Shear bands as manifestation of a criticality in yielding amorphous solids

Proceedings of the National Academy of Sciences of the United States of America
Giorgio ParisiMurari Singh

Abstract

Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterward exhibiting a steady state with a constant mean stress. In stress-controlled experiments, the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here, we offer such a theory: The mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point, there exists a divergent correlation length that is associated with the system-spanning instabilities (also known as shear bands), which are typical to the mechanical yield. The theory, the order parameter used, and the correlation functions that exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.

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Citations

Mar 7, 2018·Scientific Reports·Kamran Karimi, Jean-Louis Barrat
Jul 6, 2019·The Journal of Chemical Physics·Ludovic BerthierFrancesco Zamponi
Jan 20, 2018·Physical Review. E·Itamar ProcacciaMurari Singh
Jun 13, 2018·Proceedings of the National Academy of Sciences of the United States of America·Misaki OzawaGilles Tarjus
Dec 25, 2019·Physical Review. E·Bhanu Prasad BhowmikCorrado Rainone
May 16, 2019·Soft Matter·Éric Brillaux, Francesco Turci
Nov 26, 2019·Physical Review Letters·Bhanu Prasad BhowmikSmarajit Karmakar
Feb 1, 2020·Physical Review Letters·Vikranth Sagar ReddySurajit Sengupta
May 20, 2020·Physical Review. E·Eric De Giuli
Apr 29, 2020·Proceedings of the National Academy of Sciences of the United States of America·Pallabi DasSrikanth Sastry
Jan 23, 2020·Physical Review. E·Kamran Karimi
Aug 17, 2020·Physical Review. E·Vishwas V Vasisht, Emanuela Del Gado
Apr 21, 2018·Proceedings of the National Academy of Sciences of the United States of America·Parswa NathSurajit Sengupta
Oct 31, 2020·Physical Review Letters·Hugh J BarlowSuzanne M Fielding
Apr 15, 2021·Proceedings of the National Academy of Sciences of the United States of America·Himangsu BhaumikSrikanth Sastry
May 26, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Santhosh Kumar R, Bhaskar Sen Gupta
Jul 10, 2021·Physical Review Letters·Srikanth Sastry
Aug 21, 2021·Physical Review. E·Norihiro OyamaAtsushi Ikeda

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