Fractality of Simulated FractureFractality of Simulated Fracture

Petr Frantík Petr Frantík ●● Zbyn Zbyněk Keršner ěk Keršner Václav Veselý Václav Veselý ●● Ladislav Řoutil Ladislav Řoutil

FFACULTY OF CIVIL ENGINEERING ACULTY OF CIVIL ENGINEERING

BBRNO UNIVERSITY OF RNO UNIVERSITY OF TECHNOLOGYTECHNOLOGY

MotivationMotivationNatural properties of real Natural properties of real fracturefracture process process

●● fractal geometry of fracture surfacefractal geometry of fracture surface- - fractal dimension of surfacefractal dimension of surface- - fractal dimension of a profilefractal dimension of a profile

●● dynamics of fracturedynamics of fracture- - fractal analysis of time seriesfractal analysis of time series- - exponential law of fracture eventsexponential law of fracture events

●● fragmentationfragmentation- - exponential law of mass and number exponential law of mass and number of fragments of fragments

MotivationMotivationFragmenting caused by impactFragmenting caused by impact

OddersOddershhededee L., Dimon P., Bohr J. L., Dimon P., Bohr J. (1993)(1993):: Self-organized criticality in fragmentingSelf-organized criticality in fragmenting

Phys. Rev. Lett. 71, 3107 -- 3110Phys. Rev. Lett. 71, 3107 -- 3110

v

FragmentingFragmentingExponential lawExponential law

Exponential lawExponential lawWhat implies?What implies?

Buchanan M.Buchanan M. (2000)(2000):: Ubiquity Ubiquity Weidenfeld & Nicolson, LondonWeidenfeld & Nicolson, London

●● size of fragmentssize of fragments- - typical size does not existtypical size does not exist- - fracture is scale-invariantfracture is scale-invariant- fracture surface is fractal- fracture surface is fractal

●● fracture processfracture process- - cannot be precisely predictedcannot be precisely predicted- - extremely sensitive (chaotic)extremely sensitive (chaotic)

SimulationSimulationTwo numerical models in Two numerical models in FyDiK2D FyDiK2D applicationapplication

physical discrete elements particlesphysical discrete elements particles

MoviesMovies

Conclusions / ResultsConclusions / ResultsDiscrete elementsDiscrete elements

This outcome has been achieved with the financial This outcome has been achieved with the financial support of the support of the GA GA ČRČR proprojectject 107/07/107/07/12761276..

We specially thanks to We specially thanks to Jan EliJan Eliáš áš for mesh generation.for mesh generation.

FFACULTY OF CIVIL ENGINEERING ACULTY OF CIVIL ENGINEERING

BBRNO UNIVERSITY OF RNO UNIVERSITY OF TECHNOLOGYTECHNOLOGY