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E-raamat: Computational Plasticity: With Emphasis on the Application of the Unified Strength Theory

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Computational Plasticity with Emphasis on the Application of the Unified Strength Theory explores a new and important branch of computational mechanics and is the third book in a plasticity series published by Springer. The other two are: Generalized Plasticity, Springer: Berlin, 2006; and Structural Plasticity, Springer and Zhejiang University Press: Hangzhou, 2009.

This monograph describes the unified strength theory and associated flow rule, the implementation of these basic theories in computational programs, and shows how a series of results can be obtained by using them. The unified strength theory has been implemented in several special nonlinear finite-element programs and commercial Finite Element Codes by individual users and corporations. Many new and interesting findings for beams, plates, underground caves, excavations, strip foundations, circular foundations, slop, underground structures of hydraulic power stations, pumped-storage power stations, underground mining, high-velocity penetration of concrete structures, ancient structures, and rocket components, along with relevant computational results, are presented.

This book is intended for graduate students, researchers and engineers working in solid mechanics, engineering and materials science. The theories and methods provided in this book can also be used for other computer codes and different structures. More results can be obtained, which put the potential strength of the material to better use, thus offering material-saving and energy-saving solutions.





Mao-Hong Yu is a professor at the Department of Civil Engineering at Xi'an Jiaotong University, Xi'an, China.
1 Introduction
1(28)
1.1 Elasto-Plastic Finite Elements
1(2)
1.2 Bounds and Region of the Convex Yield Surface
3(1)
1.3 Unified Strength Theory and its Implementation in Computer Codes
4(3)
1.4 The Effect of Yield Criteria on the Numerical Analysis Results
7(5)
1.5 Historical Review: With Emphasis on the Implementation and Application of Unified Strength Theory
12(5)
1.6 Brief Summary
17(12)
References
19(10)
2 Stress and Strain
29(24)
2.1 Introduction
29(1)
2.2 Stress at a Point, Stress Invariants
29(2)
2.3 Deviatoric Stress Tensor and its Invariants
31(2)
2.4 Stresses on the Oblique Plane
33(4)
2.4.1 Stresses on the Oblique Plane
33(1)
2.4.2 Principal Shear Stresses
33(2)
2.4.3 Octahedral Shear Stress
35(2)
2.5 From Single-Shear Element to Twin-Shear Element
37(1)
2.6 Stress Space
38(4)
2.7 Stress State Parameters
42(3)
2.8 Strain Components
45(1)
2.9 Equations of Equilibrium
46(1)
2.10 Generalized Hooke's Law
46(2)
2.11 Compatibility Equations
48(1)
2.12 Governing Equations for Plane Stress Problems
49(1)
2.13 Governing Equations in Polar Coordinates
50(1)
2.14 Brief Summary
51(2)
References
52(1)
3 Material Models in Computational Plasticity
53(28)
3.1 Introduction
53(2)
3.2 Material Models for Non-SD Materials (Metallic Materials)
55(11)
3.2.1 Hydrostatic Stress Independence
55(1)
3.2.2 The Tensile Yield Stress Equals the Compressive Yield Stress
56(1)
3.2.3 Sixfold Symmetry of the Yield Function
56(1)
3.2.4 Convexity of the Yield Function
57(1)
3.2.5 Bounds of the Yield Function for Non-SD Materials
58(8)
3.3 Material Models for SD Materials
66(4)
3.3.1 General Behavior of Yield Function for SD Materials
66(1)
3.3.1.1 Six Basic Experimental Points for SD Materials
66(1)
3.3.1.2 Threefold Symmetry of the Yield Function
66(1)
3.3.1.3 Convexity of the Yield Function
67(1)
3.3.2 Three Basic Models for SD Materials
67(3)
3.4 Multi-Parameter Criteria for Geomaterials
70(5)
3.4.1 Multi-Parameter Single-Shear Failure Criterion
