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.

References

References
1.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1999
,
Cellular Solids: Structure and Properties
,
Cambridge University Press
,
Cambridge, England
.
2.
Geslain
,
A.
,
Dazel
,
O.
,
Groby
,
J. P.
,
Sahraoui
,
S.
, and
Lauriks
,
W.
,
2011
, “
Influence of Static Compression on Mechanical Parameters of Acoustic Foams
,”
J. Acoust. Soc. Am.
,
130
(
2
), pp.
818
825
.
3.
Jaouen
,
L.
,
Renault
,
A.
, and
Deverge
,
M.
,
2008
, “
Elastic and Damping Characterizations of Acoustical Porous Materials: Available Experimental Methods and Applications to a Melamine Foam
,”
Appl. Acoust.
,
69
(
12
), pp.
1129
1140
.
4.
Thomson
,
W.
,
1887
, “
LXIII. On the Division of Space With Minimum Partitional Area
,”
Lond. Edinb. Dublin Philos. Mag. J. Sci.
,
24
(
151
), pp.
503
514
.
5.
Warren
,
W. E.
, and
Kraynik
,
A. M.
,
1988
, “
The Linear Elastic Properties of Open-Cell Foams
,”
J. Appl. Mech.
,
55
(
2
), pp.
341
346
.
6.
Zhu
,
H. X.
,
Knott
,
J. F.
, and
Mills
,
N. J.
,
1997
, “
Analysis of the Elastic Properties of Open-Cell Foams With Tetrakaidecahedral Cells
,”
J. Mech. Phys. Solids
,
45
(
3
), pp.
319
343
.
7.
Laroussi
,
M.
,
Sab
,
K.
, and
Alaoui
,
A.
,
2002
, “
Foam Mechanics: Nonlinear Response of an Elastic 3D-Periodic Microstructure
,”
Int. J. Solids Struct.
,
39
(
13–14
), pp.
3599
3623
.
8.
Gong
,
L.
,
Kyriakides
,
S.
, and
Jang
,
W. Y.
,
2005
, “
Compressive Response of Open-Cell Foams. Part I: Morphology and Elastic Properties
,”
Int. J. Solids Struct.
,
42
(
5–6
), pp.
1355
1379
.
9.
Jang
,
W. Y.
,
Kraynik
,
A. M.
, and
Kyriakides
,
S.
,
2008
, “
On the Microstructure of Open-Cell Foams and Its Effect on Elastic Properties
,”
Int. J. Solids Struct.
,
45
(
7–8
), pp.
1845
1875
.
10.
Jang
,
W. Y.
,
Kyriakides
,
S.
, and
Kraynik
,
A. M.
,
2010
, “
On the Compressive Strength of Open-Cell Metal Foams With Kelvin and Random Cell Structures
,”
Int. J. Solids Struct.
,
47
(
21
), pp.
2872
2883
.
11.
Zhu
,
W.
,
Blal
,
N.
,
Cunsolo
,
S.
, and
Baillis
,
D.
,
2017
, “
Micromechanical Modeling of Effective Elastic Properties of Open-Cell Foam
,”
Int. J. Solids Struct.
,
115
, pp.
61
72
.
12.
Sotomayor
,
O. E.
, and
Tippur
,
H. V.
,
2014
, “
Role of Cell Regularity and Relative Density on Elastoplastic Compression Response of 3-D Open-Cell Foam Core Sandwich Structure Generated Using Voronoi Diagrams
,”
Acta Mater.
,
78
, pp.
301
313
.
13.
Melon
,
M.
,
Mariez
,
E.
,
Ayrault
,
C.
, and
Sahraoui
,
S.
,
1998
, “
Acoustical and Mechanical Characterization of Anisotropic Open-Cell Foams
,”
J. Acoust. Soc. Am.
,
104
(
5
), pp.
2622
2627
.
14.
Hosseini
,
S. M. H.
,
Willberg
,
C.
,
Kharaghani
,
A.
, and
Gabbert
,
U.
,
2014
, “
Characterization of the Guided Wave Propagation in Simplified Foam, Honeycomb and Hollow Sphere Structures
,”
Compos. Part B: Eng.
,
56
, pp.
553
566
.
15.
Álvarez-Láinez
,
M.
,
Rodríguez-Pérez
,
M. A.
, and
de Saja
,
J. A.
,
2014
, “
Acoustic Absorption Coefficient of Open-Cell Polyolefin-Based Foams
,”
Mater. Lett.
,
121
, pp.
26
30
.
16.
Park
,
J. H.
,
Minn
,
K. S.
,
Lee
,
H. R.
,
Yang
,
S. H.
,
Yu
,
C. B.
,
Pak
,
S. Y.
,
Oh
,
C. S.
,
Song
,
Y. S.
,
Kang
,
Y. J.
, and
Youn
,
J. R.
,
2017
, “
Cell Openness Manipulation of Low Density Polyurethane Foam for Efficient Sound Absorption
,”
J. Sound Vib.
,
406
, pp.
224
236
.
17.
Sigalas
,
M. M.
,
Soukoulis
,
C. M.
,
Chan
,
C. T.
,
Biswas
,
R.
, and
Ho
,
K. M.
,
1999
, “
Effect of Disorder on Photonic Band Gaps
,”
Phys. Rev. B
,
59
(
20
), pp.
