  A granular system composed of frictional glass beads is simulated using the
Discrete Element Method. The inter-grain forces are based on the Hertz contact
law in the normal direction with frictional tangential force. The damping due
to collision is also accounted for. Systems are loaded at various stresses and
their quasi-static elastic moduli are characterized. Each system is subjected
to an extensive dynamic testing protocol by measuring the resonant response to
a broad range of AC drive amplitudes and frequencies via a set of diagnostic
strains. The system, linear at small AC drive amplitudes has resonance
frequencies that shift downward (i.e., modulus softening) with increased AC
drive amplitude. Detailed testing shows that the slipping contact ratio does
not contribute significantly to this dynamic modulus softening, but the
coordination number is strongly correlated to this reduction. This suggests
that the softening arises from the extended structural change via break and
remake of contacts during the rearrangement of bead positions driven by the AC
amplitude.
