Nonlinear behavior of heterogeneous materials containing snapping acoustic metamaterial inclusions

Abstract

This work studies the forced dynamical behavior of a heterogeneous material containing metamaterial inclusions undergoing large deformations. The inclusions exhibit non-monotonic stress-strain behavior, modeled with an expansion to third order in volume strain, where the coefficients of the expansion depend on the metamaterial structure. The resulting constitutive behavior of interest displays regimes of both positive and negative stiffness and the inclusion therefore exhibits hysteretic snapping when forced by an acoustic pressure. Two cases are explored using a generalized Rayleigh-Plesset analysis to model the large-deformation dynamics of the metamaterial inclusion following an approach similar to Emelianov et al. [J. Acoust. Soc. Am., 115, 581 (2004)]. The first case focuses on the forced dynamics of a single inclusion embedded in a weakly compressible elastic medium. The second case broadens the model to analyze the behavior of a heterogeneous material comprised of a low volume fraction of non-interacting metamaterial inclusions embedded in a weakly compressible material. Finally, estimates of the effective bulk modulus and loss factor of the heterogeneous medium are presented for instances of the forcing pressure inducing either large or small inclusion deformation. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and the Office of Naval Research.]