The in-plane flexible shear property of hexagonal honeycombs may be useful for the compliant structural applications. In this paper, hyperelastic strain energy functions are developed for a finite in-plane shear deformation of hexagonal honeycombs over a constituent material’s elastic range. Effective shear stress-strain curves of hexagonal structures and local cell wall deformation are investigated using the finite element based homogenization method. The hyperelastic models, which are only related to the effective properties of a honeycomb, may not be good enough to capture the nonlinear behavior at a high macroscopic shear strain level. The primary microscopic cell wall deformation mode under macroscopic in-plane shear loading was identified to be the bending of the vertical cell wall h, which is perpendicular to the macroscopic loading direction. The re-entrant hexagonal structures having a negative Poisson’s ratio shows a high macroscopic shear flexible property associated with the high h when the honeycombs are designed to have the same macroscopic shear modulus.

1.
Patel
,
M. R.
, and
Finnie
,
I.
, 1970, “
Structural Features and Mechanical Properties of Rigid Cellular Plastics
,”
J. Mater.
0022-2453,
5
, pp.
909
932
.
2.
Abd El-Sayed
,
F. K.
,
Jones
,
R.
, and
Burgess
,
I. W.
, 1979, “
A Theoretical Approach to the Deformation of Honeycomb Based Composite Materials
,”
Composites
0010-4361,
10
(
4
), pp.
209
214
.
3.
Gibson
,
L. J.
,
Ashby
,
M. F.
,
Schiajer
,
G. S.
, and
Robertson
,
C. I.
, 1982, “
The Mechanics of Two Dimensional Cellular Materials
,”
Proc. R. Soc. London, Ser. A
0950-1207,
382
, pp.
25
42
.
4.
Masters
,
I. G.
, and
Evans
,
K. E.
, 1996, “
Models for the Elastic Deformation of Honeycombs
,”
Compos. Struct.
0263-8223,
35
, pp.
403
422
.
5.
Gibson
,
L. J.
, and
Ashby
,
M. F.
, 1997,
Cellular Solids: Structures and Properties
,
2nd ed.
,
Cambridge University Press
,
Cambridge, UK
.
6.
Stronge
,
W. J.
, and
Shim
,
V. P.-W.
, 1988, “
Microdynamics of Crushing in Cellular Solids
,”
ASME J. Eng. Mater. Technol.
0094-4289,
110
, pp.
185
190
.
7.
Papka
,
S.
, and
Kyriakides
,
S.
, 1998, “
In-Plane Crushing of a Polycarbonate Honeycomb
,”
Int. J. Solids Struct.
0020-7683,
35
, pp.
239
267
.
8.
Chung
,
J.
, and
Wass
,
A. M.
, 1999, “
Compressive Response and Failure of Circular Cell Polycarbonate Honeycombs Under In-Plane Uni-Axial Stresses
,”
ASME J. Eng. Mater. Technol.
0094-4289,
121
, pp.
494
502
.
9.
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.
0020-7683,
42
, pp.
1777
1795
.
10.
Park
,
S. K.
, and
Gao
,
X. -L.
, 2008, “
Micromechanical Modeling of Honeycomb Structures Based on a Modified Couple Stress Theory
,”
Mech. Adv. Mater. Structures
,
15
, pp.
574
593
.
11.
Wang
,
A. -J.
, and
McDowell
,
D. L.
, 2004, “
In-Plane Stiffness and Yield Strength of Periodic Metal Honeycombs
,”
ASME J. Eng. Mater. Technol.
0094-4289,
126
, pp.
137
156
.
12.
Bezazi
,
A.
,
Scarpa
,
F.
, and
Remillat
,
C.
, 2005, “
A Novel Centresymmetric Honeycomb Composite Structure
,”
Compos. Struct.
0263-8223,
71
, pp.
356
364
.
13.
Scarpa
,
S.
,
Blain
,
S.
,
Lew
,
T.
,
Perrott
,
D.
