Generalized Plasticity,9783540251279

Generalized Plasticity

by ; ; ;
ISBN13: 9783540251279
ISBN10: 3540251278
Format: Hardcover
Pub. Date: 2005-12-16
Publisher(s): Springer Verlag
List Price: $249.99

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Summary

Generalized Plasticity deals with the plasticity of materials and structures. It is an expansion of the "Unified Strength Theory to Plasticity Theory", leading to a unified treatment of metal plasticity and plasticity of geomaterials, generally. It includes the metal plasticity for Tresca materials, Huber-von-Mises materials and twin-shear materials and the geomaterial plasticity for Mohr-Coulomb materials, generalized twin-shear materials and the Unified Strength Theory.

Table of Contents

Preface
Notations
1 Introduction
1(14)
1.1 Linear Elasticity
1(1)
1.2 Classical Plasticity
2(3)
1.3 Concrete Plasticity
5(1)
1.4 Soil Plasticity
6(1)
1.5 Rock Plasticity
7(1)
1.6 Generalized Plasticity
8(1)
1.7 Generalized Plasticity Based on the Unified Strength Theory
8(2)
References and Bibliography
10(5)
2 Stress Space and Stress State
15(18)
2.1 Elements
15(1)
2.2 Stress at a Point, Stress Invariants
15(1)
2.3 Deviatoric Stress Tensor, Deviatoric Tensor Invariants
16(1)
2.4 Stresses on the Oblique Plane
17(4)
2.5 Hexahedron, Octahedron, Dodecahedron
21(1)
2.6 Stress Space
22(5)
2.7 Stress State Parameters
27(4)
Summary
31(1)
References
31(2)
3 Basic Characteristics of Yield of Materials under Complex Stress
33(17)
3.1 Introduction
33(1)
3.2 Strength Difference Effect (SD effect)
33(2)
3.3 Effect of Hydrostatic Stress
35(2)
3.4 Effect of Normal Stress
37(1)
3.5 Effect of Intermediate Principal Stress
38(5)
3.6 Effect of Intermediate Principal Shear-Stress
43(3)
3.7 Bounds of the Convex Strength Theories
46(1)
Summary
47(1)
References
47(3)
4 Unified Strength Theory and Its Material Parameters
50(45)
4.1 Introduction
50(1)
4.2 Mechanical Model of the Unified Strength Theory
51(2)
4.3 Unified Strength Theory
53(1)
4.4 Special Cases of the Unified Strength Theory
54(6)
4.5 Material Parameters of the Unified Strength Theory
60(3)
4.6 Other Material Parameters of the Unified Strength Theory
63(3)
4.7 Yield Surfaces and Yield Loci
66(3)
4.8 Yield Loci of the Unified Strength Theory in the π- Plane
69(3)
4.9 Yield Surfaces of the Unified Strength Theory in Principal Stress Space
72(3)
4.10 Yield Loci of the Unified Strength Theory in Plane Stress State
75(3)
4.11 Unified Strength Theory in Meridian Plane
78(3)
4.12 Yield Surfaces of the Non-linear Unified Strength Theory
81(4)
Summary
85(2)
Problems
87(6)
References and Bibliography
93(2)
5 Reasonable Choice of a Yield Function
95(27)
5.1 Introduction
95(1)
5.2 Some Experimental Data of Metallic Materials
96(4)
5.3 Reasonable Choice of a Yield Function for Non-SD Materials
100(2)
5.4 Experiments for Iron under σ-τ Stress State
102(1)
5.5 Experiments for Concrete under Complex Stress
103(2)
5.6 Experiments for Rock under Complex Stress
105(3)
5.7 Experiments on Clay and Loess under Complex Stress
108(1)
5.8 Experiments on Sand under Complex Stress
109(3)
5.9 Reasonable Choice of a Yield Function for SD-Materials
112(1)
5.10 The Beauty of the Unified Strength Theory
113(4)
Summary
