Generalized Plasticity / Edition 1

Generalized Plasticity / Edition 1

by Mao-Hong Yu
     
 

ISBN-10: 3540251278

ISBN-13: 9783540251279

Pub. Date: 10/20/2005

Publisher: Springer Berlin Heidelberg

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

Overview

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.

The book is divided into five major parts: 1. Yield function and choice; 2. Constitutive relation; 3. Slip-line Field Theory for plane strain problems, Characteristics Field Theory for plane stress problems and Characteristics Field Theory for spatial axisymmetrical problems; 4. Plastic zone analysis at crack tip and fracture criterion for mixed mode crack; 5. Limit loads and shakedown loads for pressure vessel. Examples of applications and problems are given for most chapters.

Product Details

ISBN-13:
9783540251279
Publisher:
Springer Berlin Heidelberg
Publication date:
10/20/2005
Edition description:
2006
Pages:
448
Product dimensions:
6.10(w) x 9.25(h) x 0.05(d)

Table of Contents


Preface
Notations
1 Introduction     1
Linear Elasticity     1
Classical Plasticity     2
Concrete Plasticity     5
Soil Plasticity     6
Rock Plasticity     7
Generalized Plasticity     8
Generalized Plasticity Based on the Unified Strength Theory     8
References and Bibliography     10
Stress Space and Stress State     15
Elements     15
Stress at a Point, Stress Invariants     15
Deviatoric Stress Tensor, Deviatoric Tensor Invariants     16
Stresses on the Oblique Plane     17
Hexahedron, Octahedron, Dodecahedron     21
Stress Space     22
Stress State Parameters     27
Summary     31
References     31
Basic Characteristics of Yield of Materials under Complex Stress     33
Introduction     33
Strength Difference Effect (SD effect)     33
Effect of Hydrostatic Stress     35
Effect of Normal Stress     37
Effect of Intermediate Principal Stress     38
Effect of Intermediate Principal Shear-Stress     43
Bounds of the Convex Strength Theories     46
Summary     47
References     47
Unified Strength Theory and Its Material Parameters     50
Introduction     50
Mechanical Model of the Unified Strength Theory     51
Unified Strength Theory     53
Special Cases of the Unified Strength Theory     54
Material Parameters of the Unified Strength Theory     60
Other Material Parameters of the Unified Strength Theory     63
Yield Surfaces and Yield Loci     66
Yield Loci of the Unified Strength Theory in the [pi] - Plane     69
Yield Surfaces of the Unified Strength Theory in Principal Stress Space     72
Yield Loci of the Unified Strength Theory in Plane Stress State     75
Unified Strength Theory in Meridian Plane     78
Yield Surfaces of the Non-linear Unified Strength Theory     81
Summary     85
Problems     87
References and Bibliography     93
Reasonable Choice of a Yield Function     95
Introduction     95
Some Experimental Data of Metallic Materials     96
Reasonable Choice of a Yield Function for Non-SD Materials     100
Experiments for Iron under [sigma]-[tau]Stress State     102
Experiments for Concrete under Complex Stress     103
Experiments for Rock under Complex Stress     105
Experiments on Clay and Loess under Complex Stress     108
Experiments on Sand under Complex Stress     109
Reasonable Choice of a Yield Function for SD-Materials     112
The Beauty of the Unified Strength Theory     113
Summary     117
Problems     118
References and Bibliography     119
Elasto-Plastic Costitutive Relations     122
Introduction     122
Plastic Deformation in Uniaxial Stress State     122
Three-dimensional Elastic Stress-strain Relation     124
Plastic Work Hardening and Strain Hardening     125
Plastic Flow Rule     127
Drucker's Postulate - Convexity of the Loading Surface     129
Incremental Constitutive Equations in Matrix Formulation     132
Determination of Flow Vector for Different Yield Functions     135
Singularity of Piecewise-Linear Yield Functions     137
Process of the Plastic Flow Singularity     142
Suggested Methods     145
Unified Process of the Corner Singularity     148
Summary     152
Problems     152
References and Bibliography     153
Concrete Plasticity     155
Introduction     155
Multi-Parameter Yield Criteria     157
Multi-Parameter Unified Yield Criterion     162
Yield and Loading Functions     168
Processing of Corner Singularity     176
Strain Softening Phenomena and Material Damage     179
Applcations     182
Summary     192
Problems     192
References and Bibliography     193
Twin-Shear Slip-Line Field for Plane Strain Problem     195
Introduction     195
Stress State in Plane Strain Problem     198
Twin-Shear Strength Theory of Plane Strain Problem     200
Twin-Shear Line Field Theory for Plane Strain Problem (Statically Admissible Field)     202
