A fragmentation model with neighborhood interaction

Several models of fragmentation have been studied that suppose random fracture forces. In this article, we did a numerical study on a dynamic model for fragmentation in which the fracture forces are generated by neighboring fragments and are proportional to the size of the common boundary between two fragments. The following assumptions were also considered: the material defects are represented by a random distribution of point flaws; the total mass is conserved; and the iterative fracture of each fragment is randomly stopped by a condition that considers a constant probability and a minimal fragment size. The motivation for this model was to determine under what circumstances a continuous fragmentation model with fracture forces defined by the neighbors' interaction produces results that are in agreement with the experimental evidence. The main result of this work establishes that the fragment size distribution follows a power-law for fragments of greater area than the minimal fragment size mfs. The visualizations present complex fracture patterns that resemble real systems.