,
Ruzzene
,
M.
, and
Yates
,
J. R.
, 2007, “
Elastic Buckling of Hexagonal Chiral Cell Honeycombs
,”
Composites, Part A
1359-835X,
38
, pp.
280
289
.
14.
Spadoni
,
A.
, and
Ruzzene
,
M.
, 2007, “
Static Aeroelastic Response of Chiral-Core Airfoils
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
18
, pp.
1067
1075
.
15.
Ju
,
J.
,
Summers
,
J. D.
,
Ziegert
,
J.
, and
Fadel
,
G.
, 2009, “
Design of Honeycomb Meta-Materials for High Shear Flexure
,”
Proceedings of the ASME International Design Engineering Technical Conferences
, San Diego, CA, Paper No. DETC2009-87730.
16.
Ju
,
J.
,
Summers
,
J. D.
,
Ziegert
,
J.
, and
Fadel
,
G.
, 2010, “
Compliant Hexagonal Meso-Structures Having Both High Shear Strength and High Shear Strain
,”
Proceedings of the ASME International Design Engineering Technical Conferences
, Montreal, Quebec, Canada, Paper No. DETC2010-28672.
17.
Zhu
,
H. X.
, and
Mills
,
N. J.
, 2000, “
The In-Plane Non-Linear Compression of Regular Honeycombs
,”
Int. J. Solids Struct.
0020-7683,
37
, pp.
1931
1949
.
18.
Lan
,
L. -H.
, and
Fu
,
M. -H.
, 2009, “
Nonlinear Constitutive Relations of Cellular Materials
,”
AIAA J.
0001-1452,
47
(
1
), pp.
264
270
.
19.
Hohe
,
J.
, and
Becker
,
W.
, 2003, “
Effective Mechanical Behavior of Hyperelastic Honeycombs and Two-Dimensional Model Foams at Finite Strain
,”
Int. J. Mech. Sci.
0020-7403,
45
, pp.
891
913
.
20.
Demiray
,
S.
,
Becker
,
W.
, and
Hohe
,
J.
, 2006, “
Analysis of Two-and Three-Dimensional Hyperelastic Model Foams Under Complex Loading Conditions
,”
Mech. Mater.
0167-6636,
38
, pp.
985
1000
.
21.
Guo
,
Z.
,
Caner
,
F.
,
Peng
,
X.
, and
Moran
,
B.
, 2008, “
On Constitutive Modeling of Porous Neo-Hookean Composites
,”
J. Mech. Phys. Solids
0022-5096,
56
, pp.
2338
2357
.
22.
Hill
,
R.
, 1972, “
On Constitutive Macro-Variables for Heterogeneous Solids at Finite Strain
,”
Proc. R. Soc. London, Ser. A
0950-1207,
326
, pp.
131
147
.
23.
Abeyaratne
,
R.
, and
Triantafyllidis
,
N.
, 1984, “
An Investigation of Localization in a Porous Elastic Material Using Homogenization Theory
,”
ASME J. Appl. Mech.
0021-8936,
51
, pp.
481
486
.
24.
Ponte Castaneda
,
P.
, 1989, “
The Overall Constitutive Behavior of Nonlinear Elastic Composites
,”
Proc. R. Soc. London, Ser. A
0950-1207,
422
, pp.
147
171
.
25.
Lopez-Pamies
,
O.
, and
Ponte Castaneda
,
P.
, 2003, “
Second Order Estimates for the Macroscopic for the Large Deformation Response of Particle Reinforced Rubbers
,”
C. R. Mec.
1631-0721,
331
, pp.
1
8
.
26.
Lopez-Pamies
,
O.
, and
Ponte Castaneda
,
P.
, 2004, “
Second Order Estimates for the Macroscopic Response and Loss of Ellipticity in Porous Rubbers at Large Deformations
,”
J. Elast.
0374-3535,
76
, pp.
247
287
.
27.
Triantafyllidis
,
N.
