Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials

Abstract

We describe in this work a composite metamaterial with a hierarchical topology made by tessellating perforations that exhibit an auxetic (negative Poisson's ratio) behaviour. We perform an analysis of the hierarchical structure by evaluating the fractal order of the topologies associated to the perforared composites.The periodic hierarchical lattice configuration shows negative Poisson's ratio characteristics at higher levels of hierarchy, even when the baseline configuration has a topology not exhibiting an auxetic behaviour. We investigate the wave propagation characteristics of these particular hierarchical lattices by using a Bloch Wave approach applied to detailed Finite Element geometries of the unit cell configurations. We show that the level of

Programmable Hierarchical Kirigami

“…[16][17][18][19] Interestingly, it has also been shown that the introduction of hierarchy into kirigami structures further enrich their functionality as it enables higher stretchability, [20,21] wider tunability of the bandgaps, [21][22][23] and larger negative Poisson's ratios. [16][17][18][19] Interestingly, it has also been shown that the introduction of hierarchy into kirigami structures further enrich their functionality as it enables higher stretchability, [20,21] wider tunability of the bandgaps, [21][22][23] and larger negative Poisson's ratios.…”

“…[16][17][18][19] Interestingly, it has also been shown that the introduction of hierarchy into kirigami structures further enrich their functionality as it enables higher stretchability, [20,21] wider tunability of the bandgaps, [21][22][23] and larger negative Poisson's ratios. [20][21][22][23][24][25] The out-of-plane buckling behavior of thin hierarchical kirigami sheets remains largely unexplored, and the only closely related study focuses on a system in which patterned notches are introduced in addition to cuts to guide the pop-up in a preferred direction. [20][21][22][23][24][25] The out-of-plane buckling behavior of thin hierarchical kirigami sheets remains largely unexplored, and the only closely related study focuses on a system in which patterned notches are introduced in addition to cuts to guide the pop-up in a preferred direction.…”

“…[20][21][22][23][24][25] The out-of-plane buckling behavior of thin hierarchical kirigami sheets remains largely unexplored, and the only closely related study focuses on a system in which patterned notches are introduced in addition to cuts to guide the pop-up in a preferred direction. We find that for sufficiently small thicknesses, the behavior is completely different from that previously reported for thick sheets, [20][21][22][23][24][25][26][27][28][29][30] as mechanical instabilities triggered by the applied deformation result in the formation of complex 3D patterns and sequential pop-up processes. We first use a combination of experiments and numerical simulations to study the response under uniaxial tension of kirigami sheets with hierarchical cuts arranged to form an array of squares connected at their vertices via thin ligaments and investigate in detail both the effect of geometry as well as plasticity of the sheets.…”

Design and experimental validation of a temperature-driven adaptive phononic crystal slab

“…Mechanical metamaterials have been recently hailed as a new class of structural concept able to bring novel multifunctionalities 4 by changes of compliance, shape, or by embedding oscillators or smart material inserts. Some examples (to name a few) are multiscale architecturally structured topologies, 5 zig-zag folded sheets, 6 pentamodal lattices, 7 systems with distributed resonators, 8,9 smart/magnetic materials, 10 tunable connectivity, 11 phononic stubbed plates, 12 flat lenses (super lenses), 13 3D tunable phononic crystals, 14 tunable metamaterial beam with shape memory alloy resonators, 15,16 auxetic periodic structure (with negative Poisson ratio) 17,18 and nonlinear auxetic dampers. 19 Further author information: (Send correspondence to Morvan Ouisse) E-mail: morvan.ouisse@femto-st.fr, Telephone: +33 3 81 66 60 00 A phononic crystal is a metamaterial with a periodic structure, that exhibits spatial periodicity.…”

Study on Band‐Gap Behaviors of 2D Hierarchical Re‐Entrant Lattice Structures

“…Wang et al have studied the bandgap structures of a periodic beam lattice activated via local resonance of the beam elements . Recent works have investigated the wave propagation behaviors in hierarchical structures, and found that both Bragg bandgaps and local resonance bandgaps exist in the hierarchical structures. However, few works have been performed to study the bandgaps of hierarchical auxetic structures …”