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Research Papers

Kirigami Auxetic Pyramidal Core: Mechanical Properties and Wave Propagation Analysis in Damped Lattice

[+] Author and Article Information
Fabrizio Scarpa

Advanced Composites Centre for Innovation and Science (ACCIS),
University of Bristol,
BS8 1TR Bristol, UK
e-mail: f.scarpa@bristol.ac.uk

Manuel Collet

e-mail: morvan.ouisse@univ-fcomte.fr
Institut FEMTO-ST,
Département Mécanique Appliquée,
UMR CNRS 6174,
Besançon 25000,France

Kazuya Saito

Institute of Industrial Science (IIS),
University of Tokyo,
Tokyo 153-8505, Japan
e-mail: saito-k@iis.u-tokyo.ac.jp

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 13, 2012; final manuscript received May 4, 2013; published online June 6, 2013. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 135(4), 041001 (Jun 06, 2013) (11 pages) Paper No: VIB-12-1100; doi: 10.1115/1.4024433 History: Received April 13, 2012; Revised May 04, 2013

The work describes the manufacturing, mechanical properties, and wave propagation characteristics of a pyramidal lattice made exhibiting an auxetic (negative Poisson's ratio) behavior. Contrary to similar lattice tessellations produced using metal cores, the pyramidal lattice described in this work is manufactured using a kirigami (origami plus cutting pattern) technique, which can be applied to a large variety of thermoset and thermoplastic composites. Due to the particular geometry created through this manufacturing technique, the kirigami pyramidal lattice shows an inversion between in-plane and out-of-plane mechanical properties compared to classical honeycomb configurations. Long wavelength approximations are used to calculate the slowness curves, showing unusual zero-curvature phononic properties in the transverse plane. A novel 2D wave propagation technique based on Bloch waves for damped structures is also applied to evaluate the dispersion behavior of composite (Kevlar/epoxy) lattices with intrinsic hysteretic loss. The 2D wave propagation analysis shows evanescence directivity at different frequency bandwidths and complex modal behavior due to unusual deformation mechanism of the lattice.

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Figures

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Fig. 1

Production of pyramidal lattice core using perforation/rolling/folding technique on metals (from Ref. [4])

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Fig. 2

Steps for the manufacturing for the kirigami auxetic pyramidal lattice core

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Fig. 3

(a) RVE of the pyramidal kirigami core with its nondimensional geometry parameters; (b) FE RVE with α = 1,β = 0.05,δ = 6,θ = 20 deg

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Fig. 4

Generic 3D periodic cells

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Fig. 5

Layout of the damped kirigami lattice unit cell considered for the 2D wave propagation study

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Fig. 6

Unrefined (a) and refined (b) mesh cases

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Fig. 7

Distribution of the Poisson's ratios (a) νxy and (b) νxz versus the angle θ for different δ parameters and α = 1

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Fig. 8

(a) Nondimensional in-plane and transverse Young's modulus versus the internal angle θ for different aspect ratios δ; (b) similar parametric curves for nondimensional in-plane shear and transverse modulus. For all calculations, α = 1.

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Fig. 10

Slowness curves in the xy plane for α = 1.0,θ = 20 deg

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Fig. 9

Slowness curve in the xz plane for α = 1,θ = 20 deg

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Fig. 11

Dispersion curves of all modes of the studied system (imaginary part of λn(ω) or real part of kn(ω))

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Fig. 12

Dispersion curves of propagative modes of the studied system (imaginary part of λn(ω) or real part of kn(ω))

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Fig. 13

Dispersion curves of propagative modes of the studied system (imaginary part of λn(ω) or real part of kn(ω))

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Fig. 14

Propagative wave numbers of damped system (Im(λn(ω)) for different angles

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Fig. 15

Directivity using the evanescence index in Eq. (23) saturated at unit value for (a) undamped and (b) damped lattice

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