Nonlinear compressive deformations of buckled 3D ribbon mesostructures

Abstract

Three-dimensional (3D) mesostructures with complex ribbon geometries have widespread applications in a diversified range of areas. The mechanically-guided 3D assembly approach based on precisely controlled buckling provides a versatile route to complex 3D ribbon-shaped mesostructures in a broad set of high-performance materials, thereby allowing the development of 3D flexible electronic devices with new functionalities. In many scenarios of practical operations, especially the biointegrated applications, the 3D flexible electronics would inevitably experience the out-of-plane compression, due to loadings of surrounding bones/organs or clothes, which could affect device functions significantly. A clear understanding of the deformation mode of 3D ribbon-shaped mesostructures is thereby essential to the design of 3D flexible electronics. This paper presents a systematic investigation of nonlinear compressive deformations and mode transitions of bridge-shaped and helical mesostructures assembled through controlled lateral buckling. Based on the elastica theory, a finite-deformation model is developed for the bridge-shaped mesostructure compressed by a frictional wall. Validated by results of experiments and finite element analyses (FEA), this theoretical model enables the establishment of the phase diagram of all possible deformation modes, indicating the crucial roles of friction coefficient and in-plane compressive strain on the mode transition. Experimental and computational studies further show that five distinct deformation modes could possibly occur during the compression of helical mesostructures. The mode transitions in the compressed helical mesostructures are found to arise mainly from the downward collapse, either at the middle or the side region of the mesostructure. These results can serve as design guidelines for the development of 3D flexible electronic devices, especially those for biointegrated applications.