This paper presents a new mechanics-based framework for the qualitative analysis and conceptual design of mechanical metamaterials, and specifically materials exhibiting auxetic behavior. The methodology is inspired by recent advances in the insightful synthesis of compliant mechanisms by visualizing a kinetostatic field of forces that flow through the mechanism geometry. The framework relates load flow in the members of the microstructure to the global material properties, thereby enabling a novel synthesis technique for auxetic microstructures. This understanding is used to qualitatively classify auxetic materials into two classes, namely, high-shear and low-shear microstructures. The ability to achieve additional attributes such as isotropy is shown to be related to the qualitative class that the microstructure belongs.

References

References
1.
Baughman
,
R. H.
,
Shacklette
,
J. M.
,
Zakhidov
,
A. A.
, and
Stafström
,
S.
,
1998
, “
Negative Poisson's Ratios as a Common Feature of Cubic Metals
,”
Nature
,
392
(
6674
), pp.
362
365
.
2.
Ziolkowski
,
R. W.
,
Jin
,
P.
, and
Lin
,
C.-C.
,
2011
, “
Metamaterial-Inspired Engineering of Antennas
,”
Proc. IEEE
,
99
(
10
), pp.
1720
1731
.
3.
Lee
,
S. H.
,
Park
,
C. M.
,
Seo
,
Y. M.
,
Wang
,
Z. G.
, and
Kim
,
C. K.
,
2009
, “
Acoustic Metamaterial With Negative Modulus
,”
J. Phys.: Condens. Matter
,
21
(
17
), p.
175704
.
4.
Evans
,
K. E.
, and
Alderson
,
A.
,
2000
, “
Auxetic Materials: Functional Materials and Structures From Lateral Thinking!
,”
Adv. Mater.
,
12
(
9
), pp.
617
628
.
5.
White
,
L.
,
2009
, “
Auxetic Foam Set for Use in Smart Filters and Wound Dressings
,”
Urethanes Technol. Int.
,
26
(
4
), pp.
34
36
.
6.
Sanami
,
M.
,
Ravirala
,
N.
,
Alderson
,
K.
, and
Alderson
,
A.
,
2014
, “
Auxetic Materials for Sports Applications
,”
Procedia Eng.
,
72
, pp.
453
458
.
7.
Mir
,
M.
,
Ali
,
M. N.
,
Sami
,
J.
, and
Ansari
,
U.
,
2014
, “
Review of Mechanics and Applications of Auxetic Structures
,”
Adv. Mater. Sci. Eng.
,
2014
p.
753496
.
8.
Lakes
,
R.
,
1987
, “
Foam Structures With a Negative Poisson's Ratio
,”
Science
,
235
(
4792
), pp.
1038
1041
.
9.
Almgren
,
R. F.
,
1985
, “
An Isotropic Three-Dimensional Structure With Poisson's Ratio–1
,”
J. Elasticity
,
15
(
4
), pp.
427
430
.
10.
Cherkaev
,
A. V.
,
1995
, “
Which Elasticity Tensors are Realizable?
,”
ASME J. Eng. Mater. Technol.
,
117
(
4
), pp.
483
493
.
11.
Sigmund
,
O.
,
1994
, “
Materials With Prescribed Constitutive Parameters: An Inverse Homogenization Problem
,”
Int. J. Solids Struct.
,
31
(
17
), pp.
2313
2329
.
12.
Bendsøe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.
13.
Sigmund
,
O.
,
2000
, “
A New Class of Extremal Composites
,”
J. Mech. Phys. Solids
,
48
(
2
), pp.
397
428
.
14.
Xia
,
L.
, and
Breitkopf
,
P.
,
2015
, “
Design of Materials Using Topology Optimization and Energy-Based Homogenization Approach in Matlab
,”
Struct. Multidiscip. Optim.
,
52
(
6
), pp.
1229
1241
.
15.
Neves
,
M. M.
,
Rodrigues
,
H.
, and
Guedes
,
J. M.
,
2000
, “
Optimal Design of Periodic Linear Elastic Microstructures
,”
Comput. Struct.
,
76
(
1
), pp.
421
429
.
16.
Vogiatzis
,
P.
,
Chen
,
S.
,
Wang
,
X.
,
Li
,
T.
, and
Wang
,
L.
,
2017
, “
Topology Optimization of Multi-Material Negative Poisson's Ratio Metamaterials Using a Reconciled Level Set Method
,”
Comput.-Aided Des.
