Cover -- Title Page -- Copyright -- Contents -- Series Editors' Preface -- Preface -- Notations -- Chapter 1 Introduction -- Chapter 2 Mechanical and Fracture Properties of Solids -- 2.1 Mechanical Response in Materials -- 2.1.1 Elastic and Plastic Regions -- 2.1.2 Linear Elastic Region -- 2.1.3 Nonlinear Plastic Region -- 2.2 Ductile, Quasi-brittle, and Brittle Materials -- 2.3 Ductile and Brittle Fracture -- 2.3.1 Macroscopic Features of Ductile and Brittle Fractures -- 2.3.2 Microscopic Features of Ductile and Brittle Fractures -- Chapter 3 Crystal Defects and Disorder in Lattice Models -- 3.1 Point Defects -- 3.2 Line Defects -- 3.3 Planar Defects -- 3.4 Lattice Defects: Percolation Theory -- 3.5 Summary -- Chapter 4 Nucleation and Extreme Statistics in Brittle Fracture -- 4.1 Stress Concentration Around Defect -- 4.1.1 Griffith's Theory of Crack Nucleation in Brittle Fracture -- 4.2 Strength of Brittle Solids: Extreme Statistics -- 4.2.1 Weibull and Gumbel Statistics -- 4.3 Extreme Statistics in Fiber Bundle Models of Brittle Fracture -- 4.3.1 Fiber Bundle Model -- 4.3.1.1 Strength of the Local Load Sharing Fiber Bundles -- 4.3.1.2 Crossover from Extreme to Self-averaging Statistics in the Model -- 4.4 Extreme Statistics in Percolating Lattice Model of Brittle Fracture -- 4.5 Molecular Dynamics Simulation of Brittle Fracture -- 4.5.1 Comparisons with Griffith's Theory -- 4.5.2 Simulation of Highly Disordered Solids -- 4.6 Summary -- Chapter 5 Roughness of Fracture Surfaces -- 5.1 Roughness Properties in Fracture -- 5.1.1 Self-affine Scaling of Fractured Surfaces -- 5.1.2 Out-of-plane Fracture Roughness -- 5.1.3 Distribution of Roughness: Mono- and Multi-affinity -- 5.1.3.1 Nonuniversal Cases -- 5.1.3.2 Anisotropic Scaling -- 5.1.4 In-plane Roughness of Fracture Surfaces.

5.1.4.1 Waiting Time Distributions in Crack Propagation -- 5.1.5 Effect of Probe Size -- 5.1.6 Effect of Spatial Correlation and Anisotropy -- 5.2 Molecular Dynamics Simulation of Fractured Surface -- 5.3 Summary -- Chapter 6 Avalanche Dynamics in Fracture -- 6.1 Probing Failure with Acoustic Emissions -- 6.2 Dynamics of Fiber Bundle Model -- 6.2.1 Dynamics Around Critical Load -- 6.2.2 Dynamics at Critical Load -- 6.2.3 Avalanche Statistics of Energy Emission -- 6.2.4 Precursors of Global Failure in the Model -- 6.2.5 Burst Distribution: Crossover Behavior -- 6.2.6 Abrupt Rupture and Tricritical Point -- 6.2.7 Disorder in Elastic Modulus -- 6.3 Interpolations of Global and Local Load Sharing Fiber Bundle Models -- 6.3.1 Power-law Load Sharing -- 6.3.2 Mixed-mode Load Sharing -- 6.3.3 Heterogeneous Load Sharing -- 6.3.3.1 Dependence on Loading Process -- 6.3.3.2 Results in One Dimension -- 6.3.3.3 Results in Two Dimensions -- 6.3.3.4 Comparison with Mixed Load Sharing Model -- 6.4 Random Threshold Spring Model -- 6.5 Summary -- Chapter 7 Subcritical Failure of Heterogeneous Materials -- 7.1 Time of Failure Due to Creep -- 7.1.1 Fluctuating Load -- 7.1.2 Failure Due to Fatigue in Fiber Bundles -- 7.1.3 Creep Rupture Propagation in Rheological Fiber Bundles -- 7.1.3.1 Modification for Local Load Sharing Scheme -- 7.2 Dynamics of Strain Rate -- 7.3 Summary -- Chapter 8 Dynamics of Fracture Front -- 8.1 Driven Fluctuating Line -- 8.1.1 Variation of Universality Class -- 8.1.2 Depinning with Constant Volume -- 8.1.3 Infinite-range Elastic Force with Local Fluctuations -- 8.2 Fracture Front Propagation in Fiber Bundle Models -- 8.2.1 Interfacial Crack Growth in Fiber Bundle Model -- 8.2.2 Crack Front Propagation in Fiber Bundle Models -- 8.2.3 Self-organized Dynamics in Fiber Bundle Model -- 8.3 Hydraulic Fracture -- 8.4 Summary.

