Elastic wave dispersion in pre-strained negative stiffness honeycombs

A doubly periodic array of curved beams, known as a negative stiffness (NS) honeycomb, has recently been shown to exhibit tunable impact isolation by exploiting nonlinear mechanical behavior [Correa et al., Rapid Prototyping J., 21 (2), 2015]. The primary benefit of NS honeycombs over standard honeycomb materials lies in their ability to return to their original shape after experiencing an impact. The recoverable nature of their response is a result of the curved beam structure which has a single stable configuration but experiences one or more buckling events when loaded. The complex nonlinear elastic response of NS honeycombs lead to large variations in mechanical stiffness, which makes these materials compelling candidates for tunable control of elastic waves. The present work investigates linear elastic wave propagation of a representative NS honeycomb lattice at varying levels of pre-strain. Eigenfrequency finite element analysis is performed on the unit cell subjected to finite uniaxial deformation. The longitudinal and transverse phase speeds are shown to be anisotropic and highly dependent on uniaxial pre-strain. This is especially true near points of instability, where one observes very different functional dependence of longitudinal and transverse wave motion on pre-strain.