Double arrowhead honeycombs (DAHs) are a type of auxetic materials, i.e., showing negative Poisson's ratio (NPR), and are promising for energy absorption applications. Their in-plane impact responses are theoretically and numerically explored. Theoretical models for the collapse stress under quasi-static, low-velocity, and high-velocity impacts are developed, based upon the corresponding microstructural deformation modes. Obtained results show that the collapse stress under quasi-static and low velocity impacts depends upon the two re-entrant angles responsible for NPR, while it is insensitive to them under high-velocity impact. The developed theoretical models are employed to analyze the energy absorption capacity of DAHs, showing the absorbed energy under high-velocity impact approximately proportional to the second power of velocity. Extension of the high-velocity impact model to functionally graded (FG) DAHs is also discussed. Good agreement between the theoretical and finite element (FE) predictions on the impact responses of DAHs is obtained.

References

References
1.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1999
,
Cellular Solids: Structure and Properties
,
Cambridge University Press
,
Cambridge, UK
.
2.
Reid
,
S. R.
, and
Peng
,
C.
,
1997
, “
Dynamic Uniaxial Crushing of Wood
,”
Int. J. Impact Eng.
,
19
(
5–6
), pp.
531
570
.10.1016/S0734-743X(97)00016-X
3.
Lopatnikov
,
S. L.
,
Gama
,
B. A.
,
Haque
,
M. J.
,
Krauthauser
,
C.
,
Gillespie
,
J. W.
,
Guden
,
M.
, and
Hall
,
I. W.
,
2003
, “
Dynamics of Metal Foam Deformation During Taylor Cylinder-Hopkinson Bar Impact Experiment
,”
Compos. Struct.
,
61
(
1–2
), pp.
61
71
.10.1016/S0263-8223(03)00039-4
4.
Harrigan
,
J. J.
,
Reid
,
S. R.
,
Tan
,
P. J.
, and
Reddy
,
T. Y.
,
2005
, “
High Rate Crushing of Wood Along the Grain
,”
Int. J. Mech. Sci.
,
47
(
4–5
), pp.
521
544
.10.1016/j.ijmecsci.2004.12.013
5.
Tan
,
P. J.
,
Reid
,
S. R.
,
Harrigan
,
J. J.
,
Zou
,
Z.
, and
Li
,
S.
,
2005
, “
Dynamic Compressive Strength Properties of Aluminium Foams—Part II: ‘Shock’ Theory and Comparison With Experimental Data and Numerical Models
,”
J. Mech. Phys. Solids
,
53
(
10
), pp.
2206
2230
.10.1016/j.jmps.2005.05.003
6.
Wang
,
L. L.
,
Yang
,
L. M.
, and
Ding
,
Y. Y.
,
2013
, “
On the Energy Conservation and Critical Velocities for the Propagation of a “Steady-Shock” Wave in a Bar Made of Cellular Material
,”
Acta Mech. Sin.
,
29
(
3
), pp.
420
428
.10.1007/s10409-013-0024-3
7.
Zheng
,
Z. J.
,
Liu
,
Y. D.
,
Yu
,
J. L.
, and
Reid
,
S. R.
,
2012
, “
Dynamic Crushing of Cellular Materials: Continuum-Based Wave Models for the Transitional and Shock Modes
,”
Int. J. Impact Eng.
,
42
, pp.
66
79
.10.1016/j.ijimpeng.2011.09.009
8.
Zheng
,
Z. J.
,
Wang
,
C. F.
,
Yu
,
J. L.
,
Reid
,
S. R.
, and
Harrigan
,
J. J.
,
2014
, “
Dynamic Stress–Strain States for Metal Foams Using a 3D Cellular Model
,”
J. Mech. Phys. Solids
,
72
, pp.
93
114
.10.1016/j.jmps.2014.07.013
9.
Fleck
,
N. A.
, and
Deshpande
,
V. S.
,
2004
, “
The Resistance of Clamped Sandwich Beams to Shock Loading
,”
ASME J. Appl. Mech.
,
71
(
3
), pp.
386
401
.10.1115/1.1629109
10.
Yi
,
T.
