Unified Strength Theory and its Applications (2004. 450 p.)

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Unified Strength Theory and its Applications (2004. 450 p.)

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  • 製本 Hardcover:ハードカバー版/ページ数 450 p.
  • 商品コード 9783540437215

Full Description


It has been ten years since I presented the paper entitled "A new model and theory on yield and failure of materials under the complex stress state" at the Sixth Conference on Mechanical Behaviour of Materials held at Kyoto, Japan in 1991. The proceedings edited by Jono and Inoue were published by Pergamon Press in 1991. At that conference Professor Murakami and I were invited to act as the chairperson and co-chairperson of a session, and I presented the paper at another session. Few days before the conference, I had given a seminar regarding the tw- shear strength theory and the unified strength theory at Nagoya Technological University. These were the first two presentations of the unified strength theory, although I had completed the research of the unified strength theory in 1990. The paper "Twin-shear strength theory and its generalization" was published in the English edition of Sciences in China, the top journal in China, in 1985. The th original generalized twin-shear strength theory was presented at the 16 International Theoretical and Applied Mechanics Congress held at Copenhagen in Denmark and MPA (MaterialPrufungsAnstalt) at Stuttgart University, Germany in 1984. After this Congress I visited the MPA and School of Civil Engineering of Stuttgart University, and gave a seminar regarding the generalized twin-shear strength theory at MPA of Stuttgart University. Professor Otto Mohr (1835-1918) has had worked at the Stuttgart University. He was a very good professor, his lectures aroused great interest in his students.

Table of Contents

  1 Introduction                                   1  (10)
1.1 Strength of Materials under Complex 1 (3)
Stress States
1.2 Definition of Strength Theory 4 (1)
1.3 Significance and Development of 5 (2)
Strength Theory
1.4 Shape of the Limit Surface of Strength 7 (4)
Theory
2 Stress States of Elements 11 (18)
2.1 Elements 11 (1)
2.2 Stress at a Point: Stress Invariants 12 (1)
2.3 Stress Deviatoric Tensor, Deviatoric 13 (1)
Tensor Invariants
2.4 Stresses on the Oblique Plane 14 (4)
2.4.1 Stresses on the Oblique Plane 14 (1)
2.4.2 Principal Shear Stresses 15 (1)
2.4.3 Octahedral Shear Stress 16 (2)
2.5 Hexahedron, Octahedron, Dodecahedron 18 (2)
2.6 Stress Space 20 (5)
2.6.1 Relationship between (σ1, 23 (1)
σ2, σ3) and (x, y, z)
2.6.2 Relationship between (σ1, 23 (2)
σ2, σ3) and (ξ, r,
theta)or(J2, τm, theta)23
2.7 Stress State Parameters 25 (3)
Summary 28 (1)
3 Unified Yield Criteria 29 (34)
3.1 Introduction 29 (1)
3.2 General Behaviour of the Yield 30 (3)
Function
3.3 Yield Surface 33 (1)
3.4 Mechanical Model of the Unified Yield 34 (2)
Criterion
3.5 Unified Yield Criterion 36 (2)
3.6 Other Forms of the Unified Yield 38 (1)
Criterion
3.7 Special Cases of the Unified Yield 38 (8)
Criterion
3.7.1 Single-Shear Yield Criterion (b=0) 38 (2)
3.7.2 New Yield Criterion (b=1/4) 40 (1)
3.7.3 New Yield Criterion (b=1/2) 41 (3)
3.7.4 New Yield Criterion (b=3/4) 44 (1)
3.7.5 Twin-Shear Yield Criterion (b=1) 45 (1)
