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E-raamat: Statistical Physics of Fracture, Beakdown and Earthquake - Effects of Disorder and Heterogeneity: Effects of Disorder and Heterogeneity [Wiley Online]

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Statistical Physics of Fracture, Beakdown and Earthquake - Effects of Disorder and Heterogeneity: Effects of Disorder and HeterogeneitySuurem pilt
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9783527672646
In this book, the authors bring together basic ideas from fracture mechanics and statistical physics, classical theories, simulation and experimental results to make the statistical physics aspects of fracture more accessible.

In this book, the authors bring together basic ideas from fracture mechanics and statistical physics, classical theories, simulation and experimental results to make the statistical physics aspects of fracture more accessible.
They explain fracture-like phenomena, highlighting the role of disorder and heterogeneity from a statistical physical viewpoint. The role of defects is discussed in brittle and ductile fracture, ductile to brittle transition, fracture dynamics, failure processes with tension as well as compression: experiments, failure of electrical networks, self-organized critical models of earthquake and their extensions to capture the physics of earthquake dynamics. The text also includes a discussion of dynamical transitions in fracture propagation in theory and experiments, as well as an outline of analytical results in fiber bundle model dynamics
With its wide scope, in addition to the statistical physics community, the material here is equally accessible to engineers, earth scientists, mechanical engineers, and material scientists. It also serves as a textbook for graduate students and researchers in physics.
Series Editors' Preface xiii
Preface xv
Notations xvii
1 Introduction 1(6)
2 Mechanical and Fracture Properties of Solids 7(10)
2.1 Mechanical Response in Materials
8(3)
2.1.1 Elastic and Plastic Regions
8(1)
2.1.2 Linear Elastic Region
9(1)
2.1.3 Nonlinear Plastic Region
10(1)
2.2 Ductile, Quasi-brittle, and Brittle Materials
11(1)
2.3 Ductile and Brittle Fracture
11(6)
2.3.1 Macroscopic Features of Ductile and Brittle Fractures
12(2)
2.3.2 Microscopic Features of Ductile and Brittle Fractures
14(3)
3 Crystal Defects and Disorder in Lattice Models 17(10)
3.1 Point Defects
17(1)
3.2 Line Defects
18(2)
3.3 Planar Defects
20(2)
3.4 Lattice Defects: Percolation Theory
22(3)
3.5 Summary
25(2)
4 Nucleation and Extreme Statistics in Brittle Fracture 27(18)
4.1 Stress Concentration Around Defect
27(5)
4.1.1 Griffith's Theory of Crack Nucleation in Brittle Fracture
30(2)
4.2 Strength of Brittle Solids: Extreme Statistics
32(2)
4.2.1 Weibull and Gumbel Statistics
32(2)
4.3 Extreme Statistics in Fiber Bundle Models of Brittle Fracture
34(3)
4.3.1 Fiber Bundle Model
34(5)
4.3.1.1 Strength of the Local Load Sharing Fiber Bundles
35(1)
4.3.1.2 Crossover from Extreme to Self-averaging Statistics in the Model
35(2)
4.4 Extreme Statistics in Percolating Lattice Model of Brittle Fracture
37(2)
4.5 Molecular Dynamics Simulation of Brittle Fracture
39(3)
4.5.1 Comparisons with Griffith's Theory
39(2)
4.5.2 Simulation of Highly Disordered Solids
41(1)
4.6 Summary
42(3)
5 Roughness of Fracture Surfaces 45(24)
5.1 Roughness Properties in Fracture
45(21)
5.1.1 Self-affine Scaling of Fractured Surfaces
46(1)
5.1.2 Out-of-plane Fracture Roughness
47(2)
5.1.3 Distribution of Roughness: Mono- and Multi-affinity
49(7)
5.1.3.1 Nonuniversal Cases
50(4)
5.1.3.2 Anisotropic Scaling
54(2)
5.1.4 In-plane Roughness of Fracture Surfaces
56(6)
5.1.4.1 Waiting Time Distributions in Crack Propagation
60(2)
5.1.5 Effect of Probe Size
62(3)
5.1.6 Effect of Spatial Correlation and Anisotropy
