Nonlinear behavior of a coupled multiscale material containing snapping acoustic metamaterial inclusions

Abstract

Snapping acoustic metamaterial (SAMM) inclusions are engineered sub-wavelength structures that exhibit regimes of both positive and negative stiffness. Snapping is defined as large, rapid deformations resulting from the application of an infinitesimal change in externally applied pressure. This snapping leads to a large hysteretic response at the inclusion scale and is thus of interest for enhancing absorption of energy in acoustic waves. The research presented here models the forced dynamics of a multiscale material consisting of SAMM inclusions embedded in a nearly incompressible viscoelastic matrix material to explore the influence of small-scale snapping on enhanced macroscopic absorption. The microscale is characterized by a single SAMM inclusion, while the macroscale is sufficiently large to encompass a low volume fraction of non-interacting SAMM inclusions within the nearly incompressible matrix. A model of the forced dynamical response of this heterogeneous material is achieved by coupling the two scales in time and space using a generalized Rayleigh-Plesset analysis, which has been adapted from the field of bubble dynamics. A loss factor for the heterogeneous medium is examined to characterize energy dissipation due to the forced behavior of these metamaterial inclusions. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and Office of Naval Research.]