Effect of mechanical nonlinearity on the electromagnetic response of a microwave tunable metamaterial

Abstract

Tunable metamaterials functionalities change in response to external stimuli. Mechanical deformation is known to be an efficient approach to tune the electromagnetic response of a deformable metamaterial. However, in the case of large mechanical deformations, which are usually required to fully exploit the potential of the tunable metamaterials, the linear elastic mechanical analysis is no longer suitable. Nevertheless, nonlinear mechanical analysis is missing in the studies of mechanically tunable metamaterials. In this paper, we study the importance of considering nonlinearity in mechanical behavior when analyzing the response of a deformable metamaterial and its effects on electromagnetic behavior. We consider a microwave metamaterial formed by copper four-cut split ring resonators on a Polydimethylsiloxane (PDMS) substrate. Applying both displacement and force stimuli, we show that when the deformation is large, more than 10 percent strain, the use of nonlinear analysis considering the geometrical and material nonlinearities is imperative. We further show that the discrepancies between the linear and nonlinear analyses appear in overestimating the stress, underestimating the tunability of the metamaterial responses, and mispredicting the negative permeability regions.

Bandgap evolution of metamaterials with continuous solid–liquid phase change

“…In contrast, nonlinear stiffness mechanisms have attracted more and more attention due to their great potential in improving vibration performance [20,21]. Specifically, mechanism motion has been widely used due to its natural geometric nonlinear variation, including the introduction of thermally, electrically, and optically responsive materials as a medium to achieve mechanism motion [22][23][24][25][26][27], for instance, Zhao et al [23] created structures with large actuation deformation and high load carrying capacity, as well as a SMA springs within to provide adjustable stiffness. Liquid crystal elastomer (LCE) was 3D printed into a multilayer structure by Yuan et al [25], and the LCE layer was then thermally bent, causing the actuator's behavior to alter in both directions.…”