, and
Chen
,
C. Q.
,
2012
, “
The Impact Response of Clamped Sandwich Beams With Ordinary and Hierarchical
,”
Int. J. Impact Eng.
,
47
, pp.
14
23
.10.1016/j.ijimpeng.2012.03.001
11.
Yu
,
B.
,
Han
,
B.
,
Ni
,
C. Y.
,
Zhang
,
Q. C.
,
Chen
,
C. Q.
, and
Lu
,
T. J.
,
2015
, “
Dynamic Crushing of All-Metallic Corrugated Panels Filled With Close-Celled Aluminum Foams
,”
ASME J. Appl. Mech.
,
82
(
1
), p.
011006
.10.1115/1.4028995
12.
Hönig
,
A.
, and
Stronge
,
W. J.
,
2002
, “
In-Plane Dynamic Crushing of Honeycomb—Part II: Application to Impact
,”
Int. J. Mech. Sci.
,
44
(
8
), pp.
1697
1714
.10.1016/S0020-7403(02)00061-9
13.
Ruan
,
D.
,
Lu
,
G.
,
Wang
,
B.
, and
Yu
,
T. X.
,
2003
, “
In-Plane Dynamic Crushing of Honeycombs-Finite Element Study
,”
Int. J. Impact Eng.
,
28
(
2
), pp.
161
182
.10.1016/S0734-743X(02)00056-8
14.
Li
,
K.
,
Gao
,
X. L.
, and
Wang
,
J.
,
2007
, “
Dynamic Crushing Behavior of Honeycomb Structures With Irregular Cell Shapes and Non-Uniform Cell Wall Thickness
,”
Int. J. Solids Struct.
,
44
(
14–15
), pp.
5003
5026
.10.1016/j.ijsolstr.2006.12.017
15.
Qiu
,
X. M.
,
Zhang
,
J.
, and
Yu
,
T. X.
,
2009
, “
Collapse of Periodic Planar Lattices Under Uniaxial Compression—Part II: Dynamic Crushing Based on Finite Element Simulation
,”
Int. J. Impact Eng.
,
36
(
10–11
), pp.
1231
1241
.10.1016/j.ijimpeng.2009.05.010
16.
Liao
,
S. F.
,
Zheng
,
Z. J.
, and
Yu
,
J. L.
,
2013
, “
Dynamic Crushing of 2D Cellular Structures: Local Strain Field and Shock Wave Velocity
,”
Int. J. Impact Eng.
,
57
, pp.
7
16
.10.1016/j.ijimpeng.2013.01.008
17.
Liao
,
S. F.
,
Zheng
,
Z. J.
, and
Yu
,
J. L.
,
2014
, “
On the Local Nature of the Strain Field Calculation Method for Measuring Heterogeneous Deformation of Cellular Materials
,”
Int. J. Solids Struct.
,
51
(
2
), pp.
478
490
.10.1016/j.ijsolstr.2013.10.019
18.
Hu
,
L. L.
, and
Yu
,
T. X.
,
2010
, “
Dynamic Crushing Strength of Hexagonal Honeycombs
,”
Int. J. Impact Eng.
,
37
(
5
), pp.
467
474
.10.1016/j.ijimpeng.2009.12.001
19.
Hu
,
L. L.
, and
Yu
,
T. X.
,
2013
, “
Mechanical Behavior of Hexagonal Honeycombs Under Low-Velocity Impact—Theory and Simulations
,”
Int. J. Solids Struct.
,
50
(
20–21
), pp.
3152
3165
.10.1016/j.ijsolstr.2013.05.017
20.
Barnes
,
A. T.
,
Ravi-Chandar
,
K.
,
Kyriakides
,
S.
, and
Gaitanaros
,
S.
,
2013
, “
Dynamic Crushing of Aluminum Foams—Part I: Experiments
,”
Int. J. Solids Struct.
,
51
(
9
), pp.
1631
1645
.10.1016/j.ijsolstr.2013.11.019
21.
Barnes
,
A. T.
, and
Kyriakides
,
S.
,
2013
, “
Dynamic Crushing of Aluminum Foams—Part II: Analysis
,”
Int. J. Solids Struct.
,
51
(
9
), pp.
