Negative stiffness honeycombs as tunable elastic metamaterials

Abstract

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Shear Stiffness and Energy Absorption of Auxetic Open Cell Foams as Sandwich Cores

“…Another aspect that this work has highlighted is the quasi‐zero stiffness shown by the auxetic sandwich beams under large bending deformations. Negative stiffness has been considered both for controllable large deformations at reduced actuation force, and large damping/energy dissipation, even with auxetic characteristic . Zero stiffness is, however, another type of anomalous mechanical system with interesting characteristics.…”

Mechanical Performance of Multidirectional Buckling-Based Negative Stiffness Metamaterials: An Analytical and Numerical Study

“…These metamaterials have all shown excellent mechanical properties, such as rate-independent mechanism, recoverability from large elastic deformation, tremendous freedom of performance-oriented design and extraordinary energy-absorption capacity, especially for dynamic loads. Works done by Goldsberry et al [ 37 ] and Nadkarni et al [ 38 ] have also shown rich dynamic response with distinct regimes of wave propagation and the ability to modify wave propagation in the metamaterial with an external stimulus.…”

Tunable elastic metamaterials using rotatable coupled dual-beam resonators

“…In addition to the active metamaterials with smart materials, tunable metamaterials can also be realized by passive means. [13][14][15][16][17][18] For example, by imposing mechanical deformation, a given bandgap can be adaptively tuned or switched on and off with buckling elastic beams. 14 With large deformations of curved beams subjected to prestrain in a honeycomb structure, tunable dispersion properties of elastic metamaterials can be achieved.…”

“…14 With large deformations of curved beams subjected to prestrain in a honeycomb structure, tunable dispersion properties of elastic metamaterials can be achieved. 17 By varying the applied temperature to change the temperaturedependent moduli of the constituent materials, metamaterialbased bandgaps can be made tunable. 18 For the buckling-based or deformation-based tunable metamaterials, substantially flexible materials/structures have to be implemented in design and fabrication.…”