PARTICLES 2025

Fragmentation processes under isotropic compression

  • Kun, Ferenc (University of Debrecen)
  • Husztek, Anna (University of Debrecen)
  • Pál, Gergő (University of Debrecen)

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Based on a two-dimensional discrete element model, our study explores the breakup process of a disc-shaped heterogeneous solid under isotropic compression, a loading mode that ensures uniform initial energy distribution and approximates conditions in ESWL kidney stone treatment up to some extent. In the model the disc-shape specimen is discretized on a random lattice of Voronoi polygons which are then coupled by breakable elastic beams. The disc is subject to isotropic compression, slowly increasing to the desired initial strain. When the confinement is released, the disc starts to expand and breaks into pieces in a complex process which strongly depends on the degree of initial compression. A key result is the identification of three distinct phases in the breakup process: segmentation, fragmentation, and shattering characterized by scaling laws. At low energies, the disc undergoes segmentation into a few large, radially separated pieces with minor central dust generation. As the input energy increases beyond a first critical point, the system enters the fragmentation phase, where both the number and diversity of fragments increase, and a central crushed zone emerges. In this regime, fragment mass distribution has a power law behaviour with a crossover between regimes of different exponents: small internal fragments follow a steep power law, while peripheral fragments show a slower decay. These arise from different fracture mechanisms—branching-merging of cracks near the surface and combined tensile-shear fracture in the interior. At even higher energies, beyond a second critical threshold, the system undergoes shattering: large fragments disintegrate rapidly, and the mass loss of non-powder pieces follows an exponential decay. This phase is characterized by the disappearance of the dual power-law regime and the dominance of fine debris. The exponents of the fragment mass distributions show weak energy dependence but tend to well defined limits for large systems, indicating universality. The findings contribute to the broader understanding of fragmentation universality and may support optimization of medical fragmentation techniques.