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

WW Jin and A Datye and UD Schwarz and MD Shattuck and CS O'Hern, SOFT MATTER, 17 (2021).

DOI: 10.1039/d1sm00898f

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, which correspond to atomic rearrangement events. 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 gradient tensor F-alpha associated with each triangle alpha. To understand the spatio-temporal evolution of the displacement fields during shear stress drops, we calculate F-alpha along 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 (rotation, dilation, simple and pure shear) to single triangles and measure the resulting displacement fields. We find that local pure shear deformations of single triangles give rise to mostly quadrupolar displacement fields, and thus pure shear strain is the primary type of local strain that is activated by bulk, athermal quasistatic simple shear. Other local perturbations, e.g. rotations, dilations, and simple shear of single triangles, give rise to vortex- like and dipolar displacement fields that are not frequently activated by bulk AQS. These results provide fundamental insights into the non- affine atomic motion that occurs in driven, glassy materials.

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