Buckling of circular rings and its applications in thin-film electronics

Buckling-guided transformations of thin-film materials into three-dimensional (3D) architectures are extensively utilized in electronic microsystems. However, the mechanically-guided assembly technique exploits a prestretched substrate, such that low-stiffness precursors would fail to realize global buckling due to the difficulty in overcoming interfacial adhesion (i.e., Van der Waals forces). Here, based on finite element analysis (FEA), a novel buckling-guided 3D assembly method by electromagnetic actuation is introduced through investigating the buckling behavior of a laminated thin circular ring. In this method, interfacial adhesion could be notably reduced by replacing soft substrates with rough platforms, thereby allowing formation of 3D structures with ultralow stiffnesses. Scaling laws for the critical current of buckling and the effect of joule heating are developed to guide controlled deformations and ensure rational designs. Numerical demonstration of a morphable, reconfigurable four-petal rose suggests the applicability and advantages of the proposed Lorentz force-guided 3D assembly method. In addition, we show that simultaneous measurement of the elastic moduli and thickness of planar materials could be possible based on the established scaling law for critical buckling current. The results presented here serve as design guidelines for applying electromagnetically-actuated buckling behavior of thin-film materials in future applications such as soft grippers and biomedicine.