Abstract
The authors introduce and study a model of granular fracture to mimic the dynamics of rock fragmentation. The model describes a rock as an assembly of interacting grains that evolve in time according to Newtonian dynamics. The main ingredient describing macroscopic rather than microscopic dynamics is a history-dependent attractive potential between pairs of grains, which is set to zero after the pair first moves beyond some threshold distance apart. They study the characteristics of the distribution of cluster sizes and compare them with the corresponding characteristics of the percolation problem. Their results show a decrease of the cluster numbers with sample size and an apparent breakdown of hyperscaling. They also find a dependence of critical exponents on the average initial kinetic energy of the system.
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