65(1)
5.2 Molecular Dynamics Simulation of Fractured Surface
66(2)
5.3 Summary
68(1)
6 Avalanche Dynamics in Fracture 69(42)
6.1 Probing Failure with Acoustic Emissions
70(4)
6.2 Dynamics of Fiber Bundle Model
74(14)
6.2.1 Dynamics Around Critical Load
77(4)
6.2.2 Dynamics at Critical Load
81(1)
6.2.3 Avalanche Statistics of Energy Emission
81(1)
6.2.4 Precursors of Global Failure in the Model
82(2)
6.2.5 Burst Distribution: Crossover Behavior
84(1)
6.2.6 Abrupt Rupture and Tricritical Point
85(2)
6.2.7 Disorder in Elastic Modulus
87(1)
6.3 Interpolations of Global and Local Load Sharing Fiber Bundle Models
88(13)
6.3.1 Power-law Load Sharing
89(1)
6.3.2 Mixed-mode Load Sharing
90(2)
6.3.3 Heterogeneous Load Sharing
92(19)
6.3.3.1 Dependence on Loading Process
93(1)
6.3.3.2 Results in One Dimension
94(2)
6.3.3.3 Results in Two Dimensions
96(5)
6.3.3.4 Comparison with Mixed Load Sharing Model
101(1)
6.4 Random Threshold Spring Model
101(6)
6.5 Summary
107(4)
7 Subcritical Failure of Heterogeneous Materials 111(24)
7.1 Time of Failure Due to Creep
111(18)
7.1.1 Fluctuating Load
112(7)
7.1.2 Failure Due to Fatigue in Fiber Bundles
119(3)
7.1.3 Creep Rupture Propagation in Rheological Fiber Bundles
122(13)
7.1.3.1 Modification for Local Load Sharing Scheme
126(3)
7.2 Dynamics of Strain Rate
129(5)
7.3 Summary
134(1)
8 Dynamics of Fracture Front 135(30)
8.1 Driven Fluctuating Line
135(11)
8.1.1 Variation of Universality Class
140(2)
8.1.2 Depinning with Constant Volume
142(2)
8.1.3 Infinite-range Elastic Force with Local Fluctuations
144(2)
8.2 Fracture Front Propagation in Fiber Bundle Models
146(15)
8.2.1 Interfacial Crack Growth in Fiber Bundle Model
146(3)
8.2.2 Crack Front Propagation in Fiber Bundle Models
149(2)
8.2.3 Self-organized Dynamics in Fiber Bundle Model
151(10)
8.3 Hydraulic Fracture
161(2)
8.4 Summary
163(2)
9 Dislocation Dynamics and Ductile Fracture 165(12)
9.1 Nonlinearity in Materials
165(1)
9.2 Deformation by Slip
165(2)
9.2.1 Critical Stress to Create Slip in Perfect Lattice
166(1)
9.3 Slip by Dislocation Motion
167(2)
9.4 Plastic Strain due to Dislocation Motion
169(1)
9.5 When Does a Dislocation Move?
170(2)
9.5.1 Dislocation Width
170(1)
9.5.2 Dependence on Grain Boundaries in Crystals
171(1)
9.5.3 Role of Temperature
171(1)
9.5.4 Effect of Applied Stress
172(1)
9.6 Ductile-Brittle Transition
172(2)
9.6.1 Role of Confining Pressure
172(1)
9.6.2 Role of Temperature
173(1)
9.7 Theoretical Work on Ductile-Brittle Transition
174(3)
10 Electrical Breakdown Analogy of Fracture 177(30)
10.1 Disordered Fuse Network
178(7)
10.1.1 Dilute Limit (p -> 1)
179(1)
10.1.2 Critical Behavior (p -> pc)
180(1)
10.1.3 Influence of the Sample Size
181(1)
10.1.4 Distribution of the Failure Current
182(1)
10.1.4.1 Dilute Limit (p -> 1)
182(1)
10.1.4.2 At Critical Region (p -> pc)
183(1)
10.1.5 Continuum Model
183(1)
10.1.6 Electromigration
184(1)
10.2 Numerical Simulations of Random Fuse Network
185(12)
10.2.1 Disorders in Failure Thresholds
187(1)
10.2.2 Avalanche Size Distribution
188(3)
10.2.3 Roughness of Fracture Surfaces in RFM
191(2)
10.2.4 Effect of High Disorder
193(3)
10.2.5 Size Effect
196(1)
10.3 Dielectric Breakdown Problem
197(8)
10.3.1 Dilute Limit (p -> 1)
198(1)
10.3.2 Close to Critical Point (p -> pc)
199(1)
10.3.3 Influence of Sample Size
199(1)
10.3.4 Distribution of Breakdown Field
200(1)
10.3.5 Continuum Model
200(1)
10.3.6 Shortest Path
201(1)
10.3.7 Numerical Simulations in Dielectric Breakdown
201(6)
10.3.7.1 Stochastic Models
201(1)
10.3.7.2 Deterministic Models
202(3)
10.4 Summary
205(2)
11 Earthquake as Failure Dynamics 207(58)
11.1 Earthquake Statistics: Empirical Laws
207(7)
11.1.1 Universal Scaling Laws
209(5)
11.2 Spring-block Models of Earthquakes
214(13)
11.2.1 Computer Simulation of the Burridge-Knopoff Model
215(4)
