Fracture propagation governed by the Laplace equation

Yoshi-hiro Taguchi

Physica A: Statistical Mechanics and its Applications, 1989, vol. 156, issue 3, 741-755

Abstract: We propose a model of fracture propagation. When it is a two dimensional system and has displacement restricted to be perpendicular to the plane, its displacement obeys the Laplace equation. Because the diffusion-limited aggregation (DLA) is also governed by the Laplace equation, we can make use of many methods developed for DLA to study our model. Monte Carlo simulations are done and df of the model turns out to be about 1.55 ± 0.05; it differs from that of DLA. Moreover Nagatani's renormalization is used to investigate the model and the multifractalities of both the growth probability and the mass distributions are found. The generalized dimension Dm(q) of the mass distribution is Dm(−∞) > df ⋍ Dm(0) > Dm(∞). A fractal pattern is proposed to show the dependence of Dm(q) upon q.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:156:y:1989:i:3:p:741-755

DOI: 10.1016/0378-4371(89)90018-6

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