  We report a combined experimental and simulation study of deformation-induced
diffusion in compacted two-dimensional amorphous granular pillars, in which
thermal fluctuations play negligible role. The pillars, consisting of
bidisperse cylindrical acetal plastic particles standing upright on a
substrate, are deformed uniaxially and quasistatically by a rigid bar moving at
a constant speed. The plastic flow and particle rearrangements in the pillars
are characterized by computing the best-fit affine transformation strain and
non-affine displacement associated with each particle between two stages of
deformation. The non-affine displacement exhibits exponential crossover from
ballistic to diffusive behavior with respect to the cumulative deviatoric
strain, indicating that in athermal granular packings, the cumulative
deviatoric strain plays the role of time in thermal systems and drives
effective particle diffusion. We further study the size-dependent deformation
of the granular pillars by simulation, and find that different-sized pillars
follow self-similar shape evolution during deformation. In addition, the yield
stress of the pillars increases linearly with pillar size. Formation of
transient shear lines in the pillars during deformation becomes more evident as
pillar size increases. The width of these elementary shear bands is about twice
the diameter of a particle, and does not vary with pillar size.
