A systematic group of multidirectional buckling-based negative stiffness metamaterials

Abstract

Negative stiffness (NS) metamaterials are kinds of artificial mechanical materials that exhibit the negative stiffness effect governed by different mechanical mechanisms, among which the buckling-based negative stiffness (BNS) metamaterial consisting of prefabricated curved beams and rigid frames have attracted considerable concern. However, the variety of the reported geometrical configurations of BNS metamaterials is relatively limited, and the study of systematically developing multidirectional buckling-based negative stiffness (MDBNS) metamaterials has rarely been seen at present, especially their mechanical performance. Therefore, the novelty of this study is to design a systematic group of MDBNS metamaterials comprising flexible cosine curved beams and stiffened supporting frames based on Bravais lattices. The group contains 15 element members and has been classified into 5 categories including the 2D bi-directional, 2D tri-directional, 3D tri-directional, 3D quadri-directional, and 3D six-directional NS functional elements. The geometrical configurations of the proposed MDBNS functional elements are respectively constructed based on the systematic arrangement rule of the Bravais lattices that provides the design guidance for the systematic metamaterial group with a fixed number of group members. The mechanical performance of some typical functional elements with the most NS directions and the metamaterial lattices composed of the proposed MDBNS metamaterials have been verified via the Finite Element Analysis (FEA) with the periodic boundary condition (PBC), respectively, while the numerical study has been validated experimentally with 2D MDBNS functional elements via 3D additive manufacturing. The results strongly prove the mechanical NS effects of the proposed MDBNS metamaterials and also indicate that the mechanical behavior is independent if the NS directions are orthogonal, whereas it interacts with each other in the case of non-orthogonal NS directions. The study can also be adopted to develop multidirectional NS metamaterials with other NS functional components and induced mechanisms.