Cellular metamaterials are of interest for many current engineering applications. The incorporation of hierarchy to cellular metamaterials enhances the properties and introduces novel tailorable metamaterials. For many complex cellular metamaterials, the only realistic manufacturing process is additive manufacturing (AM). The use of AM to manufacture large structures may lead to several types of manufacturing defects, such as imperfect cell walls, irregular thickness, flawed joints, partially missing layers, and irregular elastic–plastic behavior due to toolpath. It is important to understand the effect of defects on the overall performance of the structures to determine if the manufacturing defect(s) are significant enough to abort and restart the manufacturing process or whether the material can still be used in its nonperfect state. In this study, the performance of hierarchical honeycomb metamaterials with defects has been investigated through simulations and experiments, and hierarchical honeycombs were shown to demonstrate more sensitivity to missing cell walls than regular honeycombs. On average, the axial elastic modulus decreased by 45% with 5.5% missing cell walls for regular honeycombs, 60% with 4% missing cell walls for first-order hierarchical honeycomb and 95% with 4% missing cell walls for second-order hierarchical honeycomb. The transverse elastic modulus decreased by about 45% with more than 5.5% missing cell walls for regular honeycomb, about 75% with 4% missing cell walls for first-order and more than 95% with 4% missing cell walls for second-order hierarchical honeycomb.

References

References
1.
Ajdari
,
A.
,
Jahromi
,
B. H.
,
Papadopoulos
,
J.
,
Nayeb-Hashemi
,
H.
, and
Vaziri
,
A.
,
2012
, “
Hierarchical Honeycombs With Tailorable Properties
,”
Int. J. Solids Struct.
,
49
(
11–12
), pp.
1413
1419
.
2.
Zhang
,
Z.
,
Zhang
,
Y. W.
, and
Gao
,
H.
,
2011
, “
On Optimal Hierarchy of Load-Bearing Biological Materials
,”
Proc. R. Soc. London B: Biol. Sci.
,
278
(
1705
), pp.
519
525
.
3.
Rayneau-Kirkhope
,
D.
,
Mao
,
Y.
, and
Farr
,
R.
,
2012
, “
Ultralight Fractal Structures From Hollow Tubes
,”
Phys. Rev. Lett.
,
109
(
20
), p.
204301
.
4.
Mousanezhad
,
D.
,
Babaee
,
S.
,
Ebrahimi
,
H.
,
Ghosh
,
R.
,
Hamouda
,
A. S.
,
Bertoldi
,
K.
, and
Vaziri
,
A.
,
2015
, “
Hierarchical Honeycomb Auxetic Metamaterials
,”
Sci. Rep.
,
5
, p.
18306
.
5.
Ai
,
L.
, and
Gao
,
X. L.
,
2017
, “
Metamaterials With Negative Poisson's Ratio and Non-Positive Thermal Expansion
,”
Compos. Struct.
,
162
, pp.
70
84
.
6.
Chen
,
Y.
,
Jia
,
Z.
, and
Wang
,
L.
,
2016
, “
Hierarchical Honeycomb Lattice Metamaterials With Improved Thermal Resistance and Mechanical Properties
,”
Compos. Struct.
,
152
, pp.
395
402
.
7.
Zhao
,
L.
,
Zheng
,
Q.
,
Fan
,
H.
, and
Jin
,
F.
,
2012
, “
Hierarchical Composite Honeycombs
,”
Mater. Des.
,
40
, pp.
124
129
.
8.
Kooistra
,
G. W.
,
Deshpande
,
V.
, and
Wadley
,
H. N.
,
2007
, “
Hierarchical Corrugated Core Sandwich Panel Concepts
,”
ASME J. Appl. Mech.
,
74
(
2
), pp.
259
268
.
9.
Murphey
,
T. W.
, and
Hinkle
,
J. D.
,
2003
, “
Some Performance Trends in Hierarchical Truss Structures
,”
AIAA
Paper No. 2003-1903.
10.
Oftadeh
,
R.
,
Haghpanah
,
B.
,
Vella
,
D.
,
Boudaoud
,
A.
, and
Vaziri
,
A.
,
2014
, “
Optimal Fractal-like Hierarchical Honeycombs
,”
Phys. Rev. Lett.
,
113
(
10
), p.
104301
11.
Sun
,
Y.
, and
Pugno
,
N. M.
,
2013
, “
In Plane Stiffness of Multifunctional Hierarchical Honeycombs With Negative Poisson's Ratio Sub-Structures
,”
Compos. Struct.
