Characterization of heterogeneous solids via wave methods in computational microelasticity

Real solids are inherently heterogeneous bodies. While the resolution at which they are observed may be disparate from one material to the next, heterogeneities heavily affect the dynamic behavior of all microstructured solids. This work 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 the microelastic theory, 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, the method allows reducing the computational time with respect to classical methods based on a direct numerical simulation of the heterogeneities. The numerical method put forth in this research implements the microelastic theory through a finite-element scheme with enriched super-elements featuring microstructural degrees of freedom, and implementing constitutive laws obtained by homogenizing the microstructure characteristics over material meso-domains. It is possible to envision the use of this modeling methodology in support of diverse applications, ranging from structural health monitoring in composite materials to the simulation of biological and geomaterials. From an intellectual point of view, this work offers a mathematical explanation of some of the discrepancies often observed between one-scale models and physical experiments by targeting the area of wave propagation, one area where these discrepancies are most pronounced.