1646
1661
.10.1016/j.ijsolstr.2013.11.020
22.
Scarpa
,
F.
,
Panayiotou
,
P.
, and
Tomlinson
,
G.
,
2000
, “
Numerical and Experimental Uniaxial Loading on In-Plane Auxetic Honeycombs
,”
J. Strain Anal. Eng. Des.
,
35
(
5
), pp.
383
388
.10.1243/0309324001514152
23.
Wan
,
H.
,
Ohtaki
,
H.
,
Kotosaka
,
S.
, and
Hu
,
G.
,
2004
, “
A Study of Negative Poisson's Ratios in Auxetic Honeycombs Based on a Large Deflection Model
,”
Eur. J. Mech. A Solids
,
23
(
1
), pp.
95
106
.10.1016/j.euromechsol.2003.10.006
24.
Lira
,
C.
, and
Scarpa
,
F.
,
2010
, “
Transverse Shear Stiffness of Thickness Gradient Honeycombs
,”
Compos. Sci. Technol.
,
70
(
6
), pp.
930
936
.10.1016/j.compscitech.2010.02.007
25.
Hou
,
Y.
,
Neville
,
R.
,
Scarpa
,
F.
,
Remillat
,
C.
,
Gu
,
B.
, and
Ruzzene
,
M.
,
2014
, “
Graded Conventional-Auxetic Kirigami Sandwich Structures: Flatwise Compression and Edgewise Loading
,”
Composites, Part B
,
59
, pp.
33
42
.10.1016/j.compositesb.2013.10.084
26.
Ma
,
Z. D.
,
Bian
,
H.
,
Sun
,
C.
,
Hulbert
,
G. M.
,
Bishnoi
,
K.
, and
Rostam-Abadi
,
F.
,
2010
, “
Functionally-Graded NPR (Negative Poisson's Ratio) Material for a Blast-Protective Deflector
,”
Ground Vehicle Systems Engineering and Technology Symposium
,
Dearborn, MI
, Aug. 17–19.
27.
Zhang
,
X. C.
,
Liu
,
Y.
, and
Li
,
N.
,
2012
, “
In-Plane Dynamic Crushing of Honeycombs With Negative Poisson's Ratio Effects
,”
Explos. Shock Waves
,
32
(
5
), pp.
475
482
(in Chinese).
28.
Yang
,
S.
,
Qi
,
C.
,
Wang
,
D.
,
Gao
,
B. J.
,
Hu
,
H. T.
, and
Shu
,
J.
,
2013
, “
A Comparative Study of Ballistic Resistance of Sandwich Panels With Aluminum Foam and Auxetic Honeycomb Cores
,”
Adv. Mech. Eng.
,
2013
, p.
589216
.10.1155/2013/589216
29.
Qi
,
C.
,
Yang
,
S.
,
Wang
,
D.
, and
Yang
,
L. J.
,
2013
, “
Ballistic Resistance of Honeycomb Sandwich Panels Under In-Plane High-Velocity Impact
,”
Adv. Mech. Eng.
,
2013
, p.
892781
.10.1155/2013/892781
30.
Larsen
,
U. D.
,
Sigmund
,
O.
, and
Bouwstra
,
S.
,
1996
, “
Design and Fabrication of Compliant Micromechanisms and Structures With Negative Poisson's Ratio
,”
Micro Electro Mech. Syst.
,
6
(
2
), pp.
365
371
.10.1109/MEMSYS.1996.494009
31.
Ali
,
M.
,
Qamhiyah
,
A.
,
Flugrad
,
D.
, and
Shakoor
,
M.
,
2008
, “
Theoretical and Finite Element Study of a Compact Energy Absorber
,”
Adv. Eng. Software
,
39
(
2
), pp.
95
106
.10.1016/j.advengsoft.2006.12.006
32.
Ajdari
,
A.
,
Nayeb-Hashemi
,
H.
, and
Vaziri
,
A.
,
2011
, “
Dynamic Crushing and Energy Absorption of Regular, Irregular and Functionally Graded Cellular Structures
,”
Int. J. Solids Struct.
,
48
(
3–4
), pp.
506
516
.10.1016/j.ijsolstr.2010.10.018
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