Plasticity Theory

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Overview

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.

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Overview

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.

Editorial Reviews

Booknews
A self-contained text (the necessary mathematics, basic mechanics, and thermodynamics are covered in an introductory chapter) for advanced undergraduate and graduate students introduces the contemporary state of knowledge in basic plasticity theory and its applications. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Product Details

  • ISBN-13: 9780486462905
  • Publisher: Dover Publications
  • Publication date: 2/29/2008
  • Pages: 544
  • Sales rank: 1,213,128
  • Series: Dover Books on Engineering Series
  • Product dimensions: 6.21 (w) x 9.22 (h) x 1.03 (d)

Table of Contents

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

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