Optimization-Based Approach for the Inverse Design of Ribbon-Shaped Three-Dimensional Structures Assembled Through Compressive Buckling

Mechanically driven assembly of three-dimensional (3D) mesostructures by compressive buckling represents an area of increasing attention, owing to the excellent compatibility with planar fabrication technologies and the broad applicability to a variety of material types (from semiconductors to metals and dielectrics) and length scales (from nanometers to centimeters). As a representative class of 3D geometries, the assembly of filamentary 3D ribbon configurations has been studied extensively, either to analyze the deformation features or to explore the applications in various functional devices. Previous studies mainly focused on the modeling of the "forward problem" that enables the prediction of the assembled 3D ribbon configuration for a prescribed 2D precursor. Development of an efficient method to solve the "inverse problem" that maps the target 3D geometry onto an unknown 2D precursor design remains a challenge. In the framework of adaptive-genetic-algorithm optimization, this paper proposes a systematic computational method to solve the inverse design problem of ribbon-shaped 3D structures assembled through compressive buckling. Based on a theoretical analysis on the inherent geometric relationship between the deformed and the initial ribbon configurations, we establish an optimization-based formulation of the inverse design problem to determine the initial geometries of 2D precursors, with the aid of finite-element analyses. Both the convergence and accuracy of the developed method are verified through a set of illustrative examples. Computational and experimental studies over approximately 20 ribbon structures, each with comparison between the target and assembled configurations, show the broad applicability of the inverse design method. Demonstrated capabilities to form 3D structures that resemble the sketches of real objects (e.g., peaked hat, butterfly, and frog) suggest promising utilities in the accurate design of functional devices.