Study on the response of honeycombs subjected to in-plane shear helps establish the constitutive relations for honeycombs and shed light on the mechanics of cellular materials. The present study explores the nonlinear elastic response of honeycombs under in-plane shear by analyzing the large deflection of cell walls in a unit cell. Governing equations are established which relate the macroscopic response of honeycombs to the deflection of cell walls. Solving these equations, the behavior of regular honeycombs under in-plane shear along horizontal (X) and vertical (Y) directions was investigated. It is found that the response of regular honeycombs under in-plane shear depends on the nondimensional shear stress which is a parameter combining the thickness-to-length ratio of cell walls, the Young's modulus of base materials, and macroscopic shear stress. Lateral shrinking is a distinctive characteristic for honeycombs under in-plane shear, which should be taken into account when establishing constitutive relations and performing simple shear experiments. Expressions for predicting the shear strength of honeycombs are formulated in this paper. It is noted that the normalized shear strength of regular honeycombs depends on two ratios: the thickness-to-length ratio of cell walls and the ratio of Young's modulus to yield strength of base materials, and the former has a dominant effect. By comparing honeycombs with cell walls of uniform thickness against honeycombs with vertical cell walls of double thickness, it is found that doubling the thickness of vertical cell walls of honeycombs increases their shear strength along horizontal (X) direction nearly twice, but does not improve the shear strength that much along the vertical (Y) direction.

References

References
1.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1997
,
Cellular Solids: Structure and Properties
,
2nd ed.
,
Cambridge University Press
,
Cambridge/New York
.
2.
Zhang
,
J.
, and
Ashby
,
M.
,
1992
, “
The Out-of-Plane Properties of Honeycombs
,”
Int. J. Mech. Sci.
,
34
(
6
), pp.
475
489
.
3.
Cote
,
F.
,
Deshpande
,
V.
,
Fleck
,
N.
, and
Evans
,
A.
,
2004
, “
The Out-of-Plane Compressive Behavior of Metallic Honeycombs
,”
Mater. Sci. Eng.: A
,
380
(1–2), pp.
272
280
.
4.
Pan
,
S.-D.
,
Wu
,
L.-Z.
,
Sun
,
Y.-G.
,
Zhou
,
Z.-G.
, and
Qu
,
J.-L.
,
2006
, “
Longitudinal Shear Strength and Failure Process of Honeycomb Cores
,”
Compos. Struct.
,
72
(
1
), pp.
42
46
.
5.
Wilbert
,
A.
,
Jang
,
W.-Y.
,
Kyriakides
,
S.
, and
Floccari
,
J.
,
2011
, “
Buckling and Progressive Crushing of Laterally Loaded Honeycomb
,”
Int. J. Solids Struct.
,
48
(
5
), pp.
803
816
.
6.
Deqiang
,
S.
,
Weihong
,
Z.
, and
Yanbin
,
W.
,
2010
, “
Mean Out-of-Plane Dynamic Plateau Stresses of Hexagonal Honeycomb Cores Under Impact Loadings
,”
Compos. Struct.
,
92
(
11
), pp.
2609
2621
.
7.
Xu
,
S.
,
Beynon
,
J. H.
,
Ruan
,
D.
, and
Lu
,
G.
,
2012
, “
Experimental Study of the Out-of-Plane Dynamic Compression of Hexagonal Honeycombs
,”
Compos. Struct.
,
94
(
8
), pp.
2326
2336
.
8.
Gibson
,
L.
,
Ashby
,
M.
,
Schajer
,
G.
, and
Robertson
,
C.
,
1982
, “
The Mechanics of Two-Dimensional Cellular Materials
,”
Proc. R. Soc. London A
,
382
(
1782
), pp.
25
42
.
9.
Papka
,
S. D.
, and
Kyriakides
,
S.
,
1994
, “
In-Plane Compressive Response and Crushing of Honeycomb
,”
J. Mech. Phys. Solids
,
42
(
10
), pp.
1499
1532
.
10.
Papka
,
S. D.
, and
Kyriakides
,
S.
,
1998
, “
Experiments and Full-Scale Numerical Simulations of In-Plane Crushing of a Honeycomb
,”
Acta Mater.
,
46
(
8
), pp.
2765
2776
.
11.
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
.
12.
Chen
,
C.
,
Lu
,
T. J.
, and
Fleck
,
N. A.
,
1999
, “
Effect of Imperfections on the Yielding of Two-Dimensional Foams
,”
J. Mech. Phys. Solids
,
47
(
11
), pp.
2235
2272
.
13.
Zhu
,
H. X.
,
Hobdell
,
J. R.
, and
Windle
,
A. H.
,
2001
, “
Effects of Cell Irregularity on the Elastic Properties of 2D Voronoi Honeycombs
,”
J. Mech. Phys. Solids
,
49
(
4
), pp.
857
870
.
14.
Chuang
,
C.-H.
, and
Huang
,
J.-S.
,
2002
, “
Effects of Solid Distribution on the Elastic Buckling of Honeycombs
,”
Int. J. Mech. Sci.
,
44
(
7
), pp.
1429
1443
.
15.
Fazekas
,
A.
,
Dendievel
,
R.
,
Salvo
,
L.
, and
Bréchet
,
Y.
,
2002
, “
Effect of Microstructural Topology Upon the Stiffness and Strength of 2D Cellular Structures
,”
Int. J. Mech. Sci.
,
44
(
10
), pp.
2047
2066
.
