Reconfigurable kirigami mesostructure enables modulation of lift and drag

Abstract

Flexible surfaces can modulate fluid forces through deformation, enabling passive adaptation to flow conditions that improves aerodynamic performance, reduces drag and delays stall. Here we show that kirigami sheets, planar surfaces patterned with arrays of parallel slits, provide a simple route to tunable aerodynamics by transforming into three-dimensional porous meso-architectures that can be reversibly reconfigured in flow. When stretched and exposed to cross-flow, parallel-cut kirigami buckle out of plane to form a lattice of inclined plate-like elements. Experiments reveal that this architecture generates not only drag but also a substantial transverse lift force, even when the sheet is held perpendicular to the incoming flow. Because the mesostructure can switch between distinct states, a single sheet produces large and selective variations in drag and lift under identical flow conditions, in some cases partially decoupling these forces. The evolving mesostructure also alters the scaling of forces with flow speed, influencing both instantaneous loads and their velocity dependence. Force measurements collapse when expressed in terms of the Cauchy number, identifying stiffness, set by the cutting pattern, as the dominant control parameter, a relationship captured by a continuum elastic model. These results show how kirigami architectures encode aerodynamic functionality and behavior directly through their structure, providing a scalable platform for surfaces with reprogrammable fluid forces.

Figures (5)

• Figure 1: Kirigami surface for tunable lift and drag generation. (a) Stacked images of kirigami deformation in a water flow at increasing speeds $U \in [7-32]\, \text{cm}$, with blades color-coded by velocity. Main: clockwise blade rotation; inset: counterclockwise for the same specimen. (b) Drag $F_d$ and (c) lift $F_l$ as a function of flow velocity $U$. Right- and left-pointing triangles denote blade rotation direction. For the left-leaning case, data are averaged over 9 experiments, with shaded areas denoting the standard deviation. (d) As $U$ increases to 7.6 m/s (inset), a kirigami on a low-friction rail produces enough lift to move laterally in an airflow, with the dotted line in the inset indicating the onset of motion. (e) Active modulation of drag and lift in a water flow at fixed $U=23.5$ cm/s by manually switching blade direction: all clockwise (red), all counterclockwise (yellow) or opposite directions on each half (blue). Gray zones mark manual handling; data are averaged over a $4\mu$s sliding window.
• Figure 2: Pattern-induced stiffness as a control parameter for aerodynamic performance. (a) Drag as a function of flow velocity for kirigami specimens with different slit-row spacing $d_x$, yielding different effective stiffness $K$. (b) Dimensionless drag $F_d/KL$ as a function of the Cauchy number $C_y$ (Eq.\ref{['Eq:Cy']}), showing collapse and reduced velocity scaling compared to the quadratic law for rigid bodies. (c) Dimensionless lift $F_l/KL$ as a function of $C_y$; triangles indicate the blade rotation direction, producing opposite lift. In (b) and (c), experimental results are compared with theoretical predictions (black lines).
• Figure 3: Pattern independence at matched stiffness. (a) Stiffness from tensile tests for two iso-$K$ kirigami series (circle and square markers) with varying blade width $d_x$ (gray scale). (b) Similar drag evolution with flow speed within each series. (c) Profiles of two specimens with different blade widths, $d_x=1.7$ mm (gray) and $d_x=3$ mm (black), from the softer iso-$K$ series at velocities $U=2.3, 8.5, 14.9$ and $29.9$ cm/s. Inset: local elongation $\varepsilon$ along the curvilinear coordinate $S$ (defined in the unstrained flat configuration).(d) Membrane model with distributed normal and tangential fluid loading $\mathbf{f_{N}}$ and $\mathbf{f_{T}}$, which depend only on the flow velocity $U$ and on the local membrane state (elongation $\varepsilon$ and inclination $\alpha$). The forces $\mathbf{f_{N,T}}$ are set by the mesotructure (porosity and blade inclination $\theta$), determined solely by $\varepsilon$ and not by the cutting parameters, as illustrated schematically.
• Figure 4: Blade rotation as a mechanism for drag modulation. (a) Dimensionless drag versus Cauchy number for three kirigami specimens of different stiffness (color-coded). Mid-sheet blade rotation reversal produces two configurations, ‘+–’ and ‘–+’ (schematized in panel b; with ‘+’: clockwise, ‘–’: anticlockwise) indicated by upward and downward triangles, yielding distinct drag trends with velocity.(b) Symmetric profiles for the $K = 0.7$ N/m specimen under both rotation configurations.
• Figure 5: Tuning of lift and drag via blade rotation. (a) Profiles for different positions of rotation reversal along the kirigami sheet, characterized by parameter $a$, for '+ -' (dotted lines) and '- +' (solid lines) configurations. (b) Lift versus drag coefficient for $a \in [0, 0.5]$ in both rotation configurations (upward and downward triangles), at $U=19.2$ cm/s. Values for the untested range $a\in]0.5, 1[$ are mirrored across the horizontal line (hollow triangles).