11.2.2 Train Model of Earthquake
219(2)
11.2.3 Mapping of Train Model to Sandpile
221(2)
11.2.3.1 Mapping to Sandpile Model
222(1)
11.2.4 Two-fractal Overlap Models
223(4)
11.2.4.1 Model Description
224(1)
11.2.4.2 GR and Omori Laws
225(2)
11.3 Cellular Automata Models of Earthquakes
227(19)
11.3.1 Bak Tang Wiesenfeld (BTW) Model
228(4)
11.3.2 Zhang Model
232(2)
11.3.3 Manna Model
234(3)
11.3.4 Common Failure Precursor for BTW and Manna Models and FBM
237(3)
11.3.4.1 Precursor in BTW Model
238(2)
11.3.4.2 Precursor in Manna Model
240(1)
11.3.4.3 Precursor in Fiber Bundle Model
240(1)
11.3.5 Olami- Feder-Christensen (OFC) Model
240(6)
11.3.5.1 Moving Boundary
242(4)
11.4 Equivalence of Interface and Train Models
246(15)
11.4.1 Model
248(2)
11.4.2 Avalanche Statistics in Modified Train Model
250(3)
11.4.3 Equivalence with Interface Depinning
253(2)
11.4.4 Interface Propagation and Fluctuation in Bulk
255(6)
11.5 Summary
261(4)
12 Overview and Outlook 265(4)
A Percolation 269(12)
A.1 Critical Exponent: General Examples
269(1)
A.1.1 Scaling Behavior
270(1)
A.2 Percolation Transition
270(4)
A.2.1 Critical Exponents of Percolation Transition
272(1)
A.2.2 Scaling Theory of Percolation Transition
273(1)
A.3 Renormalization Group (RG) Scheme
274(11)
A.3.1 RG for Site Percolation in One Dimension
276(2)
A.3.2 RG for Site Percolation in Two-dimensional Triangular Lattice
278(1)
A.3.3 RG for Bond Percolation in Two-dimensional Square Lattice
279(2)
B Real-space RG for Rigidity Percolation 281(4)
C Fiber Bundle Model 285(8)
C.1 Universality Class of the Model
285(5)
C.1.1 Linearly Increasing Density of Fiber Strength
285(1)
C.1.2 Linearly Decreasing Density of Fiber Strength
286(2)
C.1.3 Nonlinear Stress-Strain Relationship
288(2)
C.2 Brittle to Quasi-brittle Transition and Tricritical Point
290(7)
C.2.1 Abrupt Failure and Tricritical Point
292(1)
D Quantum Breakdown 293(2)
E Fractals 295(2)
F Two-fractal Overlap Model 297(6)
F.1 Renormalization Group Study: Continuum Limit
297(2)
F.2 Discrete Limit
299(4)
F.2.1 Gutenberg-Richter Law
299(1)
F.2.2 Omori Law
300(3)
G Microscopic Theories of Friction 303(6)
G.1 Frenkel-Kontorova Model
303(1)
G.2 Two-chain Model
304(5)
G.2.1 Effect of Fractal Disorder
305(4)
References 309(14)
Index 323
Soumyajyoti Biswas got his PhD in 2015 for works carried out at Saha Institute of Nuclear Physics. He has been a postdoctoral fellow at the Institute of Mathematical Sciences, Chennai until March 2015. Presently he is a postdoctoral fellow at the Earthquake Research Institute, University of Tokyo.

Purusattam Ray is professor in Physics at the Institute of Mathematical Sciences (IMSC), Chennai and an adjunct professor of Homi Bhabha National Institute (HBNI), Mumbai. He received his Ph.D. from Calcutta University in 1989. He was then SERC research fellow at the University of Manchester, England and subsequently Max Planck fellow at the MPI for Polymer Studies in Mainz and at the University of Mainz, Germany. He has made major contributions in the study of statistical physics of fracture. He annually organizes the International workshop on fracture and breakdown processes.

Bikas K. Chakrabarti is a senior professor of theoretical condensed matter physics at the Saha Institute of Nuclear Physics (SINP), Kolkata, and a visiting professor of economics at the Indian Statistical Institute, Kolkata, India. He received his doctorate in physics from Calcutta University in 1979 (for research at SINP). Following postdoctoral positions at Oxford University and Cologne University, he joined SINP in 1983. His main research interests include physics of fracture, quantum glasses, etc., and the interdisciplinary sciences of optimization, brain modeling, and econophysics. He has written several books and reviews on these topics.
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