Disorder and Fracture

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J.C. Charmet, Stéphane Roux, Etienne Guyon
Springer Science & Business Media, 1990 - Mathematics - 305 pages
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Fracture, and particularly brittle fracture, is a good example of an instability. For a homogeneous solid, subjected to a uniform stress field, a crack may appear anywhere in the structure once the threshold stress is reached. However, once a crack has been nucleated in some place, further damage in the solid will in most cases propagate from the initial crack, and not somewhere else in the solid. In this sense fracture is an unstable process. This property makes the process extremely sensitive to any heterogeneity present in the medium, which selects the location of the first crack nucleated. In particular, fracture appears to be very sensitive to disorder, which can favor or impede local cracks. Therefore, in most realistic cases, a good description of fracture mechanics should include the effect of disorder. Recently this need has motivated work in this direction starting from the usual description of fracture mechanics. Parallel with this first trend, statistical physics underwent a very important development in the description of disordered systems. In particular, let us mention the emergence of some "new" concepts (such as fractals, scaling laws, finite size effects, and so on) in this field. However, many models considered were rather simple and well adapted to theoretical or numerical introduction into a complex body of problems. An example of this can be found in percolation theory. This area is now rather well understood and accurately described.
 

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Contents

Fluctuations of Interfaces and Fronts
ix
Introduction to Multifractality
13
Statistical Theory of Fragmentation
27
DiffusionLimited Aggregation Model
45
Theory and Simulation of Diffusion Limited Growth
47
Growth Patterns and Fronts Fluid Flow Experiments
59
From Flow to Fracture and Fragmentation in Colloidal Media 1 NonNewtonian Fingering and ViscoElastic Fraturing
79
From Flow to Fracture and Fragmentation in Colloidal Media 2 Local Order and Fragmentation Geometry
101
Rheology and Fracture
161
Micromechanics of Brittle Deformation Processes
163
Fracture Mechanics and Solid Adhesion
183
Damage Evolution Instability and Fracture in Ductile Solids
215
Aspects of Nonlinearity and Selforganisation in Plastic Deformation
235
Materials and Applications
249
Granular Media Effects of Disorder
251
Cracking and Fracture of Concrete Size Effect or Scaling Law?
265

Statistical Fracture Models
113
Simple Stochastic Models for Material Failure
115
Scaling Theory of the Strength of Percolation Networks
137
Scaling in Fracture
145
The Phenomenology of Earthquake Occurrence
275
The Modeling of Earthquake Occurrence
285
Index
297
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