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Nonlinear phononic materials enable superior wave responses by combining nonlinearity with their inherent periodicity, creating opportunities for the development of novel acoustic devices. However, the field has largely focused on reversible nonlinearities, whereas the role of hysteretic nonlinearity remains unexplored. In this work, we investigate nonlinear shear wave responses arising from the hysteretic nonlinearity of frictional rough contacts, and harness these responses to enable programmable functions. By using a numerical approach, we solve the strongly nonlinear problem of shear wave propagation through a single contact and a periodic array of contacts, accounting for frictional effects. Specifically, the Jenkin friction model with experimentally obtained properties is used to capture the effects of stick-slip transition at the contacts. Results show that friction gives rise to shear-polarized eigenstrains, which are residual static deformations within the system. We then demonstrate how eigenstrain generation in multiple contacts can enable programmable functionalities such as an acoustically controlled mechanical switch, precision position control, and surface reconfigurability. Overall, our findings open new avenues for designing smart materials and devices with advanced functionalities via acoustic waves using the hysteretic nonlinearity of frictional contacts. [ABSTRACT FROM AUTHOR]

Elastic bulk materials support longitudinal and transverse waves such that the former travels faster in most cases. Anomalous polarization is the case when a transverse wave travels faster, allowing us to engineer the wave propagation via wave steering, scattering control, and mode conversion, which has critical applications in vibration mitigation and ultrasonic imaging. However, realizable materials that exhibit anomalous polarization are rarely found in nature, and architected materials that exhibit this property have only been demonstrated in 2D. In this article, we present 3D auxetic periodic lattice materials that support anomalous wave polarization. Through finite element analysis, we show that these lattices can switch between normal and anomalous behavior via simple geometry changes. We confirm the elasticity condition and qualitatively discuss the guidelines to design lattice materials that support anomalous polarization along a specific wave propagation direction. We show the ability to control the anomalous wave propagation direction by modifying the lattice geometry. Further, we numerically demonstrate mode conservation, deceleration, and acceleration of an incident wave using a material that exhibits anomalous wave polarization. These demonstrations show the potential application of such materials in nondestructive evaluation and medical imaging. [ABSTRACT FROM AUTHOR]