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Jacob Lubliner

Plasticity Theory

€ 32.95



Taal / Language : English

Inhoudsopgave:
Chapter 1: Introduction to Continuum Thermomechanics
Section 1.1 Mathematical Fundamentals
1
1.1.1 Notation
1
1.1.2 Cartesian Tensors
3
1.1.3 Vector and Tensor Calculus
6
1.1.4 Curvilinear Coordinates
9
Section 1.2 Continuum Deformation
14
1.2.1 Displacement
14
1.2.2 Strain
15
1.2.3 Principal Strains
21
1.2.4 Compatibility Conditions
23
Section 1.3 Mechanics of Continuous Bodies
26
1.3.1 Introduction
26
1.3.2 Stress
29
1.3.3 Mohr`s Circle
33
1.3.4 Plane Stress
35
1.3.5 Boundary-Value Problems
36
Section 1.4 Constitutive Relations: Elastic
44
1.4.1 Energy and Thermoelasticity
44
1.4.2 Linear Elasticity
49
1.4.3 Energy Principles
54
Section 1.5 Constitutive Relations: Inelastic
59
1.5.1 Inelasticity
59
1.5.2 Linear Viscoelasticity
61
1.5.3 Internal Variables: General Theory
65
1.5.4 Flow Law and Flow Potential
69
Chapter 2: The Physics of Plasticity
Section 2.1 Phenomenology of Plastic Deformation
75
2.1.1 Experimental Stress-Strain Relations
76
2.1.2 Plastic Deformation
80
2.1.3 Temperature and Rate Dependence
85
Section 2.2 Crystal Plasticity
89
2.2.1 Crystals and Slip
89
2.2.2 Dislocations and Crystal Plasticity
94
2.2.3 Dislocation Models of Plastic Phenomena
100
Section 2.3 Plasticity of Soils, Rocks and Concrete
103
2.3.1 Plasticity of Soil
104
2.3.2 `Plasticity` of Rock and Concrete
108
Chapter 3: Constitutive Theory
Section 3.1 Viscoplasticity
111
3.1.1 Internal-Variable Theory of Viscoplasticity
111
3.1.2 Transition to Rate-Independent Plasticity
116
3.1.3 Viscoplasticity Without a Yield Surface
118
Section 3.2 Rate-Independent Plasticity
122
3.2.1 Flow Rule and Work-Hardening
122
3.2.2 Maximum-Dissipation Postulate and Normality
127
3.2.3 Strain-Space Plasticity
130
Section 3.3 Yield Criteria, Flow Rules and Hardening Rules
135
3.3.1 Introduction
135
3.3.2 Yield Criteria Independent of the Mean Stress
137
3.3.3 Yield Criteria Dependent on the Mean Stress
141
3.3.4 Yield Criteria Under Special States of Stress or Deformation
144
3.3.5 Hardening Rules
146
Section 3.4 Uniqueness and Extremum Theorems
152
3.4.1 Uniqueness Theorems
152
3.4.2 Extremum and Variational Principles
154
3.4.3 Rigid Plastic Materials
159
Section 3.5 Limit-Analysis and Shakedown Theorems
162
3.5.1 Standard Limit-Analysis Theorems
162
3.5.2 Nonstandard Limit-Analysis Theorems
168
3.5.3 Shakedown Theorems
170
Chapter 4: Problems in Contained Plastic Deformation
Section 4.1 Elementary Problems
177
4.1.1 Introduction: Statically Determinate Problems
177
4.1.2 Thin-Walled Circular Tube in Torsion and Extension
178
4.1.3 Thin-Walled Cylinder Under Pressure and Axial Force
181
4.1.4 Statically Indeterminate Problems
184
Section 4.2 Elastic Plastic Torsion
189
4.2.1 The Torsion Problem
189
4.2.2 Elastic Torsion
191
4.2.3 Plastic Torsion
194
Section 4.3 The Thick-Walled Hollow Sphere and Cylinder
205
4.3.1 Elastic Hollow Sphere Under Internal and External Pressure
206
4.3.2 Elastic Plastic Hollow Sphere Under Internal Pressure
