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.

We propose a novel solid-fluid coupling method to capture the subtle hydrophobic and hydrophilic interactions between liquid, solid, and air at their multi-phase junctions. The key component of our approach is a Lagrangian model that tackles the coupling, evolution, and equilibrium of dynamic contact lines evolving on the interface between surface-tension fluid and deformable objects. This contact-line model captures an ensemble of small-scale geometric and physical processes, including dynamic waterfront tracking, local momentum transfer and force balance, and interfacial tension calculation. On top of this contact-line model, we further developed a mesh-based level set method to evolve the three-phase T-junction on a deformable solid surface. Our dynamic contact-line model, in conjunction with its monolithic coupling system, unifies the simulation of various hydrophobic and hydrophilic solid-fluid-interaction phenomena and enables a broad range of challenging small-scale elastocapillary phenomena that were previously difficult or impractical to solve, such as the elastocapillary origami and self-assembly, dynamic contact angles of drops, capillary adhesion, as well as wetting and splashing on vibrating surfaces.