Volume 105, Number 2, January 2014
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||12 February 2014|
On the density of shear transformations in amorphous solids
1 New York University, Center for Soft Matter Research - 4 Washington Place, New York, NY, 10003, USA
2 Laboratoire de Physique Théorique et Modèles Statistiques (UMR CNRS 8626), Université de Paris-Sud Orsay Cedex, France
3 LPS, ENS - 24 rue Lhomond, 75231 Paris Cedex 05, France
Received: 9 October 2013
Accepted: 13 January 2014
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.
PACS: 63.50.-x – Vibrational states in disordered systems / 63.50.Lm – Glasses and amorphous solids / 45.70.-n – Granular systems
© EPLA, 2014
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