,
106
, pp.
681
689
.
12.
Haghpanah
,
B.
,
Oftadeh
,
R.
,
Papadopoulos
,
J.
, and
Vaziri
,
A.
,
2013
, “
Self-Similar Hierarchical Honeycombs
,”
Proc. R. Soc. A
,
469
(
2156
), p.
20130022
.
13.
Taylor
,
C. M.
,
Smith
,
C. W.
,
Miller
,
W.
, and
Evans
,
K. E.
,
2011
, “
The Effects of Hierarchy on the In-Plane Elastic Properties of Honeycombs
,”
Int. J. Solids Struct.
,
48
(
9
), pp.
1330
1339
.
14.
Mousanezhad
,
D.
,
Ebrahimi
,
H.
,
Haghpanah
,
B.
,
Ghosh
,
R.
,
Ajdari
,
A.
,
Hamouda
,
A. M. S.
, and
Vaziri
,
A.
,
2015
, “
Spiderweb Honeycombs
,”
Int. J. Solids Struct.
,
66
, pp.
218
227
.
15.
Fan
,
H. L.
,
Jin
,
F. N.
, and
Fang
,
D. N.
,
2008
, “
Mechanical Properties of Hierarchical Cellular Materials—Part I: Analysis
,”
Compos. Sci. Technol.
,
68
(
15
), pp.
3380
3387
.
16.
Prakash
,
O.
,
Bichebois
,
P.
,
Brechet
,
Y.
,
Louchet
,
F.
, and
Embury
,
J. D.
,
1996
, “
A Note on the Deformation Behaviour of Two-Dimensional Model Cellular Structures
,”
Philos. Mag. A
,
73
(
3
), pp.
739
751
.
17.
Ajdari
,
A.
,
Nayeb-Hashemi
,
H.
,
Canavan
,
P.
, and
Warner
,
G.
,
2008
, “
Effect of Defects on Elastic–Plastic Behavior of Cellular Materials
,”
Mater. Sci. Eng.: A
,
487
(
1
), pp.
558
567
.
18.
Silva
,
M. J.
, and
Gibson
,
L. J.
,
1997
, “
The Effects of Non-Periodic Microstructure and Defects on the Compressive Strength of Two-Dimensional Cellular Solids
,”
Int. J. Mech. Sci.
,
39
(
5
), pp.
549
563
.
19.
Nakamoto
,
H.
,
Adachi
,
T.
, and
Araki
,
W.
,
2009
, “
In-Plane Impact Behavior of Honeycomb Structures Randomly Filled With Rigid Inclusions
,”
Int. J. Impact Eng.
,
36
(
1
), pp.
73
80
.
20.
Wang
,
A. J.
, and
McDowell
,
D. L.
,
2003
, “
Effects of Defects on In-Plane Properties of Periodic Metal Honeycombs
,”
Int. J. Mech. Sci.
,
45
(
11
), pp.
1799
1813
.
21.
Zhang
,
X. C.
,
Liu
,
Y.
,
Wang
,
B.
, and
Zhang
,
Z. M.
,
2010
, “
Effects of Defects on the In-Plane Dynamic Crushing of Metal Honeycombs
,”
Int. J. Mech. Sci.
,
52
(
10
), pp.
1290
1298
.
22.
Guo
,
X. E.
, and
Gibson
,
L. J.
,
1999
, “
Behavior of Intact and Damaged Honeycombs: A Finite Element Study
,”
Int. J. Mech. Sci.
,
41
(
1
), pp.
85
105
.
23.
Li
,
K.
,
Gao
,
X. L.
, and
Subhash
,
G.
,
2005
, “
Effects of Cell Shape and Cell Wall Thickness Variations on the Elastic Properties of Two-Dimensional Cellular Solids
,”
Int. J. Solids Struct.
,
42
(
5
), pp.
1777
1795
.
24.
Simone
,
A. E.
, and
Gibson
,
L. J.
,
1998
, “
Effects of Solid Distribution on the Stiffness and Strength of Metallic Foams
,”
Acta Mater.
,
46
(
6
), pp.
2139
2150
.
25.
Simone
,
A. E.
, and
Gibson
,
L. J.
,
1998
, “
The Effects of Cell Face Curvature and Corrugations on the Stiffness and Strength of Metallic Foams
,”
Acta Mater.
,
46
(
11
), pp.
3929
3935
.
26.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1999
,
Cellular Solids: Structure and Properties
,
Cambridge University Press
, Cambridge, UK.
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