Generalized Plasticity

By: Mao-Hong Yu, Guo-Wei Ma (As told to), Hong-Fu Qiang (As told to)

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Hardcover | 20 October 2005

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Generalized Plasticity deals with the expansion of Unified Strength Theory to Plasticity Theory, leading to a unified treatment - of metal plasticity for Tresca materials, Huber-von-Mises materials and twin-shear materials, - of geomaterial plasticity for Mohr-Coulomb materials and generalized twin-shear materials, - of metal plasticity and plasticity of geomaterials, generally. The book is based on lectures given at Xian Jiaotong University, China and Nanyang Technological University, Singapore. It addresses researchers and students in Civil Engineering and Mechanics.

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Preface
Notations
1 Introduction	p. 1
Linear Elasticity	p. 1
Classical Plasticity	p. 2
Concrete Plasticity	p. 5
Soil Plasticity	p. 6
Rock Plasticity	p. 7
Generalized Plasticity	p. 8
Generalized Plasticity Based on the Unified Strength Theory	p. 8
References and Bibliography	p. 10
Stress Space and Stress State	p. 15
Elements	p. 15
Stress at a Point, Stress Invariants	p. 15
Deviatoric Stress Tensor, Deviatoric Tensor Invariants	p. 16
Stresses on the Oblique Plane	p. 17
Hexahedron, Octahedron, Dodecahedron	p. 21
Stress Space	p. 22
Stress State Parameters	p. 27
Summary	p. 31
References	p. 31
Basic Characteristics of Yield of Materials under Complex Stress	p. 33
Introduction	p. 33
Strength Difference Effect (SD effect)	p. 33
Effect of Hydrostatic Stress	p. 35
Effect of Normal Stress	p. 37
Effect of Intermediate Principal Stress	p. 38
Effect of Intermediate Principal Shear-Stress	p. 43
Bounds of the Convex Strength Theories	p. 46
Summary	p. 47
References	p. 47
Unified Strength Theory and Its Material Parameters	p. 50
Introduction	p. 50
Mechanical Model of the Unified Strength Theory	p. 51
Unified Strength Theory	p. 53
Special Cases of the Unified Strength Theory	p. 54
Material Parameters of the Unified Strength Theory	p. 60
Other Material Parameters of the Unified Strength Theory	p. 63
Yield Surfaces and Yield Loci	p. 66
Yield Loci of the Unified Strength Theory in the [pi] - Plane	p. 69
Yield Surfaces of the Unified Strength Theory in Principal Stress Space	p. 72
Yield Loci of the Unified Strength Theory in Plane Stress State	p. 75
Unified Strength Theory in Meridian Plane	p. 78
Yield Surfaces of the Non-linear Unified Strength Theory	p. 81
Summary	p. 85
Problems	p. 87
References and Bibliography	p. 93
Reasonable Choice of a Yield Function	p. 95
Introduction	p. 95
Some Experimental Data of Metallic Materials	p. 96
Reasonable Choice of a Yield Function for Non-SD Materials	p. 100
Experiments for Iron under [sigma]-[tau]Stress State	p. 102
Experiments for Concrete under Complex Stress	p. 103
Experiments for Rock under Complex Stress	p. 105
Experiments on Clay and Loess under Complex Stress	p. 108
Experiments on Sand under Complex Stress	p. 109
Reasonable Choice of a Yield Function for SD-Materials	p. 112
The Beauty of the Unified Strength Theory	p. 113
Summary	p. 117
Problems	p. 118
References and Bibliography	p. 119
Elasto-Plastic Costitutive Relations	p. 122
Introduction	p. 122
Plastic Deformation in Uniaxial Stress State	p. 122
Three-dimensional Elastic Stress-strain Relation	p. 124
Plastic Work Hardening and Strain Hardening	p. 125
Plastic Flow Rule	p. 127
Drucker's Postulate - Convexity of the Loading Surface	p. 129
Incremental Constitutive Equations in Matrix Formulation	p. 132
Determination of Flow Vector for Different Yield Functions	p. 135
Singularity of Piecewise-Linear Yield Functions	p. 137
Process of the Plastic Flow Singularity	p. 142
Suggested Methods	p. 145
Unified Process of the Corner Singularity	p. 148
Summary	p. 152
Problems	p. 152
References and Bibliography	p. 153
Concrete Plasticity	p. 155
Introduction	p. 155
Multi-Parameter Yield Criteria	p. 157
Multi-Parameter Unified Yield Criterion	p. 162
Yield and Loading Functions	p. 168
Processing of Corner Singularity	p. 176
Strain Softening Phenomena and Material Damage	p. 179
Applcations	p. 182
Summary	p. 192
Problems	p. 192
References and Bibliography	p. 193
Twin-Shear Slip-Line Field for Plane Strain Problem	p. 195
Introduction	p. 195
Stress State in Plane Strain Problem	p. 198
Twin-Shear Strength Theory of Plane Strain Problem	p. 200
Twin-Shear Line Field Theory for Plane Strain Problem (Statically Admissible Field)	p. 202
