Quadrupolar non-affine displacement fields in sheared two-dimensional Lennard-Jones glasses

In these studies, we compare quadrupole formation in the non-affine displacement fields during quasi-static shear deformation of packings of purely-repulsive harmonic disks with that in Lennard-Jones (LJ) glasses. For systems with purely-repulsive short-ranged interactions, the breaking of a single particle contact can suddenly trigger a strong quadrupolar displacement field. In contrast, in LJ glasses, we observe predominantly smooth transitions in the displacement fields during the quasi-elastic stress-versus-strain segments. We attribute this behavior to the fact that LJ glasses possess a broad distribution of local stiffnesses, whereas for packings of purely-repulsive harmonic disks, the local stiffness is binary, either non-zero or zero. We find that quadrupolar structures in LJ glasses occur preferentially near the ends of the quasi-elastic segments, whereas in systems with purely-repulsive short-ranged interactions, quadrupolar displacement fields occur randomly within the segments. We also calculate the local elastic moduli in LJ glasses, and observe that the softest region is not always the location where the quadrupole forms. We further show that strengthening "key" bonds between LJ particles can remove the quadrupoles from the displacement field during applied shear.