Kirigami Film Reflector for Deployable Space Antennas

TL;DR

The paper tackles the challenge of creating large, lightweight space-based reflector antennas by introducing a perforated aluminized polyimide kirigami film whose unit-cell geometry combines rotating-squares cuts with diagonal perforations to achieve tunable Poisson's ratio and low pretension. Through finite-element parametric studies, the authors map how geometry and thickness affect pretension and 10 GHz reflectance, revealing a Poisson's ratio range from $-1$ to near $0$ controlled by $s_{\text{diag}}/s_{\text{axial}}$ and identifying a Pareto frontier of designs that balance stiffness and reflectivity. Experimental tensile tests validate low pretension values (often well below $1$ N/m at modest strains) and demonstrate direction-dependent post-buckling behavior consistent with simulations. Free-space RF measurements show that carefully designed geometries maintain power reflectance above $90\%$ at $10~\mathrm{GHz}$ under deployment-like strains, suggesting the kirigami film as a viable path toward lighter, scalable space reflector surfaces with reduced truss mass. These findings point to significant practical impact for future large-aperture, deployable antennas and motivate further optimization across bands and materials.

Abstract

We propose a low-pretension reflective kirigami film as a material for the reflective surfaces of large deployable space reflector antennas with an operating frequency around 10 GHz. The kirigami cut pattern is based on the well-known rotating squares pattern but is augmented with diagonal cuts to enhance stretchability and allow control over the effective Poisson's ratio. Using finite element simulations, we analyzed how the geometric parameters of this pattern affected the reflectance of the film and the pretension required to resist thermal deformations. Tensile testing of selected designs, which are approximately half the weight of traditional metallic meshes, demonstrated a substantial reduction in the needed pretension to ~0.5 N/m and as low as ~0.1 N/m. Such low pretension represents an order-of-magnitude improvement over traditional metallic mesh reflectors and could enable the use of lighter antenna trusses. Free-space reflectance measurements also show that these perforated films can maintain power reflectance exceeding 90% at 10 GHz under the strains expected in the deployed configuration.

Figures (9)

• Figure 1: (a) A schematic diagram of the unit cell geometry; (b)--(d) photographs of the close-up view of the perforated 7.8 µ m thick aluminized polyimide film with $l_{\text{axial}} =$ 4 mm and $s_{\text{axial}} = s_{\text{diag}} = s =$ 0.2 mm (b) in the undeformed state, (c) under $\sim$15% uniaxial strain forming buckled and sheared squares, and (d) $\sim$45% uniaxial strain forming larger voids.
• Figure 2: Summary of parametric studies conducted in COMSOL: (a) effect of $s_{\text{diag}}/s_{\text{axial}}$ on the effective Poisson's ratio with a fixed $w_{\text{cut}} =$ 0.1 mm, $s_{\text{axial}} =$ 0.2 mm, and $t_{\text{PI}} =$ 25.4 µ m; (b) geometric design space segmented by reflectance and pretension requirements highlighting the Pareto frontier and the region with promising geometries; (c)--(f) color-coded effect of (c) $l_{\text{axial}}$, (d) $s_{\text{axial}}$, (e) $s_{\text{diag}}$, and (f) $t_{\text{PI}}$ on the pretension at 1% strain and reflectance at 10 GHz.
• Figure 3: (a)--(b) Fragments of the simulated deformations of the periodic strip with $l_{\text{axial}} =$ 3 mm and $s =$ 0.2 mm at different strains under (a) $\theta =$ 0° (blue) and (b) $\theta =$ 45° (red) stretching, where $\theta$ is the angle between the axial cuts and the stretching direction; (c)--(f) results of tensile tests and simulations for selected geometries stretched at $\theta =$ 0° (blue), $\theta =$ 45° (red), and $\theta =$ 18.4° (black) with: (c) $l_{\text{axial}} =$ 3 mm, $s =$ 0.2 mm, $w_{\text{cut}} =$ 0.1 mm, (d) $l_{\text{axial}} =$ 4 mm, $s =$ 0.2 mm, $w_{\text{cut}} =$ 0.1 mm, (e) $l_{\text{axial}} =$ 3 mm, $s =$ 0.08 mm, $w_{\text{cut}} =$ 0.04 mm, and (f) $l_{\text{axial}} =$ 3.5 mm, $s =$ 0.08 mm, $w_{\text{cut}} =$ 0.04 mm with insets enlarging the required pretension at 1% strain.
• Figure 4: The photographs of (a) RF reflectance measurement setup and (b) one of the 25 cm $\times$ 25 cm tested samples with $l_{\text{axial}} =$ 4 mm and $s =$ 0.2 mm (4.5 mm unit cell period) under around 4% uniaxial strain mounted on a supporting frame.
• Figure 5: Example of the raw (unsmoothed) normalized power reflectance over 2--12 GHz range for tested perforated films with $l_{\text{axial}} =$ 3 mm, $s =$ 0.2 mm (red), $l_{\text{axial}} =$ 4 mm, $s =$ 0.2 mm (blue), and $l_{\text{axial}} =$ 9.3 mm, $s=$ 0.3 mm (black) under a 30° incidence angle containing similar periodic ripples with the broadest spacings of around (a) 1.5 GHz for s-polarization and (b) 2 GHz for p-polarization. Here, the reflectance of the 25 cm $\times$ 25 cm samples with 3 mm and 4 mm cuts was normalized with respect to the reflectance of the aluminum plate and the reflectance of the 20.5 cm $\times$ 24 cm sample with 9.3 mm cuts was normalized with respect to the reflectance of the unperforated film of the same size.