Using Delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids*

We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation of each triangle. To understand the spatio-temporal evolution of the displacement fields, we follow minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop.  We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops.  We then perform local perturbations to single triangles and demonstrate that local pure shear strains of triangular elements, which give rise to mostly quadrupolar displacement fields, are activated during AQS.  These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.