3.8 Extension of the Unified Yield 46 (4)
Criterion
3.9 Nonconvex Yield Criterion (b less
than 0 or b>1)
47
3.10 Unified Yield Criterion in the Plane 50 (3)
Stress State
3.11 Unified Yield Criterion in the σ 53 (2)
- theta Stress State
3.12 Examples 55 (6)
Summary 61 (1)
Problems 61 (2)
4 Verification of the Yield Criterion 63 (16)
4.1 Introduction 63 (1)
4.2 Comparison of the Unified Yield 63 (2)
Criterion with the General Behaviour of
Yield Criterion
4.3 Comparison of the Unified Yield 65 (4)
Criterion with Experimental Data
4.4 Comparison of the Yield Criteria with 69 (1)
the Tests of Taylor and Quinney
4.5 Comparison of the Yield Criteria with 70 (1)
the Tests of Ivey
4.6 Comparison of the Yield Criteria with 71 (3)
the Tests of Winstone
4.7 Comparison of the Yield Criteria with 74 (3)
the Experimental Results of Ellyin
Summary 77 (2)
5 Extended Unified Yield Criterion 79 (14)
5.1 Introduction 79 (1)
5.2 Extended Unified Yield Criterion 80 (1)
5.3 Special Cases of the Extended Unified 81 (5)
Yield Criterion
5.3.1 Extended Single-Shear Yield 81 (1)
Criterion (Extended Tresca Yield
Criterion)
5.3.2 New Extended Yield Criterion 82 (1)
(b=1/4)
5.3.2 New Extended Yield Criterion 83 (1)
(b=1/2, Linear Drucker-Prager Criterion)
5.3.4 New Extended Yield Criterion 84 (1)
(b=3/4)
5.3.5 New Extended Yield Criterion 85 (1)
(b=1, Extended Twin-Shear Yield
Criterion)
5.4 Yield Loci of the Extended Yield 86 (3)
Criterion in the Meridian and Deviatoric
Planes
5.5 Quadratic Extended Unified Yield 89 (1)
Criterion
Summary 90 (1)
Problems 90 (3)
6 Basic Characteristics of Strength of 93 (36)
Materials under Complex Stress
6.1 Introduction 93 (1)
6.2 Strength Difference Effect in Tension 93 (2)
and Compression (SD effect)
6.3 Effect of Hydrostatic Stress 95 (5)
6.4 Effect of Normal Stress 100(3)
6.5 Research on the Effect of 103(2)
Intermediate Principal Stress
6.6 Effects of the Intermediate Principal 105(3)
Stress in Metals
6.7 Effects of the Intermediate Principal 108(10)
Stress in Rock
6.8 Characteristics of the Effect of 118(1)
Intermediate Principal Stress in Rock
6.9 Effects of the Intermediate Principal 119(6)
Stress in Concrete
6.10 Engineering Applications of the Effect 125(2)
of Intermediate Principal Stress in Concrete
6.11 Bounds of the Convex Strength Theories 127(1)
Summary 128(1)
7 Unified Strength Theory 129(46)
7.1 Introduction 129(1)
7.2 General Behaviour of Strength Theory 130(2)
7.3 Mechanical Model of the Unified 132(2)
Strength Theory
7.4 Unified Strength Theory 134(3)
7.5 Other Formulations of the Unified 137(2)
Strength Theory
7.5.1 In Terms of Stress Invariant F 137(1)
(I1, J2, theta, σt α)
7.5.2 In Terms of Principal Stress and 137(1)
Cohesive Parameter F (σ 1,
σ 2, σ 3, C0, φ)
7.5.3 In Terms of Stress Invariant and 138(1)
Cohesive Parameter F(I1, J2, theta, C0,
φ)
7.5.4 In Terms of Principal Stresses 138(1)
and Compressive Strength Parameter F
(σ 1, σ 2, σ 3,
α, σ c)
7.5.5 In Terms of Stress Invariant and 139(1)
Compressive Strength Parameter F (I1,
J2, theta, α, σ c)
7.6 Extension and Supplementation of 139(1)
Conclusions from the Unified Strength
Theory
7.7 Special Cases of the Unified Strength 140(5)
Theory
7.7.1 Varying Parameter b 140(2)
7.7.2 Varying Parameter α 142(3)
7.8 Nonconvex Strength Theory (b less
than 0 or b>
