The Fiber Bundle Model
Modeling Failure in Materials
1st Edition
Published on 24. August 2015
XVI, 236 pages
978-3-527-67199-1 (ISBN)
Description
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.
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.
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Alex Hansen | Per Christian Hemmer | Srutarshi Pradhan
The Fiber Bundle Model - Modeling Failure in Materials
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09/2015
Wiley-VCH
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Alex Hansen | Per Christian Hemmer | Srutarshi Pradhan
The Fiber Bundle Model
Modeling Failure in Materials
Book
09/2015
1st Edition
Wiley-VCH
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Persons
Alex Hansen earned his Ph.D. from Cornell University in 1986. He was then Joliot-Curie fellow at the Ecole Normale Supérieure 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.
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.
Content
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
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