117(1)
Problems
118(1)
References and Bibliography
119(3)
6 Elasto-Plastic Costitutive Relations
122(33)
6.1 Introduction
122(1)
6.2 Plastic Deformation in Uniaxial Stress State
122(2)
6.3 Three-dimensional Elastic Stress-strain Relation
124(1)
6.4 Plastic Work Hardening and Strain Hardening
125(2)
6.5 Plastic Flow Rule
127(2)
6.6 Drucker's Postulate – Convexity of the Loading Surface
129(3)
6.7 Incremental Constitutive Equations in Matrix Formulation
132(3)
6.8 Determination of Flow Vector for Different Yield Functions
135(2)
6.9 Singularity of Piecewise-Linear Yield Functions
137(5)
6.10 Process of the Plastic Flow Singularity
142(3)
6.11 Suggested Methods
145(3)
6.12 Unified Process of the Corner Singularity
148(4)
Summary
152(1)
Problems
152(1)
References and Bibliography
153(2)
7 Concrete Plasticity
155(40)
7.1 Introduction
155(2)
7.2 Multi-Parameter Yield Criteria
157(5)
7.3 Multi-Parameter Unified Yield Criterion
162(6)
7.4 Yield and Loading Functions
168(8)
7.5 Processing of Corner Singularity
176(3)
7.6 Strain Softening Phenomena and Material Damage
179(3)
7.7 Applications
182(10)
Summary
192(1)
Problems
192(1)
References and Bibliography
193(2)
8 Twin-Shear Slip-Line Field for Plane Strain Problem
195(30)
8.1 Introduction
195(3)
8.2 Stress State in Plane Strain Problem
198(2)
8.3 Twin-Shear Strength Theory of Plane Strain Problem
200(2)
8.4 Twin-Shear Line Field Theory for Plane Strain Problem (Statically Admissible Field)
202(2)
8.5 Twin-Shear Slip Line Field Theory for Plane Strain Problem (Kinematically Admissible Field)
204(5)
8.6 Applications of the Twin-Shear Slip Line Field Theory for Plane Strain Problems
209(9)
Summary
218(1)
Problems
218(5)
References and Bibliography
223(2)
9 Unified Slip-Line Field Theory for Plane Strain Problem
225(45)
9.1 Introduction
225(1)
9.2 Unified Strength Theory in Plane Strain Condition
226(4)
9.3 Unified Slip Line Field Theory for Plane Strain Problem (Statically Admissible Field)
230(3)
9.4 Unified Slip Line Field Theory for Plane Strain Problem (Kinematically Admissible Field)
233(3)
9.5 Special Cases of the Unified Slip Line Field Theory
236(4)
9.6 Applications of the Unified Slip Line Field Theory
240(12)
9.7 Comparison of the Unified Slip Line Field Theory with Finite Element Method
252(4)
9.8 Comparison of the Unified Slip Line Field Theory with Experimental Results
256(1)
9.9 Discontinuous Bifurcations of Elasto-Plastic Material For Plane Strain Problem
257(3)
Summary
260(1)
Problems
260(8)
References and Bibliography
268(2)
10 Twin-Shear Characteristics Field for Plane Stress Problem 270(23)
10.1 Introduction
270(1)
10.2 Characteristics Method Based on the Tresca Criterion and the Huber-von Mises Criterion
270(4)
10.3 Characteristics Method Based on the Twin-Shear Yield Criterion
274(4)
10.4 Twin-Shear Characteristics Field for Plane Stress Problems (Velocity Field)
278(3)
10.5 Applications of the Twin-Shear Characteristics Method
281(6)
10.6 Comparison of These Different Methods
287(1)
Summary
288(1)
Problems
288(4)
References and Bibliography
292(1)
11 Unified Characteristics Field Theory for Plane Stress Problem 293(29)
11.1 Introduction
293(1)
11.2 Unified Yield Function in Plane Stress State
293(3)