12767
12770
.
18.
Bayat
,
A.
, and
Gaitanaros
,
S.
,
2018
, “
Wave Directionality in Three-Dimensional Periodic Lattices
,”
J. Appl. Mech.
,
85
(
1
),
011004
.
19.
Kraynik
,
A. M.
,
Reinelt
,
D. A.
, and
van Swol
,
F.
,
2003
, “
Structure of Random Monodisperse Foam
,”
Phys. Rev. E
,
67
(
3
),
031403
.
20.
Kraynik
,
A. M.
,
Reinelt
,
D. A.
, and
van Swol
,
F.
,
2004
, “
Structure of Random Foam
,”
Phys. Rev. Lett.
,
93
(
20
),
208301
.
21.
Plateau
,
J. A. F.
,
1873
,
Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires
, Vol.
2
,
Gauthier-Villars
,
Paris
.
22.
Gaitanaros
,
S.
,
Kyriakides
,
S.
, and
Kraynik
,
A. M.
,
2012
, “
On the Crushing Response of Random Open-Cell Foams
,”
Int. J. Solids Struct.
,
49
(
19–20
), pp.
2733
2743
.
23.
Gaitanaros
,
S.
, and
Kyriakides
,
S.
,
2014
, “
Dynamic Crushing of Aluminum Foams: Part II–Analysis
,”
Int. J. Solids Struct.
,
51
(
9
), pp.
1646
1661
.
24.
Gaitanaros
,
S.
, and
Kyriakides
,
S.
,
2015
, “
On the Effect of Relative Density on the Crushing and Energy Absorption of Open-Cell Foams Under Impact
,”
Int. J. Impact Eng.
,
82
, pp.
3
13
.
25.
Gaitanaros
,
S.
,
Kyriakides
,
S.
, and
Kraynik
,
A. M.
,
2018
, “
On the Crushing of Polydisperse Foams
,”
Eur. J. Mech.-A/Solids
,
67
, pp.
243
253
.
26.
Phani
,
A. S.
, and
Hussein
,
M. I.
, eds.,
2017
,
Dynamics of Lattice Materials
,
John Wiley & Sons
,
New York
.
27.
Åberg
,
M.
, and
Gudmundson
,
P.
,
1997
, “
The Usage of Standard Finite Element Codes for Computation of Dispersion Relations in Materials With Periodic Microstructure
,”
J. Acoust. Soc. Am.
,
102
(
4
), pp.
2007
2013
.
28.
Langley
,
R. S.
,
1994
, “
On the Modal Density and Energy Flow Characteristics of Periodic Structures
,”
J. Sound Vib.
,
172
(
4
), pp.
491
511
.
29.
Kittel
,
C.
,
1976
,
Introduction to Solid State Physics
, Vol.
8
,
Wiley
,
New York
.
30.
Ruzzene
,
M.
,
Scarpa
,
F.
, and
Soranna
,
F.
,
2003
, “
Wave Beaming Effects in Two-Dimensional Cellular Structures
,”
Smart Mater. Struct.
,
12
(
3
), pp.
363
372
.
31.
Trainiti
,
G.
,
Rimoli
,
J. J.
, and
Ruzzene
,
M.
,
2016
, “
Wave Propagation in Undulated Structural Lattices
,”
Int. J. Solids. Struct.
,
97
, pp.
431
444
.
32.
Casadei
,
F.
, and
Rimoli
,
J. J.
,
2013
, “
Anisotropy-Induced Broadband Stress wave steering in periodic lattices
,”
Int. J. Solids. Struct.
,
50
(
9
), pp.
1402
1414
.
33.
Ku
,
W.
,
Berlijn
,
T.
, and
Lee
,
C. C.
,
2010
, “
Unfolding First-Principles Band Structures
,”
Phys. Rev. Lett.
,
104
(
21
),
216401
.
34.
Popescu
,
V.
, and
Zunger
,
A.
,
2012
, “
Extracting E versus k → effective band structure from supercell calculations on alloys and impurities
,”
Phys. Rev. B
,
85
(
8
),
085201
.
35.
Ahn
,
Y. K.
,
Oh
,
J. H.
,
Ma
,
P. S.
, and
Kim
,
Y. Y.
,
2016
, “
Dispersion Analysis With 45°-Rotated Augmented Supercells and Applications in Phononic Crystal Design
,”
Wave Motion
,
61
, pp.
63
72
.
36.
Srivastava
,
A.
,
2015
, “
Elastic Metamaterials and Dynamic Homogenization: A Review
,”
Int. J. Smart Nano Mater.
,
6
(
1
), pp.
41
60
.
37.
Nemat-Nasser
,
S.
, and
Srivastava
,
A.
,
2013
, “
Bounds on Effective Dynamic Properties of Elastic Composites
,”
J. Mech. Phys. Solids
,
61
(
1
), pp.
254
264
.
38.
Srivastava
,
A.
, and
Nemat-Nasser
,
S.
,
2014
, “
On the Limit and Applicability of Dynamic Homogenization
,”
Wave Motion
,
51
(
7
), pp.
1045
1054
.
39.
Willis
,
J. R.
,
1997
, “
Dynamics of Composites
,”
Continuum Micromechanics
,
Springer
,
Vienna
, pp.
265
290
.
You do not currently have access to this content.