Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates

J. T. Clemmer and M. O. Robbins, Physical Review Letters, 129, 078002 (2022).

Using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

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