Phononic band gap design in honeycomb lattice with combinations of auxetic and conventional core

Abstract

We present a novel design of a honeycomb lattice geometry that uses a seamless combination of conventional and auxetic cores, i.e. elements showing positive and negative Poisson's ratio. The design is aimed at tuning and improving the band structure of periodic cellular structures. The proposed cellular configurations show a significantly wide band gap at much lower frequencies compared to their pure counterparts, while still retaining their major dynamic features. Different topologies involving both auxetic inclusions in a conventional lattice and conversely hexagonal cellular inclusions in auxetic butterfly lattices are presented. For all these cases the impact of the varying degree of auxeticity on the band structure is evaluated. The proposed cellular designs may offer significant advantages in tuning high-frequency bandgap behaviour, which is relevant to phononics applications. The configurations shown in this paper may be made iso-volumetric and iso-weight to a given regular hexagonal topology, making possible to adapt the hybrid lattices to existing sandwich structures with fixed dimensions and weights. This work also features a comparative study of the wave speeds corresponding to different configurations vis-a vis those of a regular honeycomb to highlight the superior behavior of the combined hybrid lattice.

3D auxetic single material periodic structure with ultra-wide tunable bandgap

“…Several tunable PnCs, 28 , 29 which take advantage of different materials or properties combined together, are available. Auxetic materials, for example, are used in PnCs in combination with conventional cores 30 , with local resonators 31 or with distributed shunted piezoelectric patches 32 to enhance the effective Young’s modulus and to lower the frequencies limiting the bandgap 33 , 34 . Although single-phase, 3D tunable PnC structures are of great interest for the full control of 3D wave propagation and manufacturing purposes, few are the examples in the literature: tunable 3D PnCs are numerically studied 35 – 39 while experimental evidence is reported only for the 2D case 40 , 41 .…”

An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

“…In isotropic solids, the bounds for Poisson's ratio are defined as . These bounds imply the possibility of Poisson's ratio being negative; such solids expand in the lateral direction when stretched axially, and have been termed “auxetics.” Pioneering works on auxetics were spearheaded by Lakes, Wojciechowski, and Evans et al Of late auxetics research includes, but not limited to, auxetics in ligament structures, Cosserat elasticity of auxetic foams, wave properties in re‐entrant lattices, phononic band gap design, impact testing of auxetic foams for sports safety, chiral 3D lattices, 3D auxetic structure from intersecting double arrowheads, auxetic response of needle‐punched nonwoven, extrusion of auxetic PP fiber, auxetic properties in cubic materials and porous graphenes, auxetic behavior from nanochannels in degenerate crystals of hard dimers, auxetic composites from 3D textile structure and PU foam, reinforced‐core auxetic assemblies and auxetic gradient composite hexagonal honeycombs, to name a few. For a comprehensive survey on auxetic materials and structures, the reader is referred to a recent review and monograph …”

Design and Additive Manufacturing of 3D Phononic Band Gap Structures Based on Gradient Based Optimization

“…A wide range of different approaches on how to design band gap structures has been realized in the past. Most of these are 2D structures, e.g., planar grid structures with tunable non-structural masses [ 9 , 10 ], tetragonal and hexagonal chiral lattices [ 11 , 12 ], auxetic inverted honeycombs [ 13 ], or modified honeycomb lattices [ 14 ]. In three dimensions, cubic lattices with spherical holes [ 15 , 16 ], sinusoidal beams [ 17 ], octahedrons using inertial amplification mechanisms [ 18 ], and cubic lattices found by eigenmode analysis of regular lattices [ 19 ] are some examples for the geometry of PBG materials.…”