By combining theory and experiments, we seek to understand and design micro-granular metamaterials exhibiting unusual dynamic mechanical behavior and wave propagation. We use self-assembled micro-granular monolayers governed by a contact law combining van der Waals and Hertzian contact forces, and exhibiting negative stiffness and snapping in the vicinity of local separation. Preliminary work on stiff 1D micro-granular crystals on compliant substrates under impulse excitation indicates that these materials exhibit local dynamic re-clustering, solitary wave disintegration, low-to-high mode energy transfer, local resonance and inherent capacity for very high dissipation. We experimentally test this hypothesis by exciting self-assembled monolayers of aluminum oxide (hard) microparticles supported on thin compliant membranes and measure their vibration response, thus extracting their collective dynamics under a variety of excitation magnitudes and frequencies.We are designing heterogeneous particle assemblies to enable the design of new materials with unprecedented viscoelastic properties. This could enable a new class of highly damped microstructured materials for MEMS applications.