stresses in an Elastic-Plastic Hollow Sphere | |
| |
| |
| |
| Hollow Cylinder: Elastic Solution and Initial Yield Pressure | |
| |
| |
| |
| Elastic-Plastic Hollow Cylinder | |
| |
| |
| |
| Elastic-Plastic Bending | |
| |
| |
| |
| Pure Bending of Prismatic Beams | |
| |
| |
| |
| Rectangular Beams Under Transverse Loads | |
| |
| |
| |
| Plane-Strain Pure Bending of Wide Beams or Plates | |
| |
| |
| |
| Numerical Methods | |
| |
| |
| |
| Integration of Rate Equations | |
| |
| |
| |
| The Finite-Element Method | |
| |
| |
| |
| Finite-Element Methods for Nonlinear Continua | |
| |
| |
| |
| Problems in Plastic Flow and Collapse I: Theories and "Exact" Solutions | |
| |
| |
| Introduction | |
| |
| |
| |
| Plane Problems | |
| |
| |
| |
| Slip-Line Theory | |
| |
| |
| |
| Simple Slip-Line Fields | |
| |
| |
| |
| Metal-Forming Problems | |
| |
| |
| |
| Collapse of Circular Plates | |
| |
| |
| |
| Introduction to Plate Theory | |
| |
| |
| |
| Elastic Plates | |
| |
| |
| |
| Yielding of Plates | |
| |
| |
| |
| Plastic Buckling | |
| |
| |
| |
| Introduction to Stability Theory | |
| |
| |
| |
| Theories of the Effective Modulus | |
| |
| |
| |
| Plastic Buckling of Plates and Shells | |
| |
| |
| |
| Problems in Plastic Flow and Collapse II: Applications of Limit Analysis | |
| |
| |
| Introduction | |
| |
| |
| |
| Limit Analysis of Plane Problems | |
| |
| |
| |
| Blocks and Slabs with Grooves or Cutouts | |
| |
| |
| |
| Problems in Bending | |
| |
| |
| |
| Problems in Soil Mechanics | |
| |
| |
| |
| Beams Under Combined Stresses | |
| |
| |
| |
| Generalized Stress | |
| |
| |
| |
| Extension and Bending | |
| |
| |
| |
| Combined Extension, Bending and Torsion | |
| |
| |
| |
| Bending and Shear | |
| |
| |
| |
| Limit Analysis of Trusses, Beams and Frames | |
| |
| |
| |
| Trusses | |
| |
| |
| |
| Beams | |
| |
| |
| |
| Limit Analysis of Frames | |
| |
| |
| |
| Limit Design of Frames | |
| |
| |
| |
| Limit Analysis of Plates and Shells | |
| |
| |
| |
| Limit Analysis of Plates | |
| |
| |
| |
| Limit Analysis of Shells: Theory | |
| |
| |
| |
| Limit Analysis of Shells: Examples | |
| |
| |
| |
| Dynamic Problems | |
| |
| |
| |
| Dynamic Loading of Structures | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Dynamic Loading of Beams | |
| |
| |
| |
| Dynamic Loading of Plates and Shells | |
| |
| |
| |
| One-Dimensional Plastic Waves | |
| |
| |
| |
| Theory of One-Dimensional Waves | |
| |
| |
| |
| Waves in Elastic-Plastic bars | |
| |
| |
| |
| Rate Dependence | |
| |
| |
| |
| Application of the Method of Characteristics | |
| |
| |
| |
| Three-Dimensional Waves | |
| |
| |
| |
| Theory of Acceleration Waves | |
| |
| |
| |
| Special Cases | |
| |
| |
| |
| Large-Deformation Plasticity | |
| |
| |
| |
| Large-Deformation Continuum Mechanics | |
| |
| |
| |
| Continuum Deformation | |
| |
| |
| |
| Continuum Mechanics and Objectivity | |
| |
| |
| |
| Large-Deformation Constitutive Theory | |
| |
| |
| |
| Thermoelasticity | |
| |
| |
| |
| Inelasticity: Kinematics | |
| |
| |
| |
| Inelasticity: Thermomechanics | |
| |
| |
| |
| Yield Condition and Flow Rule | |
| |
| |
| |
| Numerical Methods in Large-Deformation Plasticity | |
| |
| |
| |
| Rate-Based Formulations | |
| |
| |
| |
| "Hyperelastic" Numerical Methods | |
| |
| |
| References | |
| |
| |
| Index | |