Plasticity Theory

by Lubliner, Jacob

• ISBN13: 9780486462905
• ISBN10: 0486462900
• Format: Paperback
• Copyright: 2008-02-29
• Publisher: Dover Publications

Summary

This self-contained text for advanced undergraduate and graduate students is devoted to classical quasistatic problems of rate-independent plasticity theory. It discusses the finite element method for both viscoplastic and rate-independent plastic solids, in addition to large deformation plasticity numerical methods for rate-based formulations and hyperelastic methods. 1990 edition.

Author Biography

Author Jacob Lubliner is Professor Emeritus of Engineering Science in the Department of Civil and Environmental Engineering at the University of California, Berkeley

Table of Contents

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
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