,
Nestorovic
,
M. D.
, and
Schraad
,
M. W.
, 2006, “
Failure Surfaces for Finitely Strained Two-Phase Periodic Solids Under General In-Plane Loading
,”
ASME J. Appl. Mech.
0021-8936,
73
, pp.
505
515
.
28.
Michel
,
J. C.
,
Lopez-Pamies
,
O.
,
Ponte Castaneda
,
P.
, and
Triantafyllidis
,
N.
, 2007, “
Microscopic and Macroscopic Instabilities in Finitely Strained Porous Elastomers
,”
J. Mech. Phys. Solids
0022-5096,
55
, pp.
900
938
.
29.
Mooney
,
M.
, 1940, “
A Theory of Large Elastic Deformation
,”
J. Appl. Phys.
0021-8979,
11
, pp.
582
592
.
30.
Rivlin
,
R. S.
, and
Saunders
,
D. W.
, 1951, “
Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
243
, pp.
251
288
.
31.
Blatz
,
P. J.
, and
Ko
,
W. L.
, 1962, “
Application of Finite Elastic Theory to the Deformation of Rubbery Materials
,”
Trans. Soc. Rheol.
0038-0032,
6
, pp.
223
251
.
32.
Ogden
,
R. W.
, 1972, “
Large Deformation Isotropic Elasticity: On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids
,”
Proc. R. Soc. London, Ser. A
0950-1207,
326
, pp.
565
584
.
33.
Ogden
,
R. W.
, 1972, “
Large Deformation Isotropic Elasticity: On the Correlation of Theory and Experiment for Compressible Rubberlike Solids
,”
Proc. R. Soc. London, Ser. A
0950-1207,
328
, pp.
567
583
.
34.
Yeoh
,
O. H.
, 1990, “
Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates
,”
Rubber Chem. Technol.
0035-9475,
63
, pp.
792
805
.
35.
Holzapfel
,
G. A.
, 2000,
Nonlinear Solid Mechanics—A Continuum Approach for Engineering
,
Wiley
,
UK
.
36.
Joshi
,
S.
,
Ju
,
J.
,
Berglind
,
L.
,
Rusly
,
R.
,
Summers
,
J. D.
, and
Desjardins
,
J.
, 2010, “
Experimental Damage Characterization of Hexagonal Honeycombs Subjected to In-Plane Shear Loading
,”
Proceedings of the ASME International Design Engineering Technical Conferences
, Montreal, Quebec, Canada, Paper No. DETC2010-28549.
37.
Batra
,
R. C.
, 2006,
Elements of Continuum Mechanics
,
1st ed.
,
AIAA, Inc.
,
Reston, Virginia
.
38.
Blatz
,
P. J.
, 1971,
On the Thermostatic Behavior of Elastomers, Polymer Networks, Structure and Mechanical Properties
,
Plenum
,
New York
, pp.
23
45
.
39.
Lopez-Pamies
,
O.
, 2010, “
A New I1-Based Hyperelastic Model for Rubber Elastic Materials
,”
C. R. Mec.
1631-0721,
338
, pp.
3
11
.
40.
Berglind
,
L.
,
Ju
,
J.
, and
Summers
,
J. D.
, 2010, “
Method to Design Honeycombs for a Shear Flexible Structure
,”
Proceedings of the SAE World Congress and Exhibition
, Detroit, MI, Paper No. 10AC-0107.
41.
Larsen
,
U. D.
,
Sigmund
,
O.
, and
Bouwstra
,
S.
, 1997, “
Design and Fabrication of Compliant Micromechanisms and Structures With Negative Poisson’s Ratio
,”
J. Microelectromech. Syst.
1057-7157,
6
(
2
), pp.
99
106
.
42.
Wicks
,
N.
, and
Guest
,
S. D.
, 2004, “
Single Member Actuator in Large Repetitive Truss Structures
,”
Int. J. Solids Struct.
0020-7683,
41
, pp.
965
978
.
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