143
7.8.1 Nonconvex Strength Theory (b less
than 0) 144
7.8.2 Nonconvex Strength Theory (b>1) 145(1)
7.8.3 Nonconvex yield criteria for 146(1)
α=1
7.9 Limit Loci of the Unified Strength 146(59)
Theory in the π Plane
7.9.1 Variation of the Unified Strength 148(2)
Theory with b
7.9.2 Limit Locus of the Unified 150(7)
Strength Theory by Varying α
7.10 Limit Surfaces of the Unified Strength 157(2)
Theory in Principal Stress Space
7.11 Limit Loci of the Unified Strength 159(4)
Theory in Plane Stress State
7.11.1 Variation of the Unified 160(2)
Strength Theory with b
7.11.2 Limit Locus of the Unified 162(1)
Strength Theory by Varying α
7.12 Limit Loci of the Unified Strength 163(2)
Theory under σ - τ Combined
Stress State
7.13 Unified Strength Theory in the 165(2)
Meridian Plane
7.14 Generalizations of the Unified 167(2)
strength Theory
7.15 Significance of the Unified Strength 169(2)
Theory
Summary 171(1)
Problems 172(3)
8 Experimental Verification of Strength Theory 175(32)
8.1 Introduction 175(1)
8.2 Equipments for complex stress state 175(6)
experiments
8.2.1 Experimental Equipments for 176(1)
Tension (Compression)-Torsion Stress
States
8.2.2 Biaxial Plane Experimental 176(1)
Equipments
8.2.3 Equipment for Axisymmetrical 177(1)
Triaxial Experiments
8.2.4 Equipment for True Triaxial 178(3)
Experiments
8.3 Axial-loading and Torsion Experiments 181(2)
8.4 Experimental Verification of Strength 183(7)
Theory for Rock
8.5 A Systematic Experiment on Rock under 190(5)
True Triaxial Stress
8.5.1 Strength of Rock under High 190(1)
Pressure
8.5.2 The Effect of Intermediate 191(1)
Principal Stress
8.5.3 The Effect of Stress Angle 192(1)
8.5.4 Limit Meridian Loci 193(1)
8.5.5 The Limit Loci on the π-Plane 194(1)
8.6 Experimental Verification of Strength 195(4)
Theory for Concrete
8.7 Experiments on Clay and Loess under 199(2)
Complex Stress
8.8 Experiments on Sand under Complex Stress 201(2)
8.9 The Ultimate Dynamic Strength of Sand 203(2)
under Complex Stress
Summary 205(2)
9 Applications of the Unified Yield Criterion 207(30)
9.1 Introduction 207(2)
9.2 Theorems of limit analysis 209(1)
9.2.1 Lower-Bound Theorem 210(1)
9.2.2 Upper-Bound Theorem 210(1)
9.3 Generalized Stresses and Generalized 210(2)
Strains
9.4 Basic Equations of Circular Plates 212(5)
9.5 Fields of Internal Moments 217(3)
9.6 Fields of Velocity 220(4)
9.7 Comparison with Existing Solutions 224(1)
9.8 Rotating Discs and Rotating Cylinders 225(1)
9.9 Elastic Limit of Discs 226(1)
9.10 Elasto-Plastic Analysis of Discs 227(1)
9.11 Elasto-Plastic Stress Fields of 228(2)
Rotating Discs
9.12 Solution Procedure and Results 230(4)
9.13 Plastic Limit analysis of Rotating 234(1)
Cylinder
9.14 Application of the Unified Strength 235(1)
Theory
Summary 235(1)
Problems 236(1)
10 The Effects of Failure Criteria on 237(56)
Structural Analysis
10.1 Introduction 237(3)
10.2 Bounds and the Region of the Convex 240(1)
Limit Surface
10.3 Nonconvex Limit Loci 240(1)
10.4 Effect of Failure Criteria on 241(3)
Thin-Walled Pressure Vessel Design
10.5 Limit Pressure of Thick-Walled Hollow 244(6)
Spheres
10.5.1 Elastic Limit Pressure of 246(2)
Thick-Walled Spherical Shell
10.5.2 Plastic Limit Pressure of 248(2)
Thick-Walled Spherical Shell
10.6 Effects of Failure Criteria on the 250(8)
Elastic Limit Pressure of Thick-Walled
