The Fiber Bundle Model : Modeling Failure in Materials.

Cover -- Title Page -- Copyright -- Contents -- Series Page -- Preface -- Chapter 1 The Fiber Bundle Model -- 1.1 Rivets Versus Welding -- 1.1.1 What Are Models Good For? -- 1.2 Fracture and Failure: A Short Summary -- 1.3 The Fiber Bundle Model in Statistics -- 1.4 The Fiber Bundle Model in Physics -- 1.5 The Fiber Bundle Model in Materials Science -- 1.6 Structure of the Book -- Chapter 2 Average Properties -- 2.1 Equal Load Sharing versus Local Load Sharing -- 2.2 Strain-Controlled versus Force-Controlled Experiments -- 2.3 The Critical Strength -- 2.4 Fiber Mixtures -- 2.5 Non-Hookean Forces -- 2.5.1 Fibers with Random Slacks -- 2.5.2 Elastic-Plastic Model -- Chapter 3 Fluctuation Effects -- 3.1 Range of Force Fluctuations -- 3.2 The Maximum Bundle Strength -- 3.3 Avalanches -- 3.3.1 The Burst Distribution -- 3.3.1.1 The Forward Condition -- 3.3.1.2 The Backward Condition -- 3.3.1.3 Total Number and Average Size of Bursts -- 3.3.2 Asymptotic Burst Distribution: 5/2 Law -- 3.3.2.1 Asymptotic Burst Distribution: Nongeneric Cases -- 3.3.3 Inclusive Bursts -- 3.3.4 Forward Bursts -- 3.3.5 Avalanches as Random Walks -- 3.3.5.1 The Exact Random Walk -- 3.3.5.2 Asymptotic Burst Distribution via Random Walks -- 3.3.6 Energy Release -- 3.3.6.1 High-Energy Asymptotics -- 3.3.6.2 Low-Energy Behavior -- 3.3.7 Failure Avalanches for Stepwise Load Increase -- 3.3.7.1 Uniform Threshold Distribution -- 3.3.7.2 General Threshold Distribution -- Chapter 4 Local and Intermediate Load Sharing -- 4.1 The Local-Load-Sharing Model -- 4.1.1 Redistribution of Forces -- 4.1.2 Determining the Failure Sequence -- 4.1.3 Bundle Strength -- 4.1.4 Failure of First and Second Fibers -- 4.1.4.1 Other Threshold Distributions -- 4.1.4.2 Localization -- 4.1.5 Hole Size Distribution -- 4.1.5.1 Defining the Hole Size Distribution.

4.1.5.2 Hole Size Distribution for Equal Load Sharing -- 4.1.5.3 Hole Size Distribution for Local Load Sharing: Localization -- 4.1.6 Estimating the Strength of the Local-Load-Sharing Model -- 4.1.6.1 Lower Bound for the Largest Hole -- 4.1.6.2 Competing Failure Mechanisms -- 4.1.6.3 Uniform Threshold Distribution -- 4.1.7 Force and Elongation Characteristics -- 4.1.8 Burst Distribution -- 4.2 Local Load Sharing in Two and More Dimensions -- 4.2.1 Localization -- 4.2.2 Similarity with the Equal-Load-Sharing Fiber Bundle Model -- 4.2.3 Burst Distribution -- 4.2.4 Upper Critical Dimension -- 4.3 The Soft Membrane Model -- 4.4 Intermediate-Load-Sharing Models -- 4.4.1 The γ-Model -- 4.4.2 The Mixed-Mode Model -- 4.5 Elastic Medium Anchoring -- 4.5.1 Size Equals Stiffness -- 4.5.2 Localization in the Soft Clamp Model -- 4.5.3 Asymptotic Strength -- 4.5.4 Fracture Front Propagation -- Chapter 5 Recursive Breaking Dynamics -- 5.1 Recursion and Fixed Points -- 5.2 Recursive Dynamics Near the Critical Point -- 5.2.1 Universality -- 5.2.1.1 General Threshold Distribution -- 5.2.2 Postcritical Relaxation -- 5.2.2.1 Uniform Threshold Distribution -- 5.2.2.2 General Threshold Distribution -- 5.2.3 Precritical Relaxation -- 5.2.3.1 Uniform Threshold Distribution -- 5.2.3.2 General Threshold Distribution -- 5.2.4 Critical Amplitudes -- Chapter 6 Predicting Failure -- 6.1 Crossover Phenomena -- 6.1.1 The Avalanche Size Distribution -- 6.1.1.1 Burst Avalanches at Criticality -- 6.1.2 Energy Bursts -- 6.1.3 The Crossover Phenomenon in Other Systems -- 6.1.3.1 Earthquakes -- 6.1.3.2 The Fuse Model -- 6.2 Variation of Average Burst Size -- 6.3 Failure Dynamics Under Force-Controlled Loading -- 6.4 Over-Loaded Situations -- 6.4.1 Breaking Rate of Loaded Fiber Bundles -- 6.4.1.1 Uniform Distribution -- 6.4.1.2 Weibull Distribution -- 6.4.1.3 Large Overload Situation.

