Guided Formation of 3D Helical Mesostructures by Mechanical Buckling: Analytical Modeling and Experimental Validation. (24th February 2016) - Liu, Yuan; Yan, Zheng; Lin, Qing; Guo, Xuelin; Han, Mengdi; Nan, Kewang; Hwang, Keh‐Chih; Huang, Yonggang; Zhang, Yihui; Rogers, John A.
Abstract : 3D helical mesostructures are attractive for applications in a broad range of microsystem technologies due to their mechanical and electromagnetic properties as stretchable interconnects, radio frequency antennas, and others. Controlled compressive buckling of 2D serpentine‐shaped ribbons provides a strategy to formation of such structures in wide ranging classes of materials (from soft polymers to brittle inorganic semiconductors) and length scales (from nanometer to centimeter), with an ability for automated, parallel assembly over large areas. The underlying relations between the helical configurations and fabrication parameters require a relevant theory as the basis of design for practical applications. Here, an analytic model of compressive buckling in serpentine microstructures is presented based on the minimization of total strain energy that results from various forms of spatially dependent deformations. Experiments at micro‐ and millimeter scales, together with finite element analyses, have been exploited to examine the validity of developed model. The theoretical analyses shed light on general scaling laws in terms of three groups of fabrication parameters (related to loading, material, and 2D geometry), including a negligible effect of material parameters and a square root dependence of primary displacements on the compressive strain. Furthermore, analytic solutions were obtained for the key physical quantities (e.g., displacement, curvature and maximum strain). A demonstrative example illustrates how to leverage the analytic solutions in choosing the various design parameters, such that brittle fracture or plastic yield can be avoided in the assembly process. Abstract : Analytic models, finite element analyses, and experiments are presented to capture all quantitative aspects of buckling‐guided formation of 3D helical mesostructures. The resulting scaling laws include negligible roles of cross‐sectional and material parameters on the 3D configurations, enabling predictions of physical quantities with analytic solutions. These findings can serve as design references for assembly of structures optimized for device applications.