70(1)
3.4.2 Multi-Parameter Three-Shear Failure Criterion
71(3)
3.4.3 Multi-Parameter Twin-Shear Failure Criterion
74(1)
3.5 Bounds and the Region of the Convex Yield Function
75(2)
3.6 Brief Summary
77(4)
References
78(3)
4 Unified Strength Theory and its Material Parameters
81(48)
4.1 Introduction
81(1)
4.2 Mechanical Model of Unified Strength Theory
82(3)
4.3 Mathematical Modelling and the Determination of the Material Parameters of the Unified Strength Theory
85(1)
4.4 Mathematical Expression of the Unified Strength Theory
86(1)
4.5 Special Cases of the Unified Strength Theory
87(5)
4.5.1 Special Cases of the Unified Strength Theory (Varying b)
87(2)
4.5.2 Special Cases of the Unified Strength Theory (Varying α)
89(3)
4.6 Other Formulations of the UST and Material Parameters
92(3)
4.6.1 UST with Principal Stress and Compressive Strength F(σ1,σ2,σ3,α,σc)
92(1)
4.6.2 UST with Stress Invariant and Tensile Strength F(I1, J2, θ, σt, α)
93(1)
4.6.3 UST with Stress Invariant and Compressive Strength F(I1, J2, θ, α, σc)
94(1)
4.6.4 UST with Principal Stress and Cohesive Parameter F(σ1,σ2,σ3,C0,φ)
94(1)
4.6.5 UST with Stress Invariant and Cohesive Parameter F(I1, J2, θ, C0, φ)
95(1)
4.7 Other Material Parameters of the Unified Strength Theory
95(3)
4.7.1 Material Parameters β and C are Determined by Experimental Results of Uniaxial Tension Strength σt and Shear Strength τ0
96(1)
4.7.2 Material Parameters β and C are Determined by Experimental Results of Uniaxial Compressive Strength σ, and Shear Strength τ0
96(1)
4.7.3 Material Parameters β and C are Determined by Experimental Results of Uniaxial Compressive Strength σc and Biaxial Compressive Strength σcc
97(1)
4.7.4 Material Parameters β and C are Determined by Experimental Results of Uniaxial Compressive Strength σc and Biaxial Compressive Strength σcc
97(1)
4.7.5 Material Parameters β and C are Determined by Experimental Results of Uniaxial Compressive Strength σc and Biaxial Compressive Strength σcc
97(1)
4.8 Three-Parameter Unified Strength Theory
98(1)
4.9 Stress Space and Yield Loci of the UST
98(4)
4.10 Yield Surfaces of the UST in Principal Stress Space
102(5)
4.11 Extend of UST from Convex to Non-Convex
107(1)
4.12 Yield Loci of the UST in Plane Stress State
108(4)
4.13 Unified Strength Theory in Meridian Plane
112(2)
4.14 Extend of UST from Linear to Non-Linear UST
114(2)
4.15 Equivalent Stress of the Unified Strength Theory
116(3)
4.15.1 Equivalent Stresses for Non-SD Materials
117(1)
4.15.2 Equivalent Stresses for SD Materials
117(1)
4.15.3 Equivalent Stresses of the Unified Yield Criterion
117(1)
4.15.4 Equivalent Stress of the Unified Strength Theory
118(1)
4.16 Examples
119(3)
4.17 Summary
122(7)
References
125(4)
5 Non-Smooth Multi-Surface Plasticity
129(34)
5.1 Introduction
129(1)
5.2 Plastic Deformation in Uniaxial Stress State
130(2)
5.3 Three-Dimensional Elastic Stress-Strain Relation
132(1)
5.4 Plastic Work Hardening and Strain Hardening
133(3)
5.5 Plastic Flow Rule
136(1)
5.6 Drucker's Postulate -- Convexity of the Loading Surface
137(4)
5.7 Incremental Constitutive Equations in Matrix Formulation
141(3)
5.8 Determination of Flow Vector for Different Yield Functions
144(2)
5.9 Singularity of Piecewise-Linear Yield Functions
146(5)
5.10 Process of Singularity of the Plastic Flow Vector
151(2)
5.11 Suggested Methods
153(3)
5.12 Unified Process of the Corner Singularity
156(3)
5.12.1 Tresca Yield Criterion
156(1)
5.12.2 Mohr-Coulomb Yield Criterion
157(1)
5.12.3 Twin-Shear Yield Criterion
157(1)
5.12.4 Generalized Twin-Shear Yield Criterion
157(2)
5.13 Brief Summary
159(4)
References
160(3)
6 Implementation of the Unified Strength Theory into FEM Codes
163(20)
6.1 Introduction
163(2)
6.2 Bounds of the Single Criteria for Non-SD Materials
165(1)
