TY - JOUR

T1 - On the density of shear transformations in amorphous solids

AU - Lin, Jie

AU - Saade, Alaa

AU - Lerner, Edan

AU - Rosso, Alberto

AU - Wyart, Matthieu

PY - 2014/1

Y1 - 2014/1

N2 - We study the stability of amorphous solids, focussing on the distribution P(x) of the local stress increase x that would lead to an instability. We argue that this distribution behaves as , where the exponent θ is larger than zero if the elastic interaction between rearranging regions is non-monotonic, and increases with the interaction range. For a class of finite-dimensional models we show that stability implies a lower bound on θ, which is found to lie near saturation. For quadrupolar interactions these models yield for d = 2 and in d = 3 where d is the spatial dimension, accurately capturing previously unresolved observations in atomistic models, both in quasi-static flow and after a fast quench. In addition, we compute the Herschel-Buckley exponent in these models and show that it depends on a subtle choice of dynamical rules, whereas the exponent θ does not.

AB - We study the stability of amorphous solids, focussing on the distribution P(x) of the local stress increase x that would lead to an instability. We argue that this distribution behaves as , where the exponent θ is larger than zero if the elastic interaction between rearranging regions is non-monotonic, and increases with the interaction range. For a class of finite-dimensional models we show that stability implies a lower bound on θ, which is found to lie near saturation. For quadrupolar interactions these models yield for d = 2 and in d = 3 where d is the spatial dimension, accurately capturing previously unresolved observations in atomistic models, both in quasi-static flow and after a fast quench. In addition, we compute the Herschel-Buckley exponent in these models and show that it depends on a subtle choice of dynamical rules, whereas the exponent θ does not.

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U2 - 10.1209/0295-5075/105/26003

DO - 10.1209/0295-5075/105/26003

M3 - Article

AN - SCOPUS:84894471216

SN - 0295-5075

VL - 105

JO - Europhysics Letters

JF - Europhysics Letters

IS - 2

M1 - 26003

ER -