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Botond Tyukodi1 Craig Maloney1 Damien Vandembroucq2

1, Northeastern University, Boston, Massachusetts, United States
2, ESPCI, Paris, , France

It is currently beleived that the macroscopic plastic deformation of amorphous materials is the result of the collective behavior of localized particle rearrangements called shear transformations. The triggering of shear transformations is governed by the local structural disorder, whereas their interaction by the elastic bulk in which they are embedded. Consequently, the collective complex dynamics is a result of the competition between elasticity and disorder.

Around yielding, one observes serrated flow curves, intermittency and widely distributed avalanches of rearrangements, all of them signatures of a dynamic phase transition. Therefore, under the claim of universality, it has been argued that the generic properties of such critical systems are independent of the form of the elastic interaction or the underlying disorder. Only recently has become clearer that both the elastic interaction and the form of the disorder may have a strong impact on the critical properties.
Here we compare results of a mesoscopic depinning-like model with several quadrupolar interactions (elastic kernels) and two different flavors of disorder. We work in the quasistatic limit and we find that the particular form of the disorder has little impact on the critical properties. We confirm, however, that the elastic kernel plays an important role when it comes to the scaling of the distribution of avalanche rates and we find good agreement with previous molecular dynamics studies.

The most dramatic impact of the kernel however arises when looking at fluctuations, in particular, fluctuations of strains and displacements. We show that the presence of soft modes in the Eshelby-like elastic interaction kernels allows for a continuous, diffusive increase of these fluctuations. This constant increase of fluctuations and the associated shear banding is known to lead to material failure. Such fluctuations are generally downplayed in most homogenizing procedures, we find, however, that they feature finite-size scaling, and, as such, they may not be simply disregarded. We study the finite size scaling of the associated diffusion coefficient "D" and we find that up to a strain necessary to form a single slip line, D scales linearly with system size (D~L) independently of the kernel, consistent with molecular dynamics simulations. After a crossover regime, however, a new scaling is found (D~L^1.6) for the kernel featuring soft modes, which suggests a more prominent strain localization than the one observed in MD. This later regime is not consistent with MD, it has, however, been observed in previous lattice models. We show that shear bands (slip lines) are the soft deformation modes of the elastic interaction, and as such, they can develop at no energy cost whatsoever. For kernels that lack any soft deformation modes, fluctuations saturate after a finite time and the system becomes subdiffusive.

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