The use of cellular substrates for stretchable electronics minimizes not only disruptions to the natural diffusive or convective flow of bio-fluids, but also the constraints on the natural motion of the skin. The existing analytic constitutive models for the equivalent medium of the cellular substrate under finite stretching are only applicable for stretching along the cell walls. This paper aims at establishing an analytic constitutive model for the anisotropic equivalent medium of the cellular substrate under finite stretching along any direction. The model gives the nonlinear stress–strain curves of the cellular substrate that agree very well with the finite element analysis (FEA) without any parameter fitting. For the applied strain <10%, the stress–strain curves are the same for different directions of stretching, but their differences become significant as the applied strain increases, displaying the deformation-induced anisotropy. Comparison of the results for linear and nonlinear elastic cell walls clearly suggests that the nonlinear stress–strain curves of the cellular substrate mainly result from the finite rotation of cell walls.

References

References
1.
Khang
,
D. Y.
,
Jiang
,
H. Q.
,
Huang
,
Y.
, and
Rogers
,
J. A.
,
2006
, “
A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates
,”
Science
,
311
(
5758
), pp.
208
212
.
2.
Gonzalez
,
M.
,
Axisa
,
F.
,
BuIcke
,
M. V.
,
Brosteaux
,
D.
,
Vandevelde
,
B.
, and
Vanfleteren
,
J.
,
2008
, “
Design of Metal Interconnects for Stretchable Electronic Circuits
,”
Microelectron. Reliab.
,
48
(
6
), pp.
825
832
.
3.
Jones
,
J.
,
Lacour
,
S. P.
,
Wagner
,
S.
, and
Suo
,
Z. G.
,
2004
, “
Stretchable Wavy Metal Interconnects
,”
J. Vac. Sci. Technol. A
,
22
(
4
), pp.
1723
1725
.
4.
Lacour
,
S. P.
,
Jones
,
J.
,
Wagner
,
S.
,
Li
,
T.
, and
Suo
,
Z. G.
,
2005
, “
Stretchable Interconnects for Elastic Electronic Surfaces
,”
Proc. IEEE
,
93
(
8
), pp.
1459
1467
.
5.
Li
,
Y.
,
Zhang
,
J.
,
Xing
,
Y.
, and
Song
,
J.
,
2017
, “
Thermo-Mechanical Analysis of Epidermal Electronic Devices Integrated With Human Skin
,”
ASME J. Appl. Mech.
,
84
(
11
), p.
111004
.
6.
Avila
,
R.
, and
Xue
,
Y.
,
2017
, “
Torsional Buckling by Joining Prestrained and Unstrained Elastomeric Strips With Application as Bilinear Elastic Spring
,”
ASME J. Appl. Mech.
,
84
(
10
), p.
104502
.
7.
Zhang
,
P.
, and
Parnell
,
W.
,
2017
, “
Band Gap Formation and Tunability in Stretchable Serpentine Interconnects
,”
ASME J. Appl. Mech.
,
84
(
9
), p.
091007
.
8.
Lee
,
C. H.
,
Ma
,
Y. J.
,
Jang
,
K. I.
,
Banks
,
A.
,
Pan
,
T.
,
Feng
,
X.
,
Kim
,
J. S.
,
Kang
,
D.
,
Raj
,
M. S.
,
McGrane
,
B. L.
,
Morey
,
B.
,
Wang
,
X. Y.
,
Ghaffari
,
R.
,
Huang
,
Y. G.
, and
Rogers
,
J. A.
,
2015
, “
Soft Core/Shell Packages for Stretchable Electronics
,”
Adv. Funct. Mater.
,
25
(
24
), pp.
3698
3704
.
9.
Mihai
,
L. A.
, and
Goriely
,
A.
,
2015
, “
Finite Deformation Effects in Cellular Structures With Hyperelastic Cell Walls
,”
Int. J. Solids Struct.
,
53
, pp.
107
128
.
10.
Lee
,
Y. K.
,
Jang
,
K. I.
,
Ma
,
Y. J.
,
Koh
,
A.
,
Chen
,
H.
,
Jung
,
H. N.
,
Kim
,
Y.
,
Kwak
,
J. W.
,
Wang
,
L.
,
Xue
,
Y. G.
,
Yang
,
Y. Y.
,
Tian
,
W. L.
,
Jiang
,
Y.
,
Zhang
,
Y. H.
,
Feng
,
X.
