Abstract (may include machine translation)
This chapter presents some results relevant to single-crack propagation and gives a survey of the corresponding lattice models. It presents an overview of the physics of viscous fingering or dendritic crystal growth and introduces the basic computer model—diffusion-limited aggregation (DLA). Concepts like instabilities due to moving boundaries and fractal geometry are also briefly discussed. The branching structure of some crack patterns similar to DLA patterns on the one hand and the analogies between the corresponding equations on the other lead physicists to transfer the methods and ideas used in Laplacian growth to the field of fracture. Similar to the scalar case, the nonlinearity in slow crack propagation stems from the moving boundary. Linear stability analysis is a classic tool to obtain information about the early stage of the growth and about the sensitivity of developing new modes with respect to perturbations. Lattice models show that self-similar patterns with nontrivial fractal dimension are produced by more or less realistic breaking procedures. Important concepts could be taken over from the much better understood physics of diffusion-limited or Laplacian scalar growth.
Original language | English |
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Title of host publication | Statistical models for the fracture of disordered media |
Editors | Herrmann H J, Roux S |
Place of Publication | Amsterdam |
Publisher | North-Holland Publishing |
Pages | 261-290 |
Number of pages | 30 |
ISBN (Print) | 044488551X |
DOIs | |
State | Published - 1990 |