Universal and non-universal features in coarse-grained models of flow in disordered solids

TL;DR

This study investigates the spatial and temporal correlations in 2D shear flow of amorphous solids using elastoplastic models, highlighting the effects of tensorial stress descriptions and convection on flow behavior and correlation lengths.

Contribution

It demonstrates that correlation lengths scale with shear rate as a0b1a0b2 in 2D, and compares scalar versus tensorial models and the impact of convection on flow fluctuations.

Findings

Correlation length scales as a0b1a0b2 with shear rate.

Tensorial and scalar models produce similar results.

Convection enhances fluctuations and breaks flow symmetry.

Abstract

We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local alternation between an elastic regime and plastic events during which the local stress is redistributed. The importance of a fully tensorial description of the stress and of the inclusion of (coarse-grained) convection in the model is investigated; scalar and tensorial models yield very similar results, while convection enhances fluctuations and breaks the spurious symmetry between the flow and velocity gradient directions, for instance when shear localisation is observed. Besides, correlation lengths measured with diverse protocols are discussed. One class of such correlation lengths simply scale with the spacing between homogeneously distributed, simultaneous plastic events. This leads to a scaling of the correlation length with the shear rate as $\dot{\gamma}^{\frac{-1}{2}}$ in 2D in the athermal regime, regardless of the details of the model. The radius of the cooperative disk, defined as the near-field region in which plastic events induce a stress redistribution that is not amenable to a mean-field treatment, notably follows this scaling. On the other hand, the cooperative volume measured from the four-point stress susceptibility and its dependence on the system size and the shear rate are model-dependent.