Transcript fragmentation

Fractality of Simulated Fracture
Petr Frantík ● Zbyněk Keršner
Václav Veselý ● Ladislav Řoutil
FACULTY OF CIVIL ENGINEERING
BRNO UNIVERSITY OF TECHNOLOGY
Motivation
Natural properties of real fracture process
● fractal geometry of fracture surface
- fractal dimension of surface
- fractal dimension of a profile
● dynamics of fracture
- fractal analysis of time series
- exponential law of fracture events
● fragmentation
- exponential law of mass and number
of fragments
Motivation
Fragmenting caused by impact
v
Oddershede L., Dimon P., Bohr J. (1993):
Self-organized criticality in fragmenting
Phys. Rev. Lett. 71, 3107 -- 3110
Fragmenting
Exponential law
Exponential law
What implies?
● size of fragments
- typical size does not exist
- fracture is scale-invariant
- fracture surface is fractal
● fracture process
- cannot be precisely predicted
- extremely sensitive (chaotic)
Buchanan M. (2000): Ubiquity
Weidenfeld & Nicolson, London
Simulation
Two numerical models in FyDiK2D application
physical discrete elements
particles
Movies
Conclusions / Results
Discrete elements
This outcome has been achieved with the financial
support of the GA ČR project 107/07/1276.
We specially thanks to Jan Eliáš for mesh generation.
FACULTY OF CIVIL ENGINEERING
BRNO UNIVERSITY OF TECHNOLOGY