Characterization of local-perturbation-induced non-affine displacement fields in amorphous solids

Amorphous solids exhibit complex non-affine displacement fields in response to applied stress. However, the structural origins of the non-affine displacements in amorphous solids are difficult to identify due to the lack of long-range structural order. In previous studies, we employed Delaunay triangularization to characterize the non-affine displacement fields in two dimensional binary Lennard-Jones (LJ) solids undergoing athermal, quasistatic simple shear (AQS). We showed that local pure shear of single triangles can give rise to quadrupolar displacement fields, though in most cases there were significant contributions from other types of defects. To further characterize the displacement fields that arise from single triangle perturbations, we decompose the displacement fields into an orthogonal basis of monopole, dipole, quadrupole, and vortex contributions. We find that only 20% of the displacement fields can be accurately recovered using this set of basis functions. Thus, pure shear deformations of Delaunay triangles give rise to displacement fields that are not a superposition of monopoles, dipoles, quadrupoles, and vortices. In contrast, pure shear triangle perturbations to hexagonal or disordered spring networks without pre-stress give rise to displacement fields that mimic Eshelby inclusions.