Twin-Shear Slip Line Field Theory for Plane Strain Problem (Kinematically Admissible Field)     204
Applications of the Twin-Shear Slip Line Field Theory for Plane Strain Problems     209
Summary     218
Problems     218
References and Bibliography     223
Unified Slip-Line Field Theory for Plane Strain Problem     225
Introduction     225
Unified Strength Theory in Plane Strain Condition      226
Unified Slip Line Field Theory for Plane Strain Problem (Statically Admissible Field)     230
Unified Slip Line Field Theory for Plane Strain Problem (Kinematically Admissible Field)     233
Special Cases of the Unified Slip Line Field Theory     236
Applications of the Unified Slip Line Field Theory     240
Comparison of the Unified Slip Line Field Theory with Finite Element Method     252
Comparison of the Unified Slip Line Field Theory with Experimental Results     256
Discontinuous Bifurcations of Elasto-Plastic Material For Plane Strain Problem     257
Summary     260
Problems     260
References and Bibliography     268
Twin-Shear Characteristics Field for Plane Stress Problem     270
Introduction     270
Characteristics Method Based on the Tresca Criterion and the Huber-von Mises Criterion     270
Characteristics Method Based on the Twin-Shear Yield Criterion     274
Twin-Shear Characteristics Field for Plane Stress Problems (Velocity Field)     278
Applications of the Twin-Shear Characteristics Method     281
Comparison of These Different Methods     287
Summary     288
Problems     288
References and Bibliography      292
Unified Characteristics Field Theory for Plane Stress Problem     293
Introduction     293
Unified Yield Function in Plane Stress State     293
Characteristics Filed for Plane Stress Problems     296
Applications of the Unified Characteristics Field for Plane Stress Problems     302
Discontinuous Bifurcations of Elasto-Plastic Material for Plane Stress     308
Discontinuous Bifurcations of Non-associated Flow Elasto-Plastic Materials Based on Yu Unified Strength Theory     310
Discussion and Experimental Verification     317
Summary     319
Problems     320
References and Bibliography     320
Unified Characteristics Line Theory for Spatial Axisymmetric Problem     322
Introduction     322
The Unified Strength Theory     324
Unified Characteristics Line Field Theory for Spatial Axisymmetric Problems (Stress Field)     324
Unified Characteristics Line Field Theory for Spatial Axisymmetric Problems (Velocity Field)     329
Applications of the Unified Characteristics Field Theory     331
Penetration of High Velocity Rod to Target     334
Elastic-Damage-Plastic Analysis of the Target     338
Comparison and Verification     343
Summary      346
Problems     347
References and Bibliography     348
Unified Solution of Plastic Zones at Crack Tip under Small Scale Yielding     351
Introduction     351
Unified Strength Theory     352
Stress Field Around Crack-Tip     355
Shape and Size of Plastic Zone for Mode-I Crack Tip     357
Shape and Size of Plastic Zone for Mode-II Crack Tip     361
Plastic Zone for Mode-III Crack Tip     365
Shape and Size of Plastic Zone for Non-Conventional Materials     365
Effect of 'b' Value     368
Influence of SD Effect     369
Influence of Poisson's Ratio     370
Summary     371
Problems     372
References and Bibliography     374
Unified Fracture Criteria for Mixed Mode Crack Initiation and Fatigue Crack Growth     375
Introduction     375
Main Idea of T-Criterion     377
A Generalization for T-Criterion Using UST     378
Significance of Parameters b, [alpha] and v     384
Crack Initiation Angle of the Generalized T-Criterion     388
Application of the Unified Strength Theory in Establishing the Mixed Fracture Criterion     389
Unified Fracture Criterion     392
Unified Fracture Criterion of Mixed Mode I-III     395
Unified Fracture Criterion of Mixed Mode II-III     396
Summary     397
Problems     398
References and Bibliography     399
Limit Load and Shakedown Load of Pressures Vessel     401
Introduction     401
Theorems of Limit Analysis of Structures     402
Unified Solution of Limit Pressures for Thin-Walled Pressure Vessel     403
Unified Solution of Elastic Limit Pressure for Thick-Walled Cylinders     406
Unified Solution of Plastic Limit Pressure for Thick-Walled Cylinder     416
Statical Shakedown Theorem (Melan Theorem)     423
Unified Solution of Shakedown Pressure for Thick-Walled Cylinder     425
Effects of Yield Function on the Plastic Limit Pressure and Shakedown Pressure of Thick-Walled Cylinders     430
Connection between Shakedown Theorem and Limit Load Theorem     434
Summary     435
Problems     436
References and Bibliography     437
Indexes
Author Index     441
Subject Index     445

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >