MEAM Seminar: “Dynamic Response of Resonant Metamaterials and Other Composites”

Composite materials under dynamic loading exhibit interesting emergent phenomena. Most notably are phononic crystals and metamaterials which can possess frequency dependent and negative elastic moduli and density. In general, the constitutive response is non-local in space and time and depends on both the strain and velocity. Additionally, scattering and local resonance effects can lead to frequency band gaps where no waves may propagate. Advanced manufacturing techniques allow us to produce these composites with intricate microstructures. At the same time, these processes may be costly and prototyping many designs physically may be cost prohibitive. It is then natural to turn towards modeling in order to more efficiently design and characterize such materials. These modelling efforts may include direct numerical simulations, but even then this may be computationally infeasible for composites whose microstructure is much smaller than the macroscopic length scales in which it will be operating. In these cases, we seek to describe the effective behavior of the material under static or dynamic loading.

The work discussed in this talk is situated towards modeling of resonant metamaterials and other composites under dynamic loading. Direct numerical simulations are used to explore the wave propagation behavior of simple and hierarchical resonant metamaterials made of soft polydimethylsiloxane rubber (PDMS) and removable steel insets. The role of several physical features on the transmission loss (TL) curve is assessed in detail numerically and compared to the experimental TL data. Beyond this, we develop a novel dynamic homogenization framework using one- and two-point statistics that provide estimates of the dynamic response of composites with reduced computational cost.