6.4.2 Energy Emission Bursts -- 6.4.2.1 Uniform Distribution -- 6.4.2.2 Weibull Distribution -- 6.4.2.3 Large Overload Situation -- 6.4.3 Energy Burst Pattern -- Chapter 7 Fiber Bundle Model in Material Science -- 7.1 Repeated Damage and Work Hardening -- 7.1.1 The Load Curve -- 7.1.2 Repeated Damages -- 7.1.3 Damages Ending in Complete Bundle Failure -- 7.2 Creep Failure -- 7.2.1 A Model for Creep -- 7.2.2 A Second Model for Creep -- 7.2.2.1 Damage Accumulation -- 7.2.2.2 Time Evolution -- 7.2.2.3 Healing -- 7.3 Viscoelastic Creep -- 7.4 Fatigue Failure -- 7.4.1 A Fatigue Experiment -- 7.5 Thermally Induced Failure -- 7.5.1 Failure Time for a Homogeneous Fiber Bundle -- 7.5.2 Failure Time for Low Thermal Noise -- 7.6 Noise-Induced Failure -- 7.7 Crushing: The Pillar Model -- Chapter 8 Snow Avalanches and Landslides -- 8.1 Snow Avalanches -- 8.2 Shallow Landslides -- Appendix A Mathematical Toolbox -- A.1 Lagrange's Inversion Theorem -- A.2 Some Theorems in Combinatorics -- A.2.1 Basic Selection Theorems -- A.2.2 A Distribution with Restrictions -- A.3 Biased Random Walks -- A.3.1 Probability of No Return -- A.3.2 Gambler's Ruin -- A.4 An Asymmetrical Unbiased Random Walk -- A.5 Brownian Motion as a Scaled Random Walk -- Appendix B Statistical Toolbox -- B.1 Stochastic Variables, Statistical Distributions -- B.1.1 Change of Variable -- B.1.1.1 A Useful Interpretation -- B.1.2 The Characteristic Function -- B.1.3 The Central Limit Theorem -- B.2 Order Statistics -- B.2.1 Ordering the Variables -- B.2.2 The Average of the mth Ordered Variable -- B.3 The Joint Probability Distribution -- B.3.1 Extreme Statistics -- B.3.2 The Largest Element: The Three Asymptotic Distributions -- B.3.2.1 The Gumbel Distribution -- B.3.2.2 The Second and Third Asymptotes -- B.3.3 The Smallest Element: The Weibull Distribution -- Appendix C Computational Toolbox.

C.1 Generating Random Numbers Following a Specified Probability Distribution -- C.1.1 When the Cumulative Probability May Be Inverted -- C.1.2 Gaussian Numbers -- C.1.3 None of the Above -- C.2 Fourier Acceleration -- References -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.