Twin-Shear Slip Line Field Theory for Plane Strain Problem (Kinematically Admissible Field)	p. 204
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
Unified Slip-Line Field Theory for Plane Strain Problem	p. 225
Introduction	p. 225
Unified Strength Theory in Plane Strain Condition	p. 226
Unified Slip Line Field Theory for Plane Strain Problem (Statically Admissible Field)	p. 230
Unified Slip Line Field Theory for Plane Strain Problem (Kinematically Admissible Field)	p. 233
Special Cases of the Unified Slip Line Field Theory	p. 236
Applications of the Unified Slip Line Field Theory	p. 240
Comparison of the Unified Slip Line Field Theory with Finite Element Method	p. 252
Comparison of the Unified Slip Line Field Theory with Experimental Results	p. 256
Discontinuous Bifurcations of Elasto-Plastic Material For Plane Strain Problem	p. 257
Summary	p. 260
Problems	p. 260
References and Bibliography	p. 268
Twin-Shear Characteristics Field for Plane Stress Problem	p. 270
Introduction	p. 270
Characteristics Method Based on the Tresca Criterion and the Huber-von Mises Criterion	p. 270
Characteristics Method Based on the Twin-Shear Yield Criterion	p. 274
Twin-Shear Characteristics Field for Plane Stress Problems (Velocity Field)	p. 278
Applications of the Twin-Shear Characteristics Method	p. 281
Comparison of These Different Methods	p. 287
Summary	p. 288
Problems	p. 288
References and Bibliography	p. 292
Unified Characteristics Field Theory for Plane Stress Problem	p. 293
Introduction	p. 293
Unified Yield Function in Plane Stress State	p. 293
Characteristics Filed for Plane Stress Problems	p. 296
Applications of the Unified Characteristics Field for Plane Stress Problems	p. 302
Discontinuous Bifurcations of Elasto-Plastic Material for Plane Stress	p. 308
Discontinuous Bifurcations of Non-associated Flow Elasto-Plastic Materials Based on Yu Unified Strength Theory	p. 310
Discussion and Experimental Verification	p. 317
Summary	p. 319
Problems	p. 320
References and Bibliography	p. 320
Unified Characteristics Line Theory for Spatial Axisymmetric Problem	p. 322
Introduction	p. 322
The Unified Strength Theory	p. 324
Unified Characteristics Line Field Theory for Spatial Axisymmetric Problems (Stress Field)	p. 324
Unified Characteristics Line Field Theory for Spatial Axisymmetric Problems (Velocity Field)	p. 329
Applications of the Unified Characteristics Field Theory	p. 331
Penetration of High Velocity Rod to Target	p. 334
Elastic-Damage-Plastic Analysis of the Target	p. 338
Comparison and Verification	p. 343
Summary	p. 346
Problems	p. 347
References and Bibliography	p. 348
Unified Solution of Plastic Zones at Crack Tip under Small Scale Yielding	p. 351
Introduction	p. 351
Unified Strength Theory	p. 352
Stress Field Around Crack-Tip	p. 355
Shape and Size of Plastic Zone for Mode-I Crack Tip	p. 357
Shape and Size of Plastic Zone for Mode-II Crack Tip	p. 361
Plastic Zone for Mode-III Crack Tip	p. 365
Shape and Size of Plastic Zone for Non-Conventional Materials	p. 365
Effect of 'b' Value	p. 368
Influence of SD Effect	p. 369
Influence of Poisson's Ratio	p. 370
Summary	p. 371
Problems	p. 372
References and Bibliography	p. 374
Unified Fracture Criteria for Mixed Mode Crack Initiation and Fatigue Crack Growth	p. 375
Introduction	p. 375
Main Idea of T-Criterion	p. 377
A Generalization for T-Criterion Using UST	p. 378
Significance of Parameters b, [alpha] and v	p. 384
Crack Initiation Angle of the Generalized T-Criterion	p. 388
Application of the Unified Strength Theory in Establishing the Mixed Fracture Criterion	p. 389
Unified Fracture Criterion	p. 392
Unified Fracture Criterion of Mixed Mode I-III	p. 395
Unified Fracture Criterion of Mixed Mode II-III	p. 396
Summary	p. 397
Problems	p. 398
References and Bibliography	p. 399
Limit Load and Shakedown Load of Pressures Vessel	p. 401
Introduction	p. 401
Theorems of Limit Analysis of Structures	p. 402
Unified Solution of Limit Pressures for Thin-Walled Pressure Vessel	p. 403
Unified Solution of Elastic Limit Pressure for Thick-Walled Cylinders	p. 406
Unified Solution of Plastic Limit Pressure for Thick-Walled Cylinder	p. 416
Statical Shakedown Theorem (Melan Theorem)	p. 423
Unified Solution of Shakedown Pressure for Thick-Walled Cylinder	p. 425
Effects of Yield Function on the Plastic Limit Pressure and Shakedown Pressure of Thick-Walled Cylinders	p. 430
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
Table of Contents provided by Ingram. All Rights Reserved.

Generalized Plasticity

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