Crack front propagation

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Table of contents

Introduction
1 Disordered elastic systems and the depinning transition
1.1 Phenomenology of the depinning transition
1.2 Equation of motion
1.3 The Larkin length and the upper critical dimension
1.4 Scaling relations between exponents
1.5 Middleton theorems
1.6 Conclusion
2 Experimental realisations
2.1 The Barkhausen noise
2.2 Crack front propagation
2.3 Wetting of disordered susbtrates
2.4 Earthquakes
2.5 Elastoplasticity and the yielding transition
2.6 Conclusion
3 Assessing the Universality Class of the transition
3.1 Existing methods to characterize the transition
3.2 A novel method based on the universal scaling of the local velocity field
3.3 Conjecture for the correlation functions in plasticity
3.4 Conclusion
4 Cluster Statistics
4.1 Introduction of the observables and various critical exponents
4.2 Recall of previous results
4.3 Cluster statistics
4.4 Statistics of gaps and avalanche diameter
4.5 Tables of exponents
4.6 Conclusion
5 Mean-Field models
5.1 What is mean-field ?
5.2 Fully-connected and ABBM models
5.3 Introduction of the Brownian force model
5.4 Insights into the long-range instanton equation with a local source
5.5 Conclusion
Summary and perspectives
Appendix
A Fourier transform of the elastic force
B Computation of the elastic coefficients for numerical simulations
C Analysis of the experimental data
D Computation of the generating functional using the Martin-Siggia-Rose formalism
Bibliography