Universality of Avalanche Exponents in Plastic Deformation of Disordered Solids

Abstract

Plastic yield of amorphous solids occurs by power law distributed slip avalanches whose universality is still debated. Determination of the power law exponents from experiments and molecular dynamics simulations is hampered by limited statistical sampling. On the other hand, while existing elasto-plastic depinning models give precise exponent values, these models to date have been limited to a scalar approximation of plasticity which is difficult to reconcile with the statistical isotropy of amorphous materials. Here we introduce for the first time a fully tensorial mesoscale model for the elasto-plasticity of disordered media that can not only reproduce a wide variety of shear band patterns observed experimentally for different deformation modes, but also captures the avalanche dynamics of plastic flow in disordered materials. Slip avalanches are characterized by universal distributions which are quantitatively different from mean field predictions, both regarding the exponents and regarding the form of the scaling functions, and which are independent of system dimensionality (2D vs 3D), boundary and loading conditions, and uni-or biaxiality of the stress state. We also measure average avalanche shapes, which are equally universal and inconsistent with mean field predictions. Our results provide strong evidence that the universality class of plastic yield in amorphous materials is distinct from that of mean field depinning.

18 pages, 6 figures

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