We develop a computational pipeline to facilitate the biomimetic design of winged seeds. Our approach leverages 3D scans of natural winged seeds to construct a bio-inspired design space by interpolating them with geodesic coordinates in the 3D diffeomorphism group. We formulate aerodynamic design tasks with probabilistic performance objectives and adapt a gradient-free optimizer to explore the design space and minimize the expectation of performance objectives efficiently and effectively. Our pipeline discovers novel winged seed designs that outperform natural counterparts in aerodynamic tasks, including long-distance dispersal and guided flight. We validate the physical fidelity of our pipeline by showcasing paper models of selected winged seeds in the design space and reporting their similar aerodynamic behaviors in simulation and reality.

We present a computational framework for simulating deformable surfaces from planar rest shape with second-order triangular finite elements. Our method develops numerical schemes for discretizing stretching, shearing, and bending energies of deformable surfaces in a second-order finite-element setting. In particular, we introduce a novel discretization scheme for approximating mean curvatures on a curved triangle mesh. Our framework also integrates a virtual-node finite-element scheme that supports two-way coupling between cut-cell rods without expensive remeshing. We compare our approach with traditional simulation methods using linear and higher-order finite elements and demonstrate its advantages in several challenging settings, such as low-resolution meshes, anisotropic triangulation, and stiff materials. Finally, we showcase several applications of our framework, including cloth simulation, mixed Origami and Kirigami, and biologically-inspired soft wing simulation.