Lattice Metamaterials with Mechanically Tunable Poisson’s Ratio for Vibration Control

Metamaterials with artificially designed architectures are increasingly considered as new paradigmatic material systems with unusual physical properties. Here, we report a class of architected lattice metamaterials with mechanically tunable negative Poisson’s ratios and vibration-mitigation capability. The proposed lattice metamaterials are built by replacing regular straight beams with sinusoidally shaped ones, which are highly stretchable under uniaxial tension. Our experimental and numerical results indicate that the proposed lattices exhibit extreme Poisson’s-ratio variations between $-0.7$ and 0.5 over large tensile deformations up to 50%. This large variation of Poisson’s-ratio values is attributed to the deformation pattern switching from bending to stretching within the sinusoidally shaped beams. The interplay between the multiscale (ligament and cell) architecture and wave propagation also enables remarkable broadband vibration-mitigation capability of the lattice metamaterials, which can be dynamically tuned by an external mechanical stimulus. The material design strategy provides insights into the development of classes of architected metamaterials with potential applications including energy absorption, tunable acoustics, vibration control, responsive devices, soft robotics, and stretchable electronics.

Figure 1

Schematics and deformation behavior of the sinusoidally architected lattice material. (a) Regular square lattice with $2\times 2$ unit cells. Here, $t$ and $l$ are the width and length of regular beams. (b) Buckling modes of a single beam under compression. (c) Proposed architected lattice metamaterials with $2\times 2$ unit cells with $n=1$. (d) Deformation behavior of the center area consisting of $2\times 2$ unit cells of the architected lattice material under uniaxial tension.

Figure 2

(a) Stress-strain relations of the architected lattice metamaterials. (b) Evolution of the Poisson’s ratios as a function of the applied tensile strain. (c) Deformed configuration at different macroscopic strains. The von Mises stresses are normalized with respect to the Young’s modulus of the constitutive materials. Here, $A_{n}n/l=1/3$.

Figure 3

Effect of (a) amplitude $A_{n}n/l$ and (b) number of half wavelength $n$ on the stress-strain relation and Poisson’ ratio. Here, $w/l=1/20$ for all of the simulations.

Figure 4

Effect of amplitude $A_{n}n/l$ and the number of half wavelength $n$ on the (a) effective stiffness and (b) Poisson’ ratio of the proposed lattice metamaterials.

Figure 5

Effect of $w/l$ on (a) the stress-strain relation and (b) Poisson’s ratios of the lattice metamaterials. Here, $A_{n}n/l=1/3$.

Figure 6

Effect of the topology on the stress-strain curves and Poisson’s ratio. (a) 3D printed specimens with hexagonal, kagome, square, and triangular topology. (b) Stress-strain relations and (c) evolution of Poisson’s ratio as a function of the strain. The legend is the same as that in (b). Here, $A_{n}n/l=1/3$, $n=2$, and $w/l=1/20$. Scale bar: 1 cm.

Figure 7

Phononic dispersion relations and transmission spectra of the architected lattice metamaterials. (a) $A=0$, $n=0$; (b) $A_{n}n/l=1/3$, $n=1$; (c) $A_{n}n/l=1/3$, $n=3$; (d) $A_{n}n/l=1/3$, $n=5$. Here, $w/l=1/20$ for all of the simulations.

Figure 8

Mechanically tunable band gaps for the architected lattice metamaterials. Phononic dispersion relations as a function of stretching strain for (a) $n=4$ and (b) $n=6$. (c) Evolution of band gaps as a function of strain for $n=2$, $n=4$, and $n=6$. Here, $A_{n}n/l=1/3$ and $w/l=1/20$ for all simulations. The insets show the deformation of the unit cell at each stretching strain.