Inverse design strategies for buckling-guided assembly of 3D surfaces based on topology optimization

Complex three-dimensional (3D) mesostructures in advanced functional materials are attracting increasing interest, due to their widespread applications. Mechanically-guided 3D assembly through compressive buckling provides deterministic routes to a rich diversity of 3D mesostructures and microelectronic devices, with feature sizes ranging from sub-microscale to millimeter-scale. Existing studies established inverse design methods that map the target 3D geometry onto an unknown 2D precursor, but mainly focusing on filamentary ribbon-type geometries. Although strategies relying on spatial thickness variation of 2D precursors have been reported to achieve inverse design of 3D surfaces, this could lead to a lack of compatibility with well-developed planar fabrication technologies. In the framework of buckling-guided 3D assembly, this paper presents a computational method based on topology optimization to solve the inverse design problem of 3D surfaces from 2D precursors with uniform thickness distributions. Specifically, curvy ribbon components were exploited to discretize nondevelopable target surfaces, and then optimized to ensure that the assembled 3D surface has the best match with the target geometry. Combined computational and experimental studies over a dozen of elaborate examples, encompassing both the caged and even general target surfaces, demonstrate the effectiveness and applicability of the proposed method.