6.3 Bounds of the Failure Criteria for SD Materials
166(2)
6.4 Unification of the Yield Criteria for Non-SD Materials and SD Materials
168(2)
6.5 Material Models
170(2)
6.6 Program Structure and its Subroutines Relating to the Unified Strength Theory: INVARY, YIELDY, FLOWVP
172(6)
6.6.1 Subroutine "Invar"
172(2)
6.6.2 Subroutine "Invary"
174(1)
6.6.3 Subroutine "Yieldy"
175(1)
6.6.4 Subroutine "Criten"
176(2)
6.7 Brief Summary
178(5)
References
178(5)
7 Examples of the Application of Unified Elasto-Plastic Constitutive Relations
183(16)
7.1 Introduction
183(1)
7.2 Plane Stress Problems
184(4)
7.2.1 Elasto-Plastic Analysis of a Cantilever Beam
184(3)
7.2.2 Elasto-Plastic Analysis of a Trapezoid Structure under Uniform Load
187(1)
7.3 Plane Strain Problems
188(2)
7.4 Spatial Axisymmetric Problems
190(7)
7.4.1 Analysis of Plastic Zone for Thick-Walled Cylinder
190(3)
7.4.2 Analysis for Limit-Bearing Capacity of a Circular Plate
193(2)
7.4.3 Truncated Cone under the Uniform Load on the Top
195(2)
7.5 Brief Summary
197(2)
References
198(1)
8 Strip with a Circular Hole under Tension and Compression
199(14)
8.1 Introduction
199(1)
8.2 Plastic Analysis of a Strip with a Circular Hole for Non-SD Material
200(3)
8.3 Elasto-Plastic Analysis of a Strip with a Circular Hole for SD Material under Tension
203(1)
8.4 Plastic Zone of a Strip with a Circular Hole for SD Material under Compression
204(1)
8.5 Comparison of Numerical Analysis with Experiments
205(2)
8.6 Elasto-Plastic Analysis of a Strip with a Circular Hole for a Special SD Material: Concrete
207(1)
8.7 Brief Summary
208(5)
References
211(2)
9 Plastic Analysis of Footing Foundation Based on the Unified Strenghth Theory
213(26)
9.1 Introduction
213(3)
9.2 Effect of Yield Criterion on the Limit Analysis of Footing
216(2)
9.3 Elasto-Plastic Analysis of Foundation Using UST
218(2)
9.4 Plastic Analysis of Strip Foundation Using UST
220(6)
9.5 Plastic Analysis of Circular Foundation Using UST
226(6)
9.5.1 Unified Characteristics Line Field of Spatial Axisymmetric Problem
226(1)
9.5.2 Numerical Simulation of Spatial Axisymmetric Problem
227(3)
9.5.3 Effect of UST Parameter φ on the Spread of Shear Strain
230(2)
9.6 Effect of UST Parameter b and φ on the Spread of Shear Strain
232(1)
9.7 Brief Summary
233(6)
References
234(5)
10 Underground Caves, Tunnels and Excavation of Hydraulic Power Station
239(30)
10.1 Introduction
239(2)
10.2 Effect of Yield Criterion on the Plastic Zone for a Circular Cave
241(1)
10.3 Plastic Zone for Underground Circular Cave under Two Direction Compressions
242(7)
10.3.1 Material Model
243(1)
10.3.2 Elastic Bearing Capacity
244(1)
10.3.3 Lasto-Plastic Analysis
245(1)
10.3.4 Comparison of Different Criteria
246(3)
10.4 Laxiwa Hydraulic Power Plant on the Yellow River
249(3)
10.5 Plastic Analysis for Underground Excavation at Laxiwa Hydraulic Power Station
252(4)
10.5.1 Strength of the Laxiwa Granite
252(2)
10.5.2 Plastic Zones Around the Underground Excavation Using the Single-Shear and Twin-Shear Theories
254(1)
10.5.3 Plastic Zones Around the Underground Excavation with Four Yield Cone Criteria
255(1)
10.6 The Effect of Failure Criterion on the Plastic Zone of the Underground Excavation
256(1)
10.7 Three Dimension Numerical Modeling of Underground Excavation for a Pumped-Storage Power Station
257(5)
10.8 Dynamic Response and Blast-Resistance Analysis of a Tunnel Subjected to Blast Loading
262(2)
10.9 Brief Summary
264(5)
References
266(3)
11 Implementation of the Unified Strength Theory into ABAQUS and its Application
269(20)
11.1 Introduction
269(1)
11.2 Basic Theory
270(2)
11.2.1 Expression of the Unified Strength Theory
270(1)
11.2.2 The General Expression of Elastic-Plastic Increment Theory
271(1)
11.3 ABAQUS UMAT (User Material)
272(5)
11.3.1 General Introduction of UMAT
272(1)
