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Quasi-Static Fractures in Disordered Media and Iterated Conformal Maps | | Felipe Barra
; H. George E. Hentschel
; Anders Levermann
; Itamar Procaccia
; | | Date: |
4 Oct 2001 | | Subject: | Statistical Mechanics; Materials Science; Chaotic Dynamics | cond-mat.stat-mech cond-mat.mtrl-sci nlin.CD | | Affiliation: | Dept. of Chemical Physics, The Weizmann Institute of Science, Rehovot, Israel; Dept of Physics, Emory University, Atlanta Georgia | | Abstract: | We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lamé equations without resorting to lattice models. Typical fracture patterns exhibit increased ramification due to the increase of the stress at the tips. We find the roughness exponent of the experimentally relevant backbone of the fracture pattern; it crosses over from about 0.5 for small scales to about 0.75 for large scales, in excellent agreement with experiments. We propose that this cross-over reflects the increased ramification of the fracture pattern. | | Source: | arXiv, cond-mat/0110089 | | Services: | Forum | Review | PDF | Favorites | |
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