208
4.3.3 Thermal Stresses in an Elastic Plastic Hollow Sphere
213
4.3.4 Hollow Cylinder: Elastic Solution and Initial Yield Pressure
216
4.3.5 Elastic Plastic Hollow Cylinder
220
Section 4.4 Elastic Plastic Bending
229
4.4.1 Pure Bending of Prismatic Beams
229
4.4.2 Rectangular Beams Under Transverse Loads
239
4.4.3 Plane-Strain Pure Bending of Wide Beams or Plates
245
Section 4.5 Numerical Methods
250
4.5.1 Integration of Rate Equations
251
4.5.2 The Finite-Element Method
256
4.5.3 Finite-Element Methods for Nonlinear Continua
262
Chapter 5: Problems in Plastic Flow and Collapse I: Theories and `Exact` Solutions
Introduction
275
Section 5.1 Plane Problems
276
5.1.1 Slip-Line Theory
277
5.1.2 Simple Slip-Line Fields
287
5.1.3 Metal-Forming Problems
291
Section 5.2 Collapse of Circular Plates
298
5.2.1 Introduction to Plate Theory
299
5.2.2 Elastic Plates
303
5.2.3 Yielding of Plates
308
Section 5.3 Plastic Buckling
313
5.3.1 Introduction to Stability Theory
314
5.3.2 Theories of the Effective Modulus
319
5.3.3 Plastic Buckling of Plates and Shells
326
Chapter 6: Problems in Plastic Flow and Collapse II: Applications of Limit Analysis
Introduction
337
Section 6.1 Limit Analysis of Plane Problems
338
6.1.1 Blocks and Slabs with Grooves or Cutouts
338
6.1.2 Problems in Bending
341
6.1.3 Problems in Soil Mechanics
347
Section 6.2 Beams Under Combined Stresses
355
6.2.1 Generalized Stress
355
6.2.2 Extension and Bending
358
6.2.3 Combined Extension, Bending and Torsion
364
6.2.4 Bending and Shear
369
Section 6.3 Limit Analysis of Trusses, Beams and Frames
374
6.3.1 Trusses
374
6.3.2 Beams
380
6.3.3 Limit Analysis of Frames
385
6.3.4 Limit Design of Frames
390
Section 6.4 Limit Analysis of Plates and Shells
398
6.4.1 Limit Analysis of Plates
398
6.4.2 Limit Analysis of Shells: Theory
404
6.4.3 Limit Analysis of Shells: Examples
407
Chapter 7: Dynamic Problems
Section 7.1 Dynamic Loading of Structures
417
7.1.1 Introduction
417
7.1.2 Dynamic Loading of Beams
419
7.1.3 Dynamic Loading of Plates and Shells
425
Section 7.2 One-Dimensional Plastic Waves
434
7.2.1 Theory of One-Dimensional Waves
434
7.2.2 Waves in Elastic Plastic bars
438
7.2.3 Rate Dependence
446
7.2.4 Application of the Method of Characteristics
448
Section 7.3 Three-Dimensional Waves
452
7.3.1 Theory of Acceleration Waves
453
7.3.2 Special Cases
459
Chapter 8: Large-Deformation Plasticity
Section 8.1 Large-Deformation Continuum Mechanics
465
8.1.1 Continuum Deformation
465
8.1.2 Continuum Mechanics and Objectivity
473
Section 8.2 Large-Deformation Constitutive Theory
478
8.2.1 Thermoelasticity
478
8.2.2 Inelasticity: Kinematics
480
8.2.3 Inelasticity: Thermomechanics
485
8.2.4 Yield Condition and Flow Rule
487
Section 8.3 Numerical Methods in Large-Deformation Plasticity
491
8.3.1 Rate-Based Formulations
492
8.3.2 `Hyperelastic` Numerical Methods
496
References 501
Index 517
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Paperback / softback
528 pagina's
Januari 2008
689 gram
229 x 152 x 25 mm
DOVER PUBN INC us


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