<p>Obtaining full-field \emph{dynamic} material state awareness would have profound and wide-ranging implications across many fields and disciplines. For example, achieving dynamic state awareness in soft tissues could lead to the early detection of pathophysiological conditions. Applications in geology and seismology could enhance the accuracy of locating mineral and hydrocarbon resources for extraction or unstable subsurface formations. Ensuring safe interaction at the human-machine interfaces in soft robotic applications is another example. And as a final representative example, knowing real-time material dynamics in safety-critical structures and infrastructure can mitigate catastrophic failures. Because many materials (e.g., carbon fiber-reinforced polymers composites, ceramic matrix composites, biological tissues, cementitious and geological materials, and nanocomposites) exhibit coupling between their mechanical state and electrical transport characteristics, self-sensing via the piezoresistive effect is a potential gateway to these capabilities. While piezoresistivity has been mostly explored in static and quasi-static conditions, using piezoresistivity to achieve dynamic material state awareness is comparatively unstudied. Herein lies the significant gap in the state of the art: the piezoresistive effect has yet to be studied for in-situ dynamic sensing.</p> <p><br></p> <p>In this thesis, the gap in the state of the art is addressed by studying the piezoresistive effect of carbon nanocomposites subject to high-rate and transient elastic loading. Nanocomposites were chosen merely as a representative self-sensing material in this study because of their ease of manufacturability and our good understanding of their electro-mechanical coupling. Slender rods were manufactured using epoxy, modified with a small weight fraction of nanofillers such as carbon black (CB), carbon nanofibers (CNFs), and multi-walled carbon nanotubes (MWCNTs), and subject to loading states such as steady-state vibration at structural frequencies ($10^2-10^4$ Hz), controlled wave packet excitation, and high-strain rate impact loading in a split-Hopkinson pressure bar. This work discovers foundational principles for dynamic material state awareness through piezoresistivity. </p> <p><br></p> <p>Three major scholarly contributions are made in this dissertation. First, an investigation was pursued to establish dynamic, high-strain rate sensing. This investigation clearly demonstrated the ability of piezoresistivity to accurately track rapid and spatially-varying deformation for strain rates up to $10^2$ s$^{-1}$. Second, piezoresistivity was used to detect steady-state vibrations common at structural frequencies. Utilizing simple signal processing techniques, it was possible to extract the excitation frequency embedded into the collected electrical measurements. The third contribution examined the dynamic piezoresistive effect through an array of surface-mounted electrodes on CNF/epoxy rods subject to highly-controlled wave packet excitation. Electrode-spacing adjustments were found to induce artificial signal filtering by containing larger portions of the injected wave packets. The strain state in the rod was found after employing an inverse conductivity-to-mechanics model, thereby demonstrating the possibility of deducing actual in-situ strains via this technique. A digital twin in ABAQUS was constructed, and an elastodynamic simulation was conducted using identical dynamic loading, the results of which showed very good agreement with the piezo-inverted strains. </p> <p><br></p> <p>This work creates the first intellectual pathway to full-field dynamic embedded sensing. This work has far-reaching potential applications in many fields, as numerous materials exhibit self-sensing characteristics through deformation-dependent changes to electrical properties. Therefore, \emph{piezoresistive elastodynamics} has the incredible potential to be applied not just in structural applications but in other potentially innovated applications where measuring dynamic behavior through self-sensing materials is possible.  </p>