,
Huang
,
Y. G.
, and
Rogers
,
J. A.
,
2017
, “
Chemical Sensing Systems That Utilize Soft Electronics on Thin Elastomeric Substrates With Open Cellular Designs
,”
Adv. Funct. Mater.
,
27
(
9
), p.
1605476
.
11.
Chen
,
H.
,
Zhu
,
F.
,
Jang
,
K. I.
,
Feng
,
X.
,
Rogers
,
J. A.
,
Zhang
,
Y. H.
,
Huang
,
Y.
, and
Ma
,
Y. J.
,
2018
, “
The Equivalent Medium of Cellular Substrate Under Large Stretching, With Applications to Stretchable Electronics
,”
J. Mech. Phys. Solids
, in press.
12.
Chen
,
Y. M.
,
Das
,
R.
, and
Battley
,
M.
,
2016
, “
Response of Honeycombs Subjected to In-Plane Shear
,”
ASME J. Appl. Mech.
,
83
(
6
), p.
061004
.
13.
Gibson
,
L. J.
,
Ashby
,
M. F.
, and
Schajer
,
G. S.
,
1982
, “
The Mechanics of Two-Dimensional Cellular Materials
,”
Proc. R. Soc. Loud. A
,
382
(
1782
), pp.
25
42
.
14.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1997
,
Cellular Solids: Structure and Properties
,
Cambridge University Press
, Cambridge, UK.
15.
Hasanyan
,
A. D.
, and
Waas
,
A. M.
,
2016
, “
Micropolar Constitutive Relations for Cellular Solids
,”
ASME J. Appl. Mech.
,
83
(
4
), p.
041001
.
16.
Mora
,
R. J.
, and
Waas
,
A. M.
,
2007
, “
Evaluation of the Micropolar Elasticity Constants for Honeycombs
,”
Acta Mech.
,
192
(
1–4
), pp.
1
16
.
17.
Petrikovsky
,
B. M.
,
Kaplan
,
G.
, and
Holsten
,
N.
,
2003
, “
Eyelid Movements in Normal Human Fetuses
,”
J. Clinical Ultrasound
,
31
(
6
), pp.
299
301
.
18.
Kim
,
D. H.
,
Lu
,
N. S.
,
Ma
,
R.
,
Kim
,
Y. S.
,
Kim
,
R. H.
,
Wang
,
S. D.
,
Wu
,
J.
,
Won
,
S. M.
,
Tao
,
H.
,
Islam
,
A.
,
Yu
,
K. J.
,
Kim
,
T. I.
,
Chowdhury
,
R.
,
Ying
,
M.
,
Xu
,
L. Z.
,
Li
,
M.
,
Chung
,
H. J.
,
Keum
,
H.
,
McCormick
,
M.
,
Liu
,
P.
,
Zhang
,
Y. W.
,
Omenetto
,
F. G.
,
Huang
,
Y. G.
,
Coleman
,
T.
, and
Rogers
,
J. A.
,
2011
, “
Epidermal Electronics
,”
Science
,
333
(
6044
), pp.
838
843
.
19.
Ma
,
Q.
, and
Zhang
,
Y. H.
,
2016
, “
Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics
,”
ASME J. Appl. Mech.
,
83
(
11
), p.
111008
.
20.
Ma
,
Q.
,
Cheng
,
H. Y.
,
Jang
,
K. I.
,
Luan
,
H. W.
,
Hwang
,
K. C.
,
Rogers
,
J. A.
,
Huang
,
Y. G.
, and
Zhang
,
Y. H.
,
2016
, “
A Nonlinear Mechanics Model of Bio-Inspired Hierarchical Lattice Materials Consisting of Horseshoe Microstructures
,”
J. Mech. Phys. Solids
,
90
, pp.
179
202
.
21.
Mooney
,
M.
,
1940
, “
A Theory of Large Elastic Deformation
,”
J. Appl. Phys.
,
11
(
9
), pp.
582
592
.
22.
Wang
,
S. D.
,
Li
,
M.
,
Wu
,
J.
,
Kim
,
D. H.
,
Lu
,
N. S.
,
Su
,
Y. W.
,
Kang
,
Z.
,
Huang
,
Y. G.
, and
Rogers
,
J. A.
,
2012
, “
Mechanics of Epidermal Electronics
,”
ASME J. Appl. Mech.
,
79
(
3
), p. 031022.
You do not currently have access to this content.