Extensible beam-like metastructures at the microscale: Theoretical and modified Hencky bar-chain modeling

Architected metastructures with beam-like shape configurations have demonstrated promising mechanical performance due to their corrugation-induced geometric nonlinearity. Extensibility of the metabeams caused by corrugation plays a role in the geometric nonlinearity, which, however, has been omitted in the literature. Motivated by investigating the influence of stretching (or shrinking) on the mechanical characteristics, this study analytically and numerically investigates the metabeams designed with different corrugation patterns. A new discretized model is developed to considers the extensibility of the metastructures by modifying the Hencky bar-chain method (HBM). A size-dependent (i.e., length scale factor 1) analytical model is developed using the modified couple-stress theory and closed-form results are obtained. Good agreements are observed between the HBM and theoretical results. Parametric studies are conducted to investigate the influence of extensibility and length scale factor on the mechanical behavior the metabeams with the rhombille, cylindrical, hexagonal and basketweave corrugations. Optimal pattern ratio (i.e., pattern diameter-to-pattern gap ratio D-pat/W-pat) and geometric ratio (i.e., width-to-thickness ratio W/t) are obtained by minimizing the self-weight of the patterned plates. The reported HBM accurately predict the mechanical behavior of extensible metabeams, which can be used to design plate-shaped advanced structures for applications requiring rigidity and well deformation recovery.