Universality of fragment shapes

Scientific Reports
Gábor DomokosTímea Szabó

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...Continue Reading

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Citations

Oct 16, 2015·Nature Communications·Tímea SzabóDouglas J Jerolmack
Oct 18, 2016·Nature Communications·L GuoS Y Chiam
Dec 15, 2016·Physical Review. E·Gergő PálIan G Main
Jun 23, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Sofía AllendeJérémie Bec
Apr 20, 2018·Science Advances·Tímea Novák-SzabóDouglas J Jerolmack
Nov 28, 2018·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Ferenc KunIan G Main
Jul 19, 2020·Proceedings of the National Academy of Sciences of the United States of America·Gábor DomokosJános Török
Jan 14, 2021·Scientific Reports·Mathieu CasselHervé Piégay
Sep 30, 2021·Soft Matter·Roland SzatmáriFerenc Kun

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