Characterization of Heterogenous Solids via Wave Methods in Computational Microelasticity

Stefano Gonella
Assistant Professor
Department of Civil Engineering
University of Minnesota Twin Cities

Abstract

As a discipline, wave mechanics has existed for over a century as a special branch of solid mechanics. Nevertheless, new and intriguing applications of this field continue to present themselves in the arena of modern engineering problems. The key feature that makes waves attractive is their extreme sensitivity to the inherently inhomogeneous nature of solids, and ultimately their ability to detect small scale and localized features, such as microstructural changes, interphases and defects. When properly inspected and interpreted, a wavefield provides a complete and reliable signature of a solid. The talk introduces a wave propagation simulation methodology, based on Mindlin’s microelastic continuum theory, as a tool to dynamically characterize microstructured solids in a way that naturally accounts for their inherent heterogeneities. Wave motion represents a natural benchmark problem to appreciate the full benefits of microelastic theories, as in high-frequency dynamic regimes do microstructural effects unequivocally elucidate themselves. Through a finite-element implementation of the microelastic continuum, and the interpretation of the resulting computational multiscale wavefields, one can estimate the effect of microstructures upon the wave propagation modes, phase and group velocities. By accounting for microstructures without explicitly modeling them, this method allows reducing the computational time with respect to classical methods involving direct numerical simulation of the heterogeneities.