Size of Plastic Events in Strained Amorphous Solids at Finite Temperatures

TL;DR

This paper investigates how the size of plastic deformation events in amorphous solids depends on system size, temperature, and strain rate, revealing finite size effects and scaling behaviors relevant for understanding elasto-plasticity.

Contribution

It introduces a scaling theory explaining the finite size effects and cross-over length scales governing plastic events at finite temperatures in amorphous solids.

Findings

Plastic event size grows with system size at small scales.

Two cross-over length scales determine the bounded size of plastic events.

Number of uncorrelated plastic events scales with system size and dimension.

Abstract

We address the system-size dependence of typical plastic flow events when an amorphous solid is put under a fixed external strain rate at a finite temperature. For system sizes that are accessible to numerical simulations at reasonable strain rates and at low temperatures the magnitude of plastic events grows with the system size. We explain however that this must be a finite size effect; for larger systems there exist two cross-over length-scales $\xi_1$ and $\xi_2$, the first determined by the elastic time-scale and the second by the thermal energy-scale. For system of linear size $L$ larger than any of these scales the magnitude of plastic events must be bounded. For systems of size $L\gg \xi$ there must exist $(L/\xi)^d$ uncorrelated plastic events which occur simultaneously. We present a scaling theory that culminates with the dependence of the cross-over scales on temperature and strain rate. Finally we relate these findings to the temperature and size dependence of the stress fluctuations. We comment on the importance of these considerations for theories of elasto-plasticity.