1. Fractality of Simulated Fracture Petr Frantík ● Zbyněk Keršner Václav Veselý ● Ladislav Řoutil F ACULTY OF CIVIL ENGINEERING B RNO UNIVERSITY OF TECHNOLOGY

2. 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

3. Motivation Fragmenting caused by impact Oddershede L., Dimon P., Bohr J. (1993): Self-organized criticality in fragmenting Phys. Rev. Lett. 71, 3107 -- 3110 v

4. Fragmenting Exponential law

5. What implies? Buchanan M. (2000): Ubiquity Weidenfeld & Nicolson, London ● 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)

6. Simulation Two numerical models in FyDiK2D application physical discrete elements particles

9. Movies

10. Conclusions / Results Discrete elements

11. 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. F ACULTY OF CIVIL ENGINEERING B RNO UNIVERSITY OF TECHNOLOGY