13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Number of super atoms, N CPU TIME.[sec.] Direct Method Velret Method 10 100 1000 1 10 100 1000 10000 100000 Figure 5. Plots of calculating time vs. number of super atoms on each method 3.2. Fractal analysis of the distribution of D values On the basis of Box counting method, fractal dimensional values, FD were calculated and they were plotted against the number of super atoms as shown in Figs. 6 (a), (b) and (c). These results show that FD takes a specified saturated constant value when the number of super atoms is larger than Nc = 250. Number of super atoms, N Fractal dimensionality, FD Direct Verlet Nc=250 1 10 100 1000 10000 1 1.05 1.1 1.15 1.2 Number of super atoms, N Fractal dimensionality, FD Direct Verlet Nc=150 1 10 100 1000 10000 1 1.05 1.1 1.15 1.2 Number of super atoms, N Fractal dimensionality, FD Direct Verlet Nc=100 1 10 100 1000 10000 1 1.05 1.1 1.15 1.2 (a) Condition 1 (b) Condition 2 (c) Condition 3 Figure 6. Plots of fractal dimensional value vs. the number of super atoms on each condition 3.3. Determination of dominating region of fracture using projection method To predict the dominating region of fracture, the region where a value of D takes negative value is defined as the disordered regions of super atoms. As shown in Fig. 7, they were characterized by L at the side of the crack and G at that of super dislocation. The changing characteristics of L and G were plotted against the number of super atoms as shown in Figs. 8 (a), (b) and (c). Both of characteristics of L and G were found to take constant values, respectively in the region where the distribution of D shows fractal characteristics.
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