Universality of fragment shapes

Abstract

The shape of fragments generated by the breakup of solids is central to a wide variety of problems ranging from the geomorphic evolution of boulders to the accumulation of space debris orbiting Earth. Although the statistics of the mass of fragments has been found to show a universal scaling behavior, the comprehensive characterization of fragment shapes still remained a fundamental challenge. We performed a thorough experimental study of the problem fragmenting various types of materials by slowly proceeding weathering and by rapid breakup due to explosion and hammering. We demonstrate that the shape of fragments obeys an astonishing universality having the same generic evolution with the fragment size irrespective of materials details and loading conditions. There exists a cutoff size below which fragments have an isotropic shape, however, as the size increases an exponential convergence is obtained to a unique elongated form. We show that a discrete stochastic model of fragmentation reproduces both the size and shape of fragments tuning only a single parameter which strengthens the general validity of the scaling laws. The dependence of the probability of the crack plan orientation on the linear extension of fragments proved to be essential for the shape selection mechanism.

Fragmentation and shear band formation by slow compression of brittle porous media

“…(7). Similar self-affinity of fragment shapes has been found in the explosive fragmentation of shells [30]; however, for dynamic breakup of bulk materials the shape of pieces does not have this feature [31,32]. If we now use…”

Geologic history of Martian regolith breccia Northwest Africa 7034: Evidence for hydrothermal activity and lithologic diversity in the Martian crust

“…(a) Relationship between a and b / a of igneous textured clasts (yellow outlines) and mineral clasts (green outlines) resemble the common relation found for fragmented rocks in Domokos et al . [] (gray data sets with x symbols). Well‐rounded limestone clasts (gray data set with triangles, limestone fragments abraded in the laboratory from Szabó et al .…”

A new workflow for the automated measurement of shape descriptors of rocks

“…Traditional measurement techniques often incorporate personal factors or rely on the verbal characterization of the shape (Wentworth, 1923;Boggs, 2001) to approximate these values. The number of stable (S) and unstable (U ) mechanical equilibria of a particle as a shape descriptor gained significant attention recently (Domokos et al, 2009; Miller et al, 2014;Domokos et al, 2015;Novák-Szabó et al, 2018) and it is not only insensitive for small measurement errors, but it also has a rich mathematical literature (Grayson, 1987;Domokos et al, 2015;Domokos and Lángi, 2019).…”

“…Traditional measurement techniques often incorporate personal factors or rely on the verbal characterization of the shape (Wentworth, 1923;Boggs, 2001) to approximate these values. The number of stable (S) and unstable (U ) mechanical equilibria of a particle as a shape descriptor gained significant attention recently (Domokos et al, 2009; Miller et al, 2014;Domokos et al, 2015;Novák-Szabó et al, 2018) and it is not only insensitive for small measurement errors, but it also has a rich mathematical literature (Grayson, 1987;Domokos et al, 2015;Domokos and Lángi, 2019).It is beneficial to switch from the traditional hand-measurements to automated shape analysis of the particles to avoid personal bias. Recently, several works appeared aiming to reduce subjectivity by automatically calculating shape properties from 2D digital images of the particles (Roussillon et al, 2009;Durian et al, 2007;Cassel et al, 2018;Cheng et al, 2018), 25 3D laser scanning (Hayakawa and Oguchi, 2005; Anochie-Boateng et al, 2013) or X-ray CT (Deiros Quintanilla et al, 2019).…”