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The C-level is the minimum local crack velocity that we have in a velocity cluster.
We identify the velocity cluster by setting all elements above C·〈V〉 to one (yellow) and below to zero (black).
Example of velocity map and velocity cluster map are given in Figure 9 for stiff systems and in Figure 10 for soft systems.
We have shown the feasibility of connecting the velocity cluster distribution to the distribution of seismic moment M 0 of earthquakes.
We proposed two types of events in our model that can be compared to seismic events: a classical measure, the damage burst, i.e., the number of broken fibers during an elementary rise of the loading stress, and a new measure, the velocity burst, i.e., the size of a front velocity cluster during its propagation.
We then go through the velocity matrix and create the velocity cluster map by setting every element of V x,y) above C·〈V〉 to 1 and the rest to 0. We then go trough this cluster map and identify the cluster size distribution using a Hoshen-Kopelman algorithm [Hoshen et al. (1978)].
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Experimentally, a new detection system for high velocity fragments has been recently developed allowing the fragmentation of high velocity clusters to be totally recorded.
Figure 12 Distribution of velocity clusters for soft systems.
Figure 11 Distribution of velocity clusters for stiff systems.
A link is made between the area of the velocity clusters and the seismic moment M 0 following Kanamori and Anderson (1975): M_{0}=mu s d. (11).
When we look at the velocity clusters, we can see that there is a possible b v ≈1 value for both ductile and brittle systems.
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