11.3.2 Interface and Algorithm of UMAT
273(1)
11.3.3 Elastic and Plastic State
273(2)
11.3.4 Constitutive Relationship Integration (Stress Update Method)
275(2)
11.3.5 Tangent Stiffness Method
277(1)
11.3.6 Treatment of the Singular Points on the Yield Surface
277(1)
11.4 Typical Numerical Example
277(4)
11.4.1 Model Conditions
277(1)
11.4.2 Comparison of 2D and 3D Solution from ABAQUS
278(1)
11.4.3 Results from UMAT of the United Strength Theory
278(3)
11.5 Engineering Applications
281(5)
11.5.1 Project Background and Material Parameters
281(1)
11.5.2 FEM Mesh and Boundary Condition
282(1)
11.5.3 Results of Analysis
282(4)
11.6 Conclusions
286(3)
References
287(2)
12 2D Simulation of Normal Penetration Using the Unified Strength Theory
289(32)
12.1 Introduction
289(2)
12.2 Penetration and Perforation
291(2)
12.3 Constitutive Model of Concrete
293(8)
12.4 Penetration and Perforation of Reinforced Concrete Slab
301(4)
12.5 Perforation of Fibre Reinforced Concrete Slab
305(4)
12.6 High Velocity Impact on Concrete Slabs Using UST and SPH Method
309(5)
12.6.1 Material Model for the Concrete Slab
310(1)
12.6.2 The Failure Surface
310(2)
12.6.3 The Elastic Limit Surface
312(1)
12.6.4 Strain Hardening
313(1)
12.6.5 Residual Failure Surface
313(1)
12.6.6 Damage Model
313(1)
12.7 Numerical Example
314(3)
12.8 Brief Summary
317(4)
References
318(3)
13 3D Simulation of Normal and Oblique Penetration and Perforation
321(12)
13.1 Introduction
321(1)
13.2 Simulation of Normal Impact Process
321(4)
13.3 Simulation of Oblique Impact Process
325(5)
13.4 Conclusions
330(3)
References
331(2)
14 Underground Mining
333(16)
14.1 Introduction
333(3)
14.2 Elastic-Brittle Damage Model Based on Twin-Shear Theory
336(2)
14.2.1 Damage Model
336(1)
14.2.2 Three-Dimensional Damage Model
336(2)
14.3 Non-Equilibrium Iteration for Dynamic Evolution
338(2)
14.4 Numerical Simulation of Caving Process Zone
340(4)
14.4.1 Introduction to Block Cave Mining
340(1)
14.4.2 Geometry and Undercut Scheme
340(1)
14.4.3 Result of Numerical Simulation
341(3)
14.5 Numerical Simulation for Crack Field Evolution in Long Wall Mining
344(5)
14.5.1 Geometry and FEM Model
344(1)
14.5.2 Evolution of Crack Field in the Roof
345(1)
14.5.3 Results of Displacement and Stress
346(2)
References
348(1)
15 Reinforced Concrete Beam and Plate
349(20)
15.1 Introduction
349(1)
15.2 Elasto-Plastic Analysis for Reinforced Concrete Beams
350(5)
15.2.1 Material Modelling
350(2)
15.2.2 Material Modeling of Concrete
352(1)
15.2.3 Reinforcing Steel
353(1)
15.2.4 Structural Modeling
353(1)
15.2.5 Simply Supported Beams
353(2)
15.3 Punching Shear Failure Analysis of Flat Slabs by UST
355(2)
15.3.1 Slab-Column Connections
355(1)
15.3.2 Conclusions
356(1)
15.4 Elasto-Plastic Analysis for an Ordinary RC Beam
357(2)
15.5 Elasto-Plastic Analysis of an RC Deep Beam
359(2)
15.6 Elasto-Plastic Analysis of an RC Box Sectional Beam
361(4)
15.7 Summary
365(4)
References
366(3)
16 Stability Analysis of Underground Caverns Based on the Unified Strength Theory
369(30)
16.1 Introduction
369(1)
16.2 Huanren Pumped-Storage Powerhouse and Geology
370(1)
16.2.1 The Powerhouse Region
370(1)
16.2.2 In Situ Stress Measurement in Huanren Pumped Storage Powerhouse
371(1)
16.3 Comparison of Failure Criteria for Geomaterials
371(2)
16.4 Determination of Rock Mass Strength Parameters
373(1)
16.5 Constitutive Formulation of Unified Strength Theory Used for Fast Lagrangian Analysis
374(5)
16.6 Development of Unified Strength Theory Model in Flac-3D
379(1)
16.7 Test of User-Defined Unified Strength Theory Constitutive Model in Flac-3D
379(3)
16.8 Stability Analysis of Underground Powerhouse
382(8)
16.8.1 Generation of Numerical Model and Selection of Parameters
382(1)
16.8.2 Simulations for Different Excavation Schemes
383(7)
16.9 Excavation and Support Modeling
