This work combines closed-form and computational analyses to elucidate the dynamic properties, termed signatures, of waves propagating through solids defined by the theory of elasticity with microstructure and the potential of such properties to identify microstructure evolution over a material's lifetime. First, the study presents analytical dispersion relations and frequency-dependent velocities of waves propagating in microelastic solids. A detailed parametric analysis of the results show that elastic solids with microstructure recover traditional gradient elasticity under certain conditions but demonstrate a higher degree of flexibility in adapting to observed wave forms across a wide frequency spectrum. In addition, a set of simulations demonstrates the ability of the model to quantify the presence of damage, just another type of microstructure, through fitting of the model parameters, especially the one associated with the characteristic length scale of the underlying microstructure, to an explicit geometric representation of voids in different damage states.
Bibliographical noteFunding Information:
Steven Greene is supported by a National Science Foundation Graduate Research Fellowship and warmly thanks the NSF. Stefano Gonella thanks Bojan Guzina, Egor Dontsov and Roman Tokmashev of the University of Minnesota for the many discussions on the role of length scale parameters in gradient elasticity models. The Northwestern team also acknowledges NSF Grant CMMI-0823327 .
- Generalized continua
- Wave propagation