Cylinders
10.7 Effects of Failure Criteria on the 258(7)
Plastic Limit Pressure of Thick-Walled
Cylinder
10.7.1 Stress Distribution 258(1)
10.7.2 Plastic Zone in the 259(1)
Elasto-Plastic Range
10.7.3 Plastic Zone Radius in the 260(1)
Elasto-Plastic Range
10.7.4 Plastic Limit Pressure 261(4)
10.8 Effects of Failure Criteria on the 265(6)
Shape and Size of the Crack Tip Plastic Zone
10.8.1 Mode I Crack in Plane Stress 266(2)
State
10.8.2 Mode I Crack in Plane Strain 268(1)
10.8.3 Mode II Crack in Plane Stress 269(1)
10.8.4 Mode II Crack in Plane Strain 270(1)
State
10.9 Effects of Failure Criteria on FEM 271(17)
Analysis
10.9.1 Effects of Failure Criteria on 272(1)
FEM Analysis for Limit Bearing Capacity
of Plates
10.9.2 Effects of Failure Criteria on 273(2)
FEM Analysis of Plastic Zones for
Thick-Walled Cylinders
10.9.3 Effects of Failure Criterion on 275(1)
FEM Analysis for a Strip with a Hole
10.9.4 Effects of Failure Criterion on 276(3)
FEM Analysis of Plastic Zone for
Circular Cave
10.9.5 Effects of Failure Criterion on 279(2)
Mesomechanical Analysis of Failure
Criterion
10.9.6 Effects of Failure Criteria on 281(3)
FEM Analysis of Composites
10.9.7 Effects of Failure Criteria on 284(4)
FEM Analysis for Underground Caves
Summary 288(1)
Problems 289(4)
11 Historical Reviews 293(60)
11.1 Introduction 293(1)
11.2 Strength Theories before the Twentieth 293(8)
Century
11.2.1 Early Work 293(4)
11.2.2 Strength Theories before the 297(2)
Twentieth Century
11.2.3 Strength Theories at the 299(2)
Begining of the Twentieth Century
11.3 Three Series of Strength Theories 301(14)
11.3.1 Single-Shear Strength Theory 302(3)
(SSS theory)
11.3.2 Octahedral-Shear Strength Theory 305(7)
(OSS Theory)
11.3.3 Twin-Shear Strength Theory (TSS 312(3)
theory)
11.4 Establishment of the Unified Yield 315(4)
Criteria
11.4.1 Curved General Yield Criteria 315(2)
11.4.2 Linear Unified Yield Criterion 317(2)
11.5 Failure Criteria of Rock, Concrete, 319(14)
Soil, Iron, Polymer and Other Materials
11.5.1 Failure Criteria for Rock 320(2)
11.5.2 Failure Criteria for Concrete 322(1)
11.5.3 Failure Criteria for Soil 323(2)
11.5.4 Failure Criteria for Iron 325(1)
11.5.5 Failure Criteria of Ice 325(1)
11.5.6 Failure Criteria for Wood 326(1)
11.5.7 Failure Criteria for Polymers 326(2)
11.5.8 Failure Criteria of Energetic 328(1)
Materials (TNT, RDX and Solid Rocket
Propellant)
11.5.9 Failure Criteria for Ceramic and 328(1)
Glass
11.5.10 Failure Criteria of Other 329(4)
Materials
11.6 Unified Strength Theory 333(11)
11.6.1 Octahedral-Shear Generalized 334(1)
Strength Theory
11.6.2 Unified Strength Theory (Yu and 335(2)
He 1991)
11.6.3 Special Cases of the Unified 337(3)
Strength Theory
11.6.4 Comparison and Choice 340(1)
11.6.5 Application of the Unified 341(1)
Strength Theory
11.6.6 Nonconvex Strength Theory 342(2)
11.7 Computational Implementation of the 344(4)
Strength Theory
Summary 348(3)
Problems 351(2)
12 References and Bibliography 353(54)
12.1 Early Works (before 1900) 353(1)
12.2 Works from 1901 to 1950 354(4)
12.3 Works from 1951 to 1960 358(5)
12.4 Works from 1961 to 1970 363(7)
12.5 Works from 1971 to 1980 370(9)
12.6 Works from 1981 to 1990 379(9)
12.7 Works from 1991 to 2000 388(14)
12.8 Works from 2001 to 2002 402(5)
Author Index 407(4)
Subject Index 411