390(3)
16.10 Comparison of the Stabilities in these Models with Different b Values
393(4)
16.11 Conclusions
397(2)
References
398(1)
17 Stability of Slope
399(18)
17.1 Introduction
399(3)
17.2 Effect of Yield Criterion on the Analysis of a Slope
402(5)
17.3 Stability of Three Gorges High Slope
407(3)
17.4 Stability of a Vertical Cut
410(1)
17.5 Stability for a Slope of a Highway
411(6)
References
415(2)
18 Unified Strength Theory and FLAC
417(30)
18.1 Introduction
417(2)
18.2 Unified Strength Theory Constitutive Model
419(1)
18.3 Governing Equation
420(5)
18.3.1 Balance Equation
420(2)
18.3.2 Explicit Numerical Procedure
422(1)
18.3.3 Constitutive Equation
422(3)
18.4 Unified Elasto-Plastic Constitutive Model
425(3)
18.4.1 Unified Elasto-Plastic Constitutive Model
425(3)
18.4.2 The Key to Implementation of the Constitutive Model
428(1)
18.5 Calculation and Analysis
428(11)
18.5.1 Slope Stability Analysis
428(1)
18.5.1.1 Associated Flow Rule
429(2)
18.5.1.2 Non-associated Flow Rule
431(1)
18.5.2 Thick-Walled Cylinder under Internal Pressure
432(2)
18.5.3 Bearing Capacity of Strip Footings
434(5)
18.6 Three Dimensional Simulation of a Large Landslide
439(5)
18.7 Conclusions
444(3)
References
445(2)
19 Mesomechanics and Multiscale Modelling for Yield Surface
447(34)
19.1 Introduction
447(3)
19.2 Interaction Yield Surface of Structures
450(1)
19.3 Models in Mesomechanics and Macromechanics
451(2)
19.3.1 RVE and HEM Model
451(1)
19.3.2 Equivalent Inclusion Model
451(1)
19.3.3 CSA and CCA Models
451(1)
19.3.4 Gurson Homogenized Model
452(1)
19.3.5 Periodic Distribution Model
452(1)
19.3.6 PHA Model and 3-Fold Axissymmetrical Model
452(1)
19.3.7 A Unit Cell of Masonry
452(1)
19.3.8 Topological Disorder Models
452(1)
19.3.9 Random Field Models of Heterogeneous Materials
453(1)
19.4 Failure Surface for Cellular Materials under Multiaxial Loads and Damage Surfaces of a Spheroidized Graphite Cast Iron
453(2)
19.5 Mesomechanics Analysis of Composite Using UST
455(2)
19.6 Multiscale Analysis of Yield Criterion of Metallic Glass Based on Atomistic Basis (Schuh and Lund, 2003)
457(2)
19.7 Multiscale Analysis of Yield Criterion of Molybdenum and Tungsten Based on Atomistic Basis (Groger et al, 2008)
459(1)
19.8 Phase Transformation Yield Criterion of Shape-Memory Alloys
459(2)
19.9 Atomic-Scale Study of Yield Criterion in Nanocrystalline CU
461(2)
19.10 A General Yield Criteria for Unit Cell in Multiscale Plasticity
463(5)
19.11 Virtual Material Testing Based on Crystal Plasticity Finite Element Simulations
468(1)
19.12 Meso-Mechanical Analysis of Failure Criterion for Concrete
469(3)
19.13 Brief Summary
472(9)
References
473(8)
20 Miscellaneous Issues: Ancient Structures, Propellant of Solid Rocket, Parts of Rocket and Generator
481(40)
20.1 Introduction
481(3)
20.2 Stability of Ancient City Wall in Xi'an
484(3)
20.3 Stability of the Foundation of Ancient Pagoda
487(5)
20.3.1 Structure of Foundation of Ancient Pagoda
487(2)
20.3.2 The Effect of Yield Criterion on Plastic Zone of Soil Foundation of Pagoda
489(3)
20.4 Plastic Analysis of Thick-Walled Cylinder
492(2)
20.5 Plastic Analysis of the Structural Part of a Rocket
494(2)
20.6 Numerical Analysis of Rocket Motor Grain
496(3)
20.7 3D Numerical Simulation for a Solid Rocket Motor
499(4)
20.8 Structural Part of the Generator of Nuclear Power Station
503(1)
20.9 The Effect of Yield Criterion on the Spread of the Shear Strain of Structure
504(1)
20.10 About the Unified Strength Theory: Reviews and Comments
505(5)
20.11 Signification and Determination of the UST Parameter b
510(4)
20.11.1 Signification of the UST Parameter b
510(2)
20.11.2 Determination of the UST Parameter b
512(2)
20.12 Brief Summary
514(7)
References
517(4)
Index 521
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