Numerical investigation of metafluid behavior in pre-strained negative stiffness honeycombs

Abstract

Negative stiffness honeycombs (NSH) are doubly periodic arrays of curved beams that have recently been shown to exhibit a reversible pseudo-plastic large deformation response and are therefore interesting candidates for impact isolation applications. The authors previously used finite element analysis to show that NSH exhibit three types of propagating modes described by (i) longitudinal, (ii) transverse, and (iii) rotational displacements with respect to the propagation direction. The phase and group velocities of each mode can be significantly altered by applying a uniaxial pre-strain imposed on the top and bottom boundaries of the NSH. The present work will show that the transverse and rotational mode phase speeds are significantly more sensitive to strain than the longitudinal modes for small but finite pre-strain levels. Consequently, for some pre-strain levels there exists a large frequency band where only longitudinal waves propagate. The pre-strained NSH therefore behaves as a pentamode metamaterial, or metafluid, and may represent a new type of structure to realize devices designed using transformation acoustics. The effect of the geometry and pre-strain on the existence and frequency range of unimodal propagation in pre-strained NSH will be investigated. [Work supported by NSF.]