Herrmann / Roux Statistical Models for the Fracture of Disordered Media

1. Auflage 2014
ISBN: 978-1-4832-9612-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 353 Seiten, Web PDF

Reihe: Random Materials and Processes

Since the beginning of the century the technological desire to master the fracture of metals, concrete or polymers has boosted research and has left behind an overwhelming amount of literature. In a field where it seems difficult to say anything simple and new, the editors and authors of this book have managed to do just that.The approach to fracture taken here was not conceived by mechanical engineers or material scientists. It is essentially the by-product of exciting developments that have occurred in the last ten to fifteen years within a branch of theoretical physics, called statistical physics. Concepts such as ``percolation'' and ``fractals'', as models for the properties of fracture are not often considered by engineers. A particular aim of this volume is to emphasize the fundamental role disorder plays in the breaking process.The main scope of the volume is pedagogical and is at the same time an overview of fracture mechanics for physicists and an introduction to new concepts of statistical physics for mechanics and engineers. To this end the first half of the book consists of introductory chapters and the second half contains the results that have emerged from this new approach.

Autoren/Hrsg.

Herrmann, H. J.

Roux, S.

Inhaltsverzeichnis

1;Front Cover;1
2;Statistical Models for the Fracture of Disordered Media;4
3;Copyright Page;5
4;Table of contents;12
5;Preface;8
6;Foreword;10
7;Chapter 1. Introduction to basic notions and facts;16
7.1;1.1 Objectives;16
7.2;1.2 The mechanical response of a solid;18
7.3;1.3 Phenomenology of fracture;20
7.4;1.4 The process of fracture;27
7.5;1.5 Materials;34
7.6;1.6 Outlook;45
7.7;References;45
8;Chapter 2. Experimental evidences for various materials;48
8.1;2.1 Rupture and deformation of ceramics;48
8.2;2.2 Failure mechanisms of composite materials;61
8.3;2.3 Concrete: Large-scale heterogeneities and size effects;67
8.4;2.4 Fracture mechanisms of metals;74
8.5;2.5 Mechanical properties of polymeric materials;81
8.6;2.6 Viscous fingering and viscoelastic fracture in clays;92
9;Chapter 3. Continuum and discrete description of elasticity and other rheological behaviour;102
9.1;3.1 Elasticity;103
9.2;3.2 Other rheological behaviours;109
9.3;3.3 Discretization: Physical approach;118
9.4;3.4 Discretization: Formal approach[7];124
10;Chapter 4. Disorder;130
10.1;4.1 Introduction;130
10.2;4.2 Percolation model;134
10.3;4.3 Electrical conductance;143
10.4;4.4 Elasticity with angular stiffness;160
10.5;4.5 Elasticity of central-force systems;163
10.6;4.6 Percolation induced by wide probability distributions;169
11;Chapter 5. Modelization of fracture in disordered systems;174
11.1;5.1 Introduction;174
11.2;5.2 Classical approaches;176
11.3;5.3 Molecular Dynamics;181
11.4;5.4 Lattice models;185
11.5;5.5 Renormalization;195
12;Chapter 6. Breakdown of diluted and hierarchical systems;204
12.1;6.1 Introduction and overview;204
12.2;6.2 Scaling theory for an isolated crack;205
12.3;6.3 Extreme scaling analysis of dilute networkst[34,38,50];210
12.4;6.4 Fractal and hierarchical microgeometries;222
12.5;6.5 Toughness of disordered materials;228
12.6;6.6 Discussion and experimental implications;234
12.7;6.7 Conclusion;239
13;Chapter 7. Randomness in breaking thresholds;244
13.1;7.1 Introduction;244
13.2;7.2 Some analytic results;249
13.3;7.3 Breaking characteristics;254
13.4;7.4 Multifractality;264
13.5;7.5 Discussion;271
14;Chapter 8. Dielectric breakdown and single crack models;276
14.1;8.1 Interfacial pattern formation;277
14.2;8.2 Diffusion limited aggregation and dielectric breakdown;285
14.3;8.3 Single crack models on lattices;293
14.4;8.4 Discussion and outlook;301
15;Chapter 9. Simple kinetic models for material failure and deformation;306
15.1;9.1 Introduction;306
15.2;9.2 The Dobrodumov-El'yashevich model;308
15.3;9.3 Surface cracking models;311
15.4;9.4 Models for the properties and failure of polymer fibers;317
15.5;9.5 Chain slippage models;322
15.6;9.6 Analog models;328
15.7;9.7 Summary;332
16;Chapter 10. Fragmentation;336
16.1;10.1 Introduction;336
16.2;10.2 Continuous fragmentation;342
16.3;10.3 Discussion and outlook;357
17;Subject index;364