Chapter 9 Dislocation Dynamics and Ductile Fracture -- 9.1 Nonlinearity in Materials -- 9.2 Deformation by Slip -- 9.2.1 Critical Stress to Create Slip in Perfect Lattice -- 9.3 Slip by Dislocation Motion -- 9.4 Plastic Strain due to Dislocation Motion -- 9.5 When Does a Dislocation Move? -- 9.5.1 Dislocation Width -- 9.5.2 Dependence on Grain Boundaries in Crystals -- 9.5.3 Role of Temperature -- 9.5.4 Effect of Applied Stress -- 9.6 Ductile-Brittle Transition -- 9.6.1 Role of Confining Pressure -- 9.6.2 Role of Temperature -- 9.7 Theoretical Work on Ductile-Brittle Transition -- Chapter 10 Electrical Breakdown Analogy of Fracture -- 10.1 Disordered Fuse Network -- 10.1.1 Dilute Limit (p → 1) -- 10.1.2 Critical Behavior (p → pc) -- 10.1.3 Influence of the Sample Size -- 10.1.4 Distribution of the Failure Current -- 10.1.4.1 Dilute Limit (p → 1) -- 10.1.4.2 At Critical Region (p → pc) -- 10.1.5 Continuum Model -- 10.1.6 Electromigration -- 10.2 Numerical Simulations of Random Fuse Network -- 10.2.1 Disorders in Failure Thresholds -- 10.2.2 Avalanche Size Distribution -- 10.2.3 Roughness of Fracture Surfaces in RFM -- 10.2.4 Effect of High Disorder -- 10.2.5 Size Effect -- 10.3 Dielectric Breakdown Problem -- 10.3.1 Dilute Limit (p → 1) -- 10.3.2 Close to Critical Point (p → pc) -- 10.3.3 Influence of Sample Size -- 10.3.4 Distribution of Breakdown Field -- 10.3.5 Continuum Model -- 10.3.6 Shortest Path -- 10.3.7 Numerical Simulations in Dielectric Breakdown -- 10.3.7.1 Stochastic Models -- 10.3.7.2 Deterministic Models -- 10.4 Summary -- Chapter 11 Earthquake as Failure Dynamics -- 11.1 Earthquake Statistics: Empirical Laws -- 11.1.1 Universal Scaling Laws -- 11.2 Spring-block Models of Earthquakes -- 11.2.1 Computer Simulation of the Burridge-Knopoff Model -- 11.2.2 Train Model of Earthquake.

11.2.3 Mapping of Train Model to Sandpile -- 11.2.3.1 Mapping to Sandpile Model -- 11.2.4 Two-fractal Overlap Models -- 11.2.4.1 Model Description -- 11.2.4.2 GR and Omori Laws -- 11.3 Cellular Automata Models of Earthquakes -- 11.3.1 Bak Tang Wiesenfeld (BTW) Model -- 11.3.2 Zhang Model -- 11.3.3 Manna Model -- 11.3.4 Common Failure Precursor for BTW and Manna Models and FBM -- 11.3.4.1 Precursor in BTW Model -- 11.3.4.2 Precursor in Manna Model -- 11.3.4.3 Precursor in Fiber Bundle Model -- 11.3.5 Olami-Feder-Christensen (OFC) Model -- 11.3.5.1 Moving Boundary -- 11.4 Equivalence of Interface and Train Models -- 11.4.1 Model -- 11.4.2 Avalanche Statistics in Modified Train Model -- 11.4.3 Equivalence with Interface Depinning -- 11.4.4 Interface Propagation and Fluctuation in Bulk -- 11.5 Summary -- Chapter 12 Overview and Outlook -- Appendix A Percolation -- A.1 Critical Exponent: General Examples -- A.1.1 Scaling Behavior -- A.2 Percolation Transition -- A.2.1 Critical Exponents of Percolation Transition -- A.2.2 Scaling Theory of Percolation Transition -- A.3 Renormalization Group (RG) Scheme -- A.3.1 RG for Site Percolation in One Dimension -- A.3.2 RG for Site Percolation in Two-dimensional Triangular Lattice -- A.3.3 RG for Bond Percolation in Two-dimensional Square Lattice -- Appendix B Real-space RG for Rigidity Percolation -- Appendix C Fiber Bundle Model -- C.1 Universality Class of the Model -- C.1.1 Linearly Increasing Density of Fiber Strength -- C.1.2 Linearly Decreasing Density of Fiber Strength -- C.1.3 Nonlinear Stress-Strain Relationship -- C.2 Brittle to Quasi-brittle Transition and Tricritical Point -- C.2.1 Abrupt Failure and Tricritical Point -- Appendix D Quantum Breakdown -- Appendix E Fractals -- Appendix F Two-fractal Overlap Model.

F.1 Renormalization Group Study: Continuum Limit -- F.2 Discrete Limit -- F.2.1 Gutenberg-Richter Law -- F.2.2 Omori Law -- Appendix G Microscopic Theories of Friction -- G.1 Frenkel-Kontorova Model -- G.2 Two-chain Model -- G.2.1 Effect of Fractal Disorder -- References -- Index -- EULA.