Enhanced hexa-missing rib auxetics for achieving targeted constant NPR and in-plane isotropy at finite deformation

Abstract

The standard hexa-missing rib structure (i.e. missing rib structure with six zigzag ligaments) exhibits in-plane isotropy at small deformation, and has a relatively constant negative Poisson’s ratio (NPR) over a finite deformation range. However, its auxeticity is relatively low, and the in-plane isotropy effect degrades rapidly with deformation. The present work aims to improve these two mechanical properties over a large deformation range, without significantly compromising the deformation range with constant NPR as well as the overall stiffness. First, the deformation mechanisms underlying a standard hexa-missing rib structure is elaborated. To enhance the auxeticity effect and to delay the loss of in-plane isotropy, an enhanced design with honeycomb reinforcement between the ligaments is proposed. By changing the size of the honeycomb reinforcement, the enhanced design is able to achieve tunable constant NPR ranging from −0.2 to −1.0 over a large deformation range, and yet maintaining its in-plane isotropy. Moreover, these enhanced properties are achieved without compromising the overall stiffness of the structure. Depending on the nature of engineering applications, the deformation range with a constant NPR can be further extended if desired, by having wavy connecting ligaments in the enhanced design. For the latter design, the structure is more compliant than the base design. It is shown that the target enhanced properties can be achieved over a large deformation range using linear elastic or nonlinear base materials.