The Fiber Bundle Model -

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Résumé :
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.

Biographie:
Alex Hansen earned his Ph.D. from Cornell University in 1986. He was then Joliot-Curie fellow at the Ecole Normale Sup?rieure in Paris, followed by postdoctoral positions at the Universities of Cologne and Oslo. In 1992, Hansen became a CNRS scientist at the University of Rennes 1 in France. From 1994, he has been professor of physics at the Norwegian University of Science and Technology in Trondheim, Norway. Hansen is member of the Norwegian Academy of Science and Letters, the Royal Norwegian Society of Science and Letters and the Norwegian Academy of Technical Sciences. He is Dr. honoris causa at the University of Rennes 1. Hansen chairs at present the Commission on Computational Physics of the International Union of Pure and Applied Physics, where he is also a vice president. Per Christian Hemmer earned his doctorate from the Norwegian Institute of Technology in 1959. He was then NORDITA fellow in Copenhagen, followed by a postdoctoral position at The Rockefeller Institute, New York. In 1959 he was appointed professor of theoretical physics at the University of Trondheim, now the Norwegian University of Science and Technology. He has been dean of the faculty for general sciences at the university. Hemmer has been secretary of the Commission on Statistical Physics of the International Union of Pure and Applied Physics, as well as a vice president of the union. He is member of the Royal Norwegian Society of Science and Letters, the Norwegian Academy of Science and Letters, and the Norwegian Academy of Technical Sciences. Srutarshi Pradhan completed his Ph.D. work at Saha Institute of Nuclear Physics, Kolkata, India in 2004 and earned his doctorate from Jadavpur University, Kolkata, India . He was then a postdoctoral fellow at the Norwegian University of Science and Technology for 4 years (2004-2007) with a fellowship from the Norwegian Research Council. In 2008 he was appointed as a research scientist at SINTEF Petroleum Research, Trondheim, Norway. Pradhan has been promoted to senior scientist position at SINTEF Petroleum Research in 2012.

Sommaire:
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