11.3 Characteristics Filed for Plane Stress Problems
296(6)
11.4 Applications of the Unified Characteristics Field for Plane Stress Problems
302(6)
11.5 Discontinuous Bifurcations of Elasto-Plastic Material for Plane Stress
308(2)
11.6 Discontinuous Bifurcations of Non-associated Flow Elasto-Plastic Materials Based on Yu Unified Strength Theory
310(7)
11.7 Discussion and Experimental Verification
317(2)
Summary
319(1)
Problems
320(1)
References and Bibliography
320(2)
12 Unified Characteristics Line Theory for Spatial Axisymmetric Problem 322(29)
12.1 Introduction
322(2)
12.2 The Unified Strength Theory
324(1)
12.3 Unified Characteristics Line Field Theory for Spatial Axisymmetric Problems (Stress Field)
324(5)
12.4 Unified Characteristics Line Field Theory for Spatial Axisymmetric Problems (Velocity Field)
329(2)
12.5 Applications of the Unified Characteristics Field Theory
331(3)
12.6 Penetration of High Velocity Rod to Target
334(4)
12.7 Elastic-Damage-Plastic Analysis of the Target
338(5)
12.8 Comparison and Verification
343(3)
Summary
346(1)
Problems
347(1)
References and Bibliography
348(3)
13 Unified Solution of Plastic Zones at Crack Tip under Small Scale Yielding 351(24)
13.1 Introduction
351(1)
13.2 Unified Strength Theory
352(3)
13.3 Stress Field Around Crack-Tip
355(2)
13.4 Shape and Size of Plastic Zone for Mode-I Crack Tip
357(4)
13.5 Shape and Size of Plastic Zone for Mode-II Crack Tip
361(4)
13.6 Plastic Zone for Mode-III Crack Tip
365(1)
13.7 Shape and Size of Plastic Zone for Non-Conventional Materials
365(3)
13.8 Effect of b' Value
368(1)
13.9 Influence of SD Effect
369(1)
13.10 Influence of Poisson's Ratio
370(1)
Summary
371(1)
Problems
372(2)
References and Bibliography
374(1)
14 Unified Fracture Criteria for Mixed Mode Crack Initiation and Fatigue Crack Growth 375(26)
14.1 Introduction
375(2)
14.2 Main Idea of T-Criterion
377(1)
14.3 A Generalization for T-Criterion Using UST
378(6)
14.4 Significance of Parameters b, α and v
384(4)
14.5 Crack Initiation Angle of the Generalized T-Criterion
388(1)
14.6 Application of the Unified Strength Theory in Establishing the Mixed Fracture Criterion
389(3)
14.7 Unified Fracture Criterion
392(3)
14.8 Unified Fracture Criterion of Mixed Mode I – III
395(1)
14.9 Unified Fracture Criterion of Mixed Mode II – III
396(1)
Summary
397(1)
Problems
398(1)
References and Bibliography
399(2)
15 Limit Load and Shakedown Load of Pressures Vessel 401(40)
15.1 Introduction
401(1)
15.2 Theorems of Limit Analysis of Structures
402(1)
15.3 Unified Solution of Limit Pressures for Thin-Walled Pressure Vessel
403(3)
15.4 Unified Solution of Elastic Limit Pressure for Thick-Walled Cylinders
406(10)
15.5 Unified Solution of Plastic Limit Pressure for Thick-Walled Cylinder
416(7)
15.6 Statical Shakedown Theorem (Melan Theorem)
423(2)
15.7 Unified Solution of Shakedown Pressure for Thick-Walled Cylinder
425(5)
15.8 Effects of Yield Function on the Plastic Limit Pressure and Shakedown Pressure of Thick-Walled Cylinders
430(4)
15.9 Connection between Shakedown Theorem and Limit Load Theorem
434(1)
Summary
435(1)
Problems
436(1)
References and Bibliography
437(4)
Indexes
Author Index
441(4)
Subject Index
445

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