Electromagnetic Reconfiguration Using Stretchable Mechanical Metamaterials

Abstract Response to environmental thermomechanical inputs in applications that range from wearable electronics to aerospace structures necessitates agile communication systems driven by reconfigurable electromagnetic structures. Antennas in these systems must dynamically preserve acceptable radiation characteristics while enabling on‐demand performance reconfiguration. However, existing reconfiguration mechanisms through stretchable conductors rely on high‐strain behavior in soft substrates, which limits their applicability. Herein, this work demonstrates the use of mechanical metamaterials for stretchable conductors and dielectrics in antennas. Metamaterials allow conductor stretching up to 30% with substrate base material tensile moduli ranging from 26 MPa to 44 GPa. It is shown, through several antenna designs, that mechanical metamaterials enable similar frequency reduction upon stretching as monolithic conductors, while simultaneously providing a miniaturization effect. The conductor patterning, furthermore, provides control over coupling between mechanical stretching and electromagnetic reconfiguration. This approach enables designing reconfigurable antenna functionality through metamaterial geometry in response to arising needs in applications ranging from body‐adapted electronics to space vehicles.

2 is observed compared to a standard helix due to the meandering of the surface current densities ( Figure S1E). The helix radiates in the axial mode with an increase in 3 dB beamwidth from 88 to 94 upon stretching ( Figure S1F). By comparison, the rotating square helix in Figure 2 maintains a constant 3 dB beamwidth of 75. As a result, control of / as a function of ε can be used for radiation pattern reconfiguration from axial to broadside radiation. [2] We find a peak realized gain for the helix of 6.4 dB when unstretched and 5.8 dB when stretched to = 100 mm. This is higher than the helix realized from the rotating square metamaterial, despite having a slightly lower number of turns ( = 3.0 compared to = 3.2 for the helix in Figure   2).
Despite the lower frequency change, this substrate is advantageous due to higher achievable strains and control over biaxial deformation.

S2. Characterization of auxetic behavior of the FRP substrate
The mechanical performance of the FRP metamaterial substrate and antennas is characterized using quasi-static geometrically non-linear finite element simulations in Abaqus/Standard. The deformation and reaction forces upon uniaxial stretching are shown in Figure S2 for the FRP substrate without the conductor as well as for the full antenna from

S3. Homogenized dielectric properties of metamaterial substrates
To derive homogenized dielectric properties for the TPU and FRP substrates as they are stretched, we use the concept of capacitances in series and parallel. This analysis neglects any gaps in the conductor and focuses on the dielectric layer of the patch antenna. This layer is a combination of the substrate material in parallel with the air gaps introduced during stretching.
In addition, the TPU substrate contains a small air gap between the ground plane and substrate (0.1 mm) due to the feed, while the FRP patches contain a 50 µm polyimide film onto which the conductor is coated. The simplified models are shown in Figure S3. We start with homogenization of the TPU dielectric ( Figure S3A). Any dependence on the patch side length, , is explicitly noted. The TPU and air gap layers are denoted by subscripts 1 and 2, respectively, and are treated as parallel capacitances,

S5. Experimental verification of simulated radiation patterns
Radiation patterns have been measured experimentally (Methods) for the FRP patch antennas to verify simulations ( Figure S5). Excellent agreement with simulations is observed with a slight increase in backlobe radiation seen in the measurements, which is expected due to constraints from the fabrication process and measurement limitations.

S6. Parameters affecting the frequency change metric of a patch antenna
The thickness and length of the hinges connecting metamaterial segments influence the impedance of the connections, which has an impact on the antenna's radiation characteristics.
The effect of these parameters on the operating frequency of the antenna upon stretching are shown in Figure S6. The study is performed for an FRP metamaterial patch with 0 = 67 mm, ℎ = 8 mm, = 5, = 0.25. It is seen that =20% ∝ ℎ / ℎ , similarly to the impedance of the hinge. [4] The changes seen are relatively small compared to the parametric study presented in Figure 6. Furthermore, the distribution of surface currents shows only a small dependence on hinge parameters. Therefore, this effect is not investigated further. To ensure that this does not affect the study in Figure 6, ℎ / ℎ is kept constant for all values of and .

S7. Repeatability of frequency reconfiguration under cyclic loading
We demonstrate the repeatability of the frequency reconfiguration for the FRP mechanical metamaterial antennas. Specifically, we study the frequency reconfiguration for the prototype with = 5, = 0.3 ( Figure 5A, gray line) under repeated mechanical loading (to = 15%) and unloading (to = 1.5%). Approximately 2 -3 mins elapse between each stretching and unstretching operation and we conduct 10 repeated cycles on the first day of testing followed by 5 additional cycles after 72 hours.  observed. This is more clearly illustrated in Figure S7B, which shows the resonance frequency in the two configurations as a function of the number of stretching cycles. The bars denote the operating bandwidth of the patch antenna in each configuration.
For a given antenna configuration, the resonant frequency fluctuates by less than 1% between the maximum and minimum measured values across all cycles. This is a small fraction of the bandwidth of the antenna for the corresponding configuration. We also observe that any fluctuations across cycles are random, with no consistent upward or downward trend.
Additionally, there is no loss of matching of the antenna in either configuration due to cycling.
The stretching history (i.e. acyclic order of reconfiguration) can impact the observed frequency adaptation of the antenna with fluctuations of the resonant frequency by up to ±2.5% compared to the average values in Figure S7B. While these fluctuations are larger than those for cyclical loading, they are within the bandwidth of the antenna for the given configuration and hence are deemed acceptable. The cause of these fluctuations is viscoelastic effects of the FRP composite material. [5] We minimize these effects by using short cycle times and prescribed displacement boundary conditions rather than prescribed loading. In addition, repetition of the tests after a long relaxation period of 72 hours does not yield any significant shift in the operating frequency.