Evolution of displacements and strains in sheared amorphous solids

TL;DR

This study uses computer simulations to analyze how displacements and strains evolve in sheared amorphous solids, revealing complex correlations, size dependence, and distinct distribution behaviors for displacement and strain.

Contribution

It provides new insights into the spatial correlations, distribution shapes, and size effects of deformation in sheared amorphous solids through detailed simulation analysis.

Findings

Displacements and strains increase linearly with strain interval.

Displacement distributions evolve from exponential tails to Gaussian.

Strain distributions show elastic peaks and persistent plastic tails.

Abstract

The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Both the mean squared displacement and mean squared strain rise linearly with the length of the strain interval $\Delta \gamma$ over which they are measured. However, the increase in displacement does not represent single-particle diffusion. There are long-range spatial correlations in displacement associated with slip lines with an amplitude of order the particle size. Strong dependence on system size is also observed. The probability distributions of displacement and strain are very different. For small $\Delta \gamma$ the distribution of displacement has a plateau followed by an exponential tail. The distribution becomes Gaussian as $\Delta \gamma$ increases to about .03. The strain distributions consist of sharp central peaks associated with elastic regions, and long exponential tails associated with plastic regions. The latter persist to the largest $\Delta \gamma$ studied.