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The Fractal Nature of Fracture
Enrique Louis,Francisco Guinea +1 more
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TLDR
In this paper, the fractal geometry of fracture patterns in materials is explored by means of a simple model which incorporates the equations of elasticity and simple rules for fracture propagation, and self-similar patterns with fractal dimensions nearly independent of the elastic constants are obtained.Abstract:
The fractal geometry of fracture patterns in materials is explored by means of a simple model which incorporates the equations of elasticity and simple rules for fracture propagation. Different isotropic media and boundary conditions are considered. Self-similar patterns with fractal dimensions nearly independent of the elastic constants are obtained.read more
Citations
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Fractal growth processes
TL;DR: The methods of fractal geometry allow the classification of non-equilibrium growth processes according to their scaling properties as mentioned in this paper, and computer simulations give insight into a great variety of complex structures.
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Universal aesthetic of fractals
TL;DR: It is shown that humans display a consistent aesthetic preference across fractal images, regardless of whether these images are generated by nature's processes, by mathematics, or by the human hand.
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Fractal aggregates in geophysics
TL;DR: Fractal geometry has been studied extensively in statistical physics for the past decade as discussed by the authors, and the role of fractal aggregates in geophysical processes such as sedimentation, air and water pollution, the evolution of river networks, and multiphase flow in porous materials is discussed.
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Non-linear and non-local transport processes in heterogeneous media: from long-range correlated percolation to fracture and materials breakdown
TL;DR: In this article, the authors review and discuss recent progress in modelling non-linear and non-local transport processes in heterogeneous media, and the interplay between the nonlinearity and nonlocality is discussed in depth with the aim of establishing that, often non linearity andnon-locality are "two sides of the same coin" such that one may have no meaning without the presence of the other one.
References
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Book
Theory of elasticity
TL;DR: The equilibrium of rods and plates Elastic waves Dislocations Thermal conduction and viscosity in solids Mechanics of liquid crystals Index as discussed by the authors The equilibrium of rod and plate elastic waves Elastic waves
Book
Fracture of Brittle Solids
TL;DR: In this article, the authors present a unified continuum, microstructural and atomistic treatment of modern day fracture mechanics from a materials perspective, focusing on the basic elements of bonding and microstructure that govern the intrinsic toughness of ceramics.
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Fractal character of fracture surfaces of metals
TL;DR: In this article, a new method, slit island analysis, is introduced to estimate the fractal dimension, D. The estimate is shown to agree with the value obtained by fracture profile analysis, a spectral method.