16.
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
(5–6), pp.
1777
1795
.
17.
Zhu
,
H. X.
,
Thorpe
,
S. M.
, and
Windle
,
A. H.
,
2006
, “
The Effect of Cell Irregularity on the High Strain Compression of 2D Voronoi Honeycombs
,”
Int. J. Solids Struct.
,
43
(
5
), pp.
1061
1078
.
18.
Alkhader
,
M.
, and
Vural
,
M.
,
2008
, “
Mechanical Response of Cellular Solids: Role of Cellular Topology and Microstructural Irregularity
,”
Int. J. Eng. Sci.
,
46
(
10
), pp.
1035
1051
.
19.
Zhu
,
H. X.
, and
Chen
,
C. Y.
,
2011
, “
Combined Effects of Relative Density and Material Distribution on the Mechanical Properties of Metallic Honeycombs
,”
Mech. Mater.
,
43
(
5
), pp.
276
286
.
20.
Hönig
,
A.
, and
Stronge
,
W.
,
2002
, “
In-Plane Dynamic Crushing of Honeycomb. Part I: Crush Band Initiation and Wave Trapping
,”
Int. J. Mech. Sci.
,
44
(
8
), pp.
1665
1696
.
21.
Ruan
,
D.
,
Lu
,
G.
,
Wang
,
B.
, and
Yu
,
T.
,
2003
, “
In-Plane Dynamic Crushing of Honeycombs—A Finite Element Study
,”
Int. J. Impact Eng.
,
28
(
2
), pp.
161
182
.
22.
Ali
,
I.
, and
Jun
,
Y. J.
,
2014
, “
Mathematical Models for In-Plane Moduli of Honeycomb Structures—A Review
,”
Res. J. Appl. Sci., Eng. Technol.
,
7
, pp.
581
592
.
23.
Kim
,
K.
,
Kim
,
S.
,
Ju
,
J.
, and
Kim
,
D.-M.
,
2011
, “
Contact Pressure of a Non-Pneumatic Tire With Three-Dimensional Cellular Spokes
,”
ASME
Paper No. IMECE2011-64233.
24.
Ju
,
J.
, and
Summers
,
J. D.
,
2011
, “
Compliant Hexagonal Periodic Lattice Structures Having Both High Shear Strength and High Shear Strain
,”
Mater. Des.
,
32
(
2
), pp.
512
524
.
25.
Ju
,
J.
, and
Summers
,
J. D.
, “
Hyperelastic Constitutive Modeling of Hexagonal Honeycombs Subjected to In-Plane Shear Loading
,”
ASME J. Eng. Mater. Technol.
,
133
(
1
), p.
011005
.
26.
Shankar
,
P.
,
Ju
,
J.
,
Summers
,
J. D.
, and
Zeigert
,
J.
,
2010
, “
Design of Sinusoidal Auxetic Structures for High Shear Flexure
,”
ASME
Paper No. DETC2010-28545.
27.
Ju
,
J.
,
Summers
,
J. D.
,
Zeigert
,
J.
, and
Fadel
,
G.
,
2012
, “
Design of Honeycombs for Modulus and Yield Strain in Shear
,”
ASME J. Eng. Mater. Technol.
,
134
(
1
), p.
011002
.
28.
Bubert
,
E. A.
,
Woods
,
B. K.
,
Lee
,
K.
,
Kothera
,
C. S.
, and
Wereley
,
N. M.
,
2010
, “
Design and Fabrication of a Passive 1D Morphing Aircraft Skin
,”
J. Intell. Mater. Syst. Struct.
,
21
(
17
), pp.
1699
1717
.
29.
Joshi
,
S.
,
Ju
,
J.
,
Berglind
,
L.
,
Rusly
,
R.
,
Summers
,
J. D.
, and
DesJardins
,
J. D.
,
2010
, “
Experimental Damage Characterization of Hexagonal Honeycombs Subjected to In-Plane Shear Loading
,”
ASME
Paper No. DETC2010-28549.
30.
Zhu
,
H. X.
, and
Mills
,
N.
,
2000
, “
The In-Plane Non-Linear Compression of Regular Honeycombs
,”
Int. J. Solids Struct.
,
37
(
13
), pp.
1931
1949
.
31.
Lan
,
L.-H.
, and
Fu
,
M.-H.
,
2009
, “
Nonlinear Constitutive Relations of Cellular Materials
,”
AIAA J.
,
47
(
1
), pp.
264
270
.
32.
Warren
,
W.
,
Kraynik
,
A.
, and
Stone
,
C.
,
1989
, “
A Constitutive Model for Two-Dimensional Nonlinear Elastic Foams
,”
J. Mech. Phys. Solids
,
37
(
6
), pp.
717
733
.
33.
Timoshenko
,
S. P.
, and
Gere
,
J. M.
,
1961
,
Theory of Elastic Stability
,
McGraw-Hill
,
New York
.
34.
Zhu
,
H.
,
Mills
,
N.
, and
Knott
,
J.
,
1997
, “
Analysis of the High Strain Compression of Open-Cell Foams
,”
J. Mech. Phys. Solids
,
45
(11–12), pp.
1875
1904
.
35.
Beléndez
,
T.
,
Neipp
,
C.
, and
Beléndez
,
A.
,
2002
, “
Large and Small Deflections of a Cantilever Beam
,”
Eur. J. Phys.
,
23
(
3
), pp.
371
–379.
You do not currently have access to this content.