On the density of shear transformations in amorphous solids

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-monoton...

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Bibliographic Details
Published in:Europhysics letters 2014-01, Vol.105 (2), p.26003-p1-26003-p6
Main Authors: Lin, Jie, Saade, Alaa, Lerner, Edan, Rosso, Alberto, Wyart, Matthieu
Format: Article
Language:English
Subjects:
45.70.-n
63.50.-x
63.50.Lm
Density
Dimensional stability
Exponents
Instability
Lower bounds
Mathematical models
Saturation
Stability
Stress concentration
Transformations
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/105/26003