The Fiber Bundle Model: Modeling Failure in Materials

Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science. The authors start by explaining why disorder is important for fracture and then go on to introduce the fiber bundle model, backed by various different applications. Appendices present the necessary mathematical, computational and statistical background required. The structure of the book allows the reader to skip some material that is too specialized, making this topic accessible to the engineering, mechanics and materials science communities, in addition to providing further reading for graduate students in statistical physics. INDICE: THE FIBER BUNDLE MODEL. Rivets Versus Welding. Fracture and Failure: A Short Summary. The Fiber Bundle Model in Statistics. The Fiber Bundle Model in Physics. The Fiber Bundle Model in Materials Science. Structure of the Book. . AVERAGE PROPERTIES . Equal Load Sharing vs. Local Load Sharing . Strain–Controlled vs. Force–Controlled Experiments . The Critical Strength . Fiber Mixtures. Non–Hookean Forces. . FLUCTUATION EFFECTS. Range of Force Fluctuations. The Maximum Bundle Strength. Avalanches. . LOCAL AND INTERMEDIATE LOAD SHARING. The Local Load Sharing Model. Local Load Sharing in Two and More Dimensions. The Soft Membrane Model. Intermediate Load Sharing Models. Elastic Medium Anchoring. . RECURSIVE BREAKING DYNAMICS. Recursion and Fixed Points. Recursive Dynamics Near the Critical Point. . PREDICTING FAILURE. Crossover Phenomena. Variation of Average Burst Size. Failure Dynamics Under Force–Controlled Loading. Over–Loaded Situations. . FIBER BUNDLE MODEL IN MATERIALS SCIENCE . Repeated Damage and Work Hardening. Creep Failure. Viscoelastic Creep. Fatigue Failure. Thermally Induced Failure. Noise–Induced Failure. Crushing: The Pillar Model. . SNOW AVALANCHES AND LANDSLIDES. Snow Avalanches. Shallow Landslides. . APPENDIX A: MATHEMATICAL TOOLBOX. Lagrange?s Inversion Theorem. Some Theorems in Combinatorics. Biased Random Walks. An Asymmetrical Unbiased Random Walk. Brownian Motion as a Scaled Random Walk. . APPENDIX B: STATISTICAL TOOLBOX. Stochastic Variables, Statistical Distributions. Order Statistics. The Joint Probability Distribution. . APPENDIX C: COMPUTATIONAL TOOLBOX. Generating Random Numbers Following a Specified Probability Distribution. Fourier Acceleration. . Index

• ISBN: 978-3-527-41214-3
• Editorial: Wiley VCH
• Encuadernacion: Cartoné
• Páginas: 272
• Fecha Publicación: 09/09/2015
• Nº Volúmenes: 1
• Idioma: Inglés