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Research Papers

Elastic Wave Propagation in Open-Cell Foams

[+] Author and Article Information
Alireza Bayat

Department of Civil Engineering,
Johns Hopkins University,
3400 N Charles Street, Latrobe Hall 205,
Baltimore, MD 21218
e-mail: abayat1@jhu.edu

Stavros Gaitanaros

Department of Civil Engineering,
Johns Hopkins University,
3400 N Charles Street, Latrobe Hall 201,
Baltimore, MD 21218
e-mail: stavrosg@jhu.edu

1Corresponding author

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 4, 2019; final manuscript received February 14, 2019; published online March 5, 2019. Assoc. Editor: Yong Zhu.

J. Appl. Mech 86(5), 051008 (Mar 05, 2019) (11 pages) Paper No: JAM-19-1007; doi: 10.1115/1.4042894 History: Received January 04, 2019; Accepted February 14, 2019

This work examines elastic wave propagation phenomena in open-cell foams with the use of the Bloch wave method and finite element analysis. Random foam topologies are generated with the Surface Evolver and subsequently meshed with Timoshenko beam elements, creating open-cell foam models. Convergence studies on band diagrams of different domain sizes indicate that a representative volume element (RVE) consists of at least 83 cells. Wave directionality and energy flow features are investigated by extracting phase and group velocity plots. Explicit dynamic simulations are performed on finite size domains of the considered foam structure to validate the RVE results. The effect of topological disorder is studied in detail, and excellent agreement is found between the wave behavior of the random foam and that of both the regular and perturbed Kelvin foams in the low-frequency regime. In higher modes and frequencies, however, as the wavelengths become smaller, disorder has a significant effect and the deviation between regular and random foam increases significantly.

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Figures

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Fig. 1

(a) Aluminum T6061 open-cell foam and (b) tomography image showing disordered cell structure consisting of cells with polyhedral faces

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Fig. 2

Random foam models of different domain size and relative density ρr = 15%

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Fig. 3

(a) Reciprocal lattice unit cell and the corresponding IBZ, (b) frequency band diagrams for random foam models of different domain size, and (c) density of states corresponding to the 83 cells model and the first ten dispersion bands

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Fig. 4

First three mode shapes of a random foam model at the high symmetry points of IBZ

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Fig. 5

Normalized (a) phase and (b) group velocity of random foam at different frequencies corresponding to kx = 0. The diamond, square, and circle markers represent the first, second, and third mode, respectively.

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Fig. 6

Isofrequency contour plots of random foam in the kykz plane for different levels of the kx component of the wave vector for the first three modes

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Fig. 7

Transient simulation snapshots for a single-point harmonic perturbation at Ω = 0.7 on a 20 × 20 × 10 cell random foam at (a) 9.5 × 10−3 s, (b) 1.4 × 10−2 s, and (c) 1.8 × 10−2 s

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Fig. 8

Three-dimensional clusters of the Kelvin foam with ρr = 15% and the corresponding band diagrams for (a) 1 × 1 × 1, (b) 2 × 2 × 2, (c) 3 × 3 × 3, (d) 4 × 4 × 4, and (e) 5 × 5 × 5 supercells

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Fig. 9

Normalized (a) phase and (b) group velocity of a Kelvin supercell at different frequencies corresponding to kx = 0. The diamond, square, and circle markers represent first, second, and third modes, respectively.

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Fig. 10

Three-dimensional clusters of 4 × 4 × 4 perturbed Kelvin lattices and the corresponding band diagrams demonstrating the effect of irregularity for (a) −10% < mi < 10% and (b) −30% < mi < 30% perturbation

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Fig. 11

Dispersion surfaces of the Kelvin supercell for the (a) first mode, (b) 10th mode, (c) 20th mode, (d) 40th mode, (e) 60th mode, and (f) 80th mode

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Fig. 12

Dispersion surfaces of random foam for the (a) first mode, (b) 10th mode, (c) 20th mode, (d) 40th mode, (e) 60th mode, and (f) 80th mode

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