Characterization and Simulation of Dispersive Elastodynamic Media in Time Domain

University Of Tennessee Space Institute, Tullahoma TN

Investigators

Abstract

Many materials are dispersive, i.e., their properties are frequency-dependent. The interaction of waves with material microstructure can result in a complex dispersive response. This effect is exploited in the design of metamaterials to effectuate novel properties that are otherwise not observed in conventional materials. This award supports fundamental research on the characterization and analysis of elastodynamic dispersive materials as a function of their mechanical layout and level of disorder at the microscale. Understanding the response of dispersive materials is important for a broad range of applications towards national prosperity and welfare and the national defense. For example, elastodynamic metamaterials find applications in seismic wave mitigation, vibration control, and blast wave mitigation. Moreover, disorder is inherent in the microstructure of many natural and man-made dispersive materials. For metamaterials, disorder is unavoidable due to manufacturing imperfections, but this inevitability can be used to improve wave mitigation properties and facilitate novel designs for non-destructive evaluation and energy harvesting applications. This award will also support student internship and faculty research opportunities through collaboration with a predominantly undergraduate institution, graduate research and course development, and publicly shared software modules. The first objective of this project is the formulation of advanced homogenization methods that derive dynamic properties of dispersive materials followed by numerical methods that incorporate such properties for transient analysis. Homogenized properties are generally valid only from quasi-static to long wavelength regimes. Higher order scattering coefficients and spatial dispersion terms will be used to extend this and derive effective dynamic properties that are meaningful up to medium to short wavelength regimes. The resulting effective properties can be quite complex, for example, by having a tensorial mass density and resulting in Willis constitutive equations. Modeling dispersive relations in time domain poses additional challenges. An automated method will be formulated to derive complex auxiliary differential equations for analysis in the time domain. The second objective is understanding the effect of disorder on various response measures of dispersive materials. Specifically, disorder can enhance wave mitigation properties of a metamaterial design by expanding the frequency range of the stopband(s), making the absorption more omnidirectional, and red-shifting the stopband which is often a welcomed effect. Statistical analysis will be used to analyze the sensitivity and stability of stopband and other dynamic properties versus disorder. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.