Critical exponents of the yielding transition of amorphous solids

I. Fernández Aguirre and E. A. Jagla
Phys. Rev. E 98, 013002 – Published 13 July 2018

Abstract

We investigate numerically the yielding transition of a two-dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, derived from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic “plastic disorder” potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate versus stress curve, close to the critical stress, is of the form γ̇(σσc)β. Remarkably, we find that the value of β depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of “dynamical” mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the β exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean-field version known as the Hébraud-Lequeux model.

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  • Received 26 March 2018

DOI:https://doi.org/10.1103/PhysRevE.98.013002

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

I. Fernández Aguirre and E. A. Jagla

  • Comisión Nacional de Energía Atómica, Instituto Balseiro (UNCu), and CONICET Centro Atómico Bariloche, (8400) Bariloche, Argentina

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Issue

Vol. 98, Iss. 1 — July 2018

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