Generalized Plasticity

by Yu, Mao-Hong; Ma, Guo-Wei; Qiang, Hong-Fu; Zhang, Yong-Qiang

• ISBN13: 9783540251279
• ISBN10: 3540251278
• Format: Hardcover
• Copyright: 2005-12-16
• Publisher: Springer Verlag

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