Propagation and dissipation of elasto-plastic stress waves in two dimensional ordered granular media

We investigate elasto-plastic wave propagation in ordered two-dimensional granular media consisting of contacting metallic granules. A Hopkinson bar generates a high-amplitude wave pulse - sufficient to yield the contact points between granules - and is used to load two configurations of brass beads: a square packing and a hexagonal packing. Selected beads that have embedded piezoelectric sensors are used to measure the arrival time and magnitude of the elasto-plastic wave in situ. Postmortem optical microscopy of the bead contact points elucidates the propagation of plasticity by allowing measurement of the residual plastic contact area. Results show that the elasto-plastic wave propagates in similar directions to a purely elastic wave, but with decaying amplitude due to the plastic deformation. It is found, however, that even small amounts of disorder in a nominally perfect 2D packing significantly affects both wave transit time and peak force. To explore the effects of such disorder further, the dynamic behavior of the 2D granular packing is numerically modeled using a molecular dynamics simulation that incorporates an elasto-plastic contact model and allows for a variability of particle size that incorporates bead diameter tolerance. The results qualitatively confirm the experimental findings of the significance of even limited amounts of disorder on wave arrival time and peak amplitude. This result has significant implications on the feasibility of designing 2D ordered granular media for practical applications.