,
83
, pp.
15
32
.
17.
Cadman
,
J. E.
,
Zhou
,
S.
,
Chen
,
Y.
, and
Li
,
Q.
,
2013
, “
On Design of Multi-Functional Microstructural Materials
,”
J. Mater. Sci.
,
48
(
1
), pp.
51
66
.
18.
Andreassen
,
E.
,
Lazarov
,
B. S.
, and
Sigmund
,
O.
,
2014
, “
Design of Manufacturable 3D Extremal Elastic Microstructure
,”
Mech. Mater.
,
69
(
1
), pp.
1
10
.
19.
Krishnan
,
G.
,
Kim
,
C.
, and
Kota
,
S.
,
2013
, “
A Kinetostatic Formulation for Load-Flow Visualization in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
5
(
2
), p.
021007
.
20.
Krishnan
,
G.
,
Kim
,
C.
, and
Kota
,
S.
,
2010
, “
Load-Transmitter Constraint Sets—Part II: A Building Block Method for the Synthesis of Compliant Mechanisms
,”
ASME
Paper No. DETC2010-28819.
21.
Krishnan
,
G.
,
Kim
,
C.
, and
Kota
,
S.
,
2010
, “
Load-Transmitter Constraint Sets—Part I: An Effective Tool for Visualizing Load Flow in Compliant Mechanisms and Structures
,”
ASME
Paper No. DETC2010-28810.
22.
Hassani
,
B.
, and
Hinton
,
E.
,
1998
, “
A Review of Homogenization and Topology Optimization—I: Homogenization Theory for Media With Periodic Structure
,”
Comput. Struct.
,
69
(
6
), pp.
707
717
.
23.
Guedes
,
J.
, and
Kikuchi
,
N.
,
1990
, “
Preprocessing and Postprocessing for Materials Based on the Homogenization Method With Adaptive Finite Element Methods
,”
Comput. Methods Appl. Mech. Eng.
,
83
(
2
), pp.
143
198
.
24.
Zhang
,
W.
,
Dai
,
G.
,
Wang
,
F.
,
Sun
,
S.
, and
Bassir
,
H.
,
2007
, “
Using Strain Energy-Based Prediction of Effective Elastic Properties in Topology Optimization of Material Microstructures
,”
Acta Mech. Sin.
,
23
(
1
), pp.
77
89
.
25.
Mehta
,
V.
,
Frecker
,
M.
, and
Lesieutre
,
G. A.
,
2012
, “
Two-Step Design of Multicontact-Aided Cellular Compliant Mechanisms for Stress Relief
,”
ASME J. Mech. Des.
,
134
(
12
), p.
121001
.
26.
Blanding
,
D. K.
,
1999
,
Exact Constraint: Machine Design Using Kinematic Principles
,
ASME Press
,
New York
.
27.
Awtar
,
S.
, and
Slocum
,
A. H.
,
2007
, “
Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms
,”
ASME J. Mech. Des.
,
129
(
8
), pp.
816
830
.
28.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2010
, “
Synthesis of Multi-Degree of Freedom, Parallel Flexure System Concepts Via Freedom and Constraint Topology (FACT)—Part I: Principles
,”
Precis. Eng.
,
34
(
2
), pp.
271
278
.
29.
Satheeshbabu
,
S.
, and
Krishnan
,
G.
,
2016
, “
Qualitative Mobility Analysis of Wire Flexure Systems Using Load Flow Visualization
,”
ASME J. Mech. Rob.
,
8
(
6
), p.
061012
.
30.
Prawoto
,
Y.
,
2012
, “
Seeing Auxetic Materials From the Mechanics Point of View: A Structural Review on the Negative Poisson's Ratio
,”
Comput. Mater. Sci.
,
58
, pp.
140
153
.
31.
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
,
23
(
1
), pp.
95
106
.
32.
Shan
,
S.
,
Kang
,
S. H.
,
Zhao
,
Z.
,
Fang
,
L.
, and
Bertoldi
,
K.
,
2015
, “
Design of Planar Isotropic Negative Poissons Ratio Structures
,”
Extreme Mech. Lett.
,
4
, pp.
96
102
.
33.
Ogden
,
R. W.
,
1997
,
Non-Linear Elastic Deformations
,
Dover Publication
,
Mineola, NY
.
You do not currently have access to this content.