Generalized plasticity

Title:

Publication Information:

Berlin : Springer-Verlag, 2005

ISBN:

9783540251279

Subject Term:

Plasticity -- Mathematical models

Elasticity -- Mathematical models

Strength of materials -- Mathematical models

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010113014	TA418.14 G46 2005	Open Access Book	Book	Searching... Unknown

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.

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

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