Statistical Models for the Fracture of Disordered Media (eBook)

Front Cover 1
Statistical Models for the Fracture of Disordered Media 4
Copyright Page 5
Table of contents 12
Preface 8
Foreword 10
Chapter 1. Introduction to basic notions and facts 16
1.1 Objectives 16
1.2 The mechanical response of a solid 18
1.3 Phenomenology of fracture 20
1.4 The process of fracture 27
1.5 Materials 34
1.6 Outlook 45
References 45
Chapter 2. Experimental evidences for various materials 48
2.1 Rupture and deformation of ceramics 48
2.2 Failure mechanisms of composite materials 61
2.3 Concrete: Large-scale heterogeneities and size effects 67
2.4 Fracture mechanisms of metals 74
2.5 Mechanical properties of polymeric materials 81
2.6 Viscous fingering and viscoelastic fracture in clays 92
Chapter 3. Continuum and discrete description of elasticity and other rheological behaviour 102
3.1 Elasticity 103
3.2 Other rheological behaviours 109
3.3 Discretization: Physical approach 118
3.4 Discretization: Formal approach[7] 124
Chapter 4. Disorder 130
4.1 Introduction 130
4.2 Percolation model 134
4.3 Electrical conductance 143
4.4 Elasticity with angular stiffness 160
4.5 Elasticity of central-force systems 163
4.6 Percolation induced by wide probability distributions 169
Chapter 5. Modelization of fracture in disordered systems 174
5.1 Introduction 174
5.2 Classical approaches 176
5.3 Molecular Dynamics 181
5.4 Lattice models 185
5.5 Renormalization 195
Chapter 6. Breakdown of diluted and hierarchical systems 204
6.1 Introduction and overview 204
6.2 Scaling theory for an isolated crack 205
6.3 Extreme scaling analysis of dilute networkst[34,38,50] 210
6.4 Fractal and hierarchical microgeometries 222
6.5 Toughness of disordered materials 228
6.6 Discussion and experimental implications 234
6.7 Conclusion 239
Chapter 7. Randomness in breaking thresholds 244
7.1 Introduction 244
7.2 Some analytic results 249
7.3 Breaking characteristics 254
7.4 Multifractality 264
7.5 Discussion 271
Chapter 8. Dielectric breakdown and single crack models 276
8.1 Interfacial pattern formation 277
8.2 Diffusion limited aggregation and dielectric breakdown 285
8.3 Single crack models on lattices 293
8.4 Discussion and outlook 301
Chapter 9. Simple kinetic models for material failure and deformation 306
9.1 Introduction 306
9.2 The Dobrodumov-El'yashevich model 308
9.3 Surface cracking models 311
9.4 Models for the properties and failure of polymer fibers 317
9.5 Chain slippage models 322
9.6 Analog models 328
9.7 Summary 332
Chapter 10. Fragmentation 336
10.1 Introduction 336
10.2 Continuous fragmentation 342
10.3 Discussion and outlook 357
Subject index 364