Role of higher-order inertia in modulating elastic wave dispersion in materials with granular microstructure

Abstract

(Meta-) materials with granular microstructures exhibit nonlinear dispersive wave propagation, which is typically attributed to the presence of a microstructure. However, this behavior can arise from two additional sources in a linear non-dissipative system – the grain-scale or micromechanical characteristics and the grain-scale or micro-inertial characteristics. The microstructure, the grain-scale mechanical and the grain-scale inertial properties in combination may be designated as micro-mechano-morphology. From a continuum modeling viewpoint, the observed dispersion behavior that accounts for micro-mechano-morphology of materials with granular microstructures can be described using a granular micromechanics based micromorphic model (Nejadsadeghi and Misra 2019b, Misra and Poorsolhjouy 2016). Following the approach outlined in these works, we elaborate on the effect of micro-scale inertia upon the wave propagation behavior. The work is motivated by the observation of negative group velocity of optical waves seen in simulations using discrete models of granular media. We show that higher-order inertia is necessary for describing this phenomena using continuum models. We further show that this phenomena can be modulated by micro-scale mass density distributions, thus affecting the widths of potential frequency band-gaps, including the negative group velocity of the acoustic branch.