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Table of contents
I Amorphous plasticity
1 Introduction
1.1 Phenomenology of amorphous plasticity
1.2 Modeling strategies
1.3 Scaling properties and the yielding transition
1.4 Analogy between depinning and plasticity mesomodels
1.5 Overview of Part I
1.6 Conclusions
2 Mesoscopic models
2.1 A tour of mesomodels
2.2 Ingredients
2.2.1 Threshold dynamics
2.2.2 Loading
2.2.3 Stress redistribution: shear transformations as inclusions
2.3 Our models
2.4 Conclusions
3 Building elastic kernels: all about Eshelby
3.1 Building elastic kernels
3.1.1 The Eshelby inclusion
3.1.2 Discretization of the Eshelby fields
3.1.3 Fourier discretization
3.1.4 A finite element method
3.2 Are fluctuations kernel-dependent?
3.2.1 Mean field depinning vs plasticity
3.2.2 Strain and displacement fluctuations in the finite element kernels
3.2.3 Fluctuations of the strain field
3.3 Soft modes control fluctuations
3.3.1 Eigenvalues and eigenmodes of the elastic kernel
3.4 Conclusions
4 Scaling properties and finite size effects
4.1 Review of MD results
4.1.1 Avalanches
4.1.2 Localization and diffusion
4.1.3 Density of shear transformation zones
4.2 Scaling properties in the lattice model
4.2.1 Distributed thresholds vs distributed slip amplitudes
4.2.2 Avalanches
4.2.3 Density of shear transformation zones
4.3 Diffusion
4.3.1 Fluctuations of the plastic strain field
4.3.2 Fluctuations of the displacement field
4.3.3 Trajectories and soft modes
4.4 Scaling properties of a minimal kernel
4.5 Summary of scaling relations
4.6 Conclusions
5 Application to amorphous composites
5.1 Inclusions in an amorphous bulk
5.2 Introducing inhomogeneities
5.3 Size dependent flow stress
5.3.1 Amorphous matrix
5.3.2 Amorphous composites
5.4 Hardening and localization
5.4.1 Statistical hardening of the amorphous matrix
5.4.2 Inclusion hardening
5.4.3 Localization and shear band percolation
5.4.4 The weakest band
5.5 An analytical model
5.5.1 Percolation
5.5.2 Effective plastic behavior is defined by the weakest band
5.6 Conclusions
Appendix A Eshelby inclusions
Appendix B Eigenvalues and eigenvectors of translation invariant
Appendix C Evolution equation of soft modes
