• Hans J. Herrmann


The breaking of solids caused by an external load is evidently a problem of technological importance and has been intensively studied for the last hundred years [5.1]. On very small length scales (≤ 10−6 m) fracture is a topic of materials science. From the electronic level [5.2] to the level of dislocations or grain boundaries [5.3] the mechanisms of fracture are highly material dependent. On very large length scales (> 10−1 m) the prevention of fracture is studied by their engineers. There results are mainly based on experience and depend essentially on the application and the shape of the sample. On intermediate length scales the behavior of the solid can be described by the methods of applied mechanics, i.e., by continuous equations of motion. There exist on this level just a few types of different behaviors — for example elastic, plastic, viscoelastic — each given by its own set of differential equations containing some material-dependent parameters. The relatively general validity of the formalism makes the study of fracture in this intermediate (or mesoscopic) range of length scales particularly attractive to statistical physicists. If the reader wants to know more about recent developments in this direction I recommend [5.4].


Fractal Dimension Hydraulic Fracture Beam Model Dielectric Breakdown Move Boundary Problem 
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© Springer-Verlag Berlin Heidelberg 1996

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  • Hans J. Herrmann

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