Abstract

Transferring completed electronic devices onto curvilinear surfaces is popular for fabricating three-dimensional curvilinear electronics with high performance, while the problems of conformality between the unstretchable devices and the surfaces need to be considered. Prior conformability design based on conformal mechanics model is a feasible way to reduce the non-conformal contact. Former studies mainly focused on stretchable film electronics conforming onto soft bio-tissue with a sinusoidal form microscopic morphology or unstretchable film conforming onto rigid sphere substrate, which limits its applicability in the aspect of shapes and modulus of the substrate. Here, a conformal mechanics model with general geometric shape and material is introduced by choosing a bicurvature surface as the target surface, and the conformal contact behavior of film electronics is analyzed. All eight fundamental local surface features are obtained by adjusting two principal curvatures of the bicurvature surface, and the conformal performance is simulated. A dimensionless conformal criterion is given by minimizing the total energy as a function of seven dimensionless parameters, including four in geometric and three in the material. Thickness–width ratio and length–width ratio of flexible electronics are two key geometric parameters that decide the conformal behavior, and smaller thickness–width ratio and length–width ratio are favorite for conformal contact. The model and analysis results are verified by the finite element analysis, and it can guide the prior conformability design of the curvilinear electronic devices during the planar manufacturing process.

References

1.
Jeong
,
H.
,
Wang
,
L.
,
Ha
,
T.
,
Mitbander
,
R.
,
Yang
,
X.
,
Dai
,
Z.
,
Qiao
,
S.
,
Shen
,
L.
,
Sun
,
N.
, and
Lu
,
N.
,
2019
, “
Modular and Reconfigurable Wireless E-Tattoos for Personalized Sensing
,”
Adv. Mater. Technol.
,
4
(
8
), p.
1900117
.
2.
Wang
,
Y. H.
,
Yin
,
L.
,
Bai
,
Y. Z.
,
Liu
,
S. Y.
,
Wang
,
L.
,
Zhou
,
Y.
,
Hou
,
C.
,
Yang
,
Z. Y.
,
Wu
,
H.
,
Ma
,
J. J.
,
Shen
,
Y. X.
,
Deng
,
P. F.
,
Zhang
,
S. C.
,
Duan
,
T. J.
,
Li
,
Z. H.
,
Ren
,
J. H.
,
Xiao
,
L.
,
Yin
,
Z. P.
,
Lu
,
N. S.
, and
Huang
,
Y. A.
,
2020
, “
Electrically Compensated, Tattoo-Like Electrodes for Epidermal Electrophysiology at Scale
,”
Sci. Adv.
,
6
(
43
), p.
eabd0996
.
3.
He
,
J. H.
,
Xie
,
Z. Q.
,
Yao
,
K. M.
,
Li
,
D. F.
,
Liu
,
Y. M.
,
Gao
,
Z.
,
Lu
,
W.
,
Chang
,
L. Q.
, and
Yu
,
X. G.
,
2021
, “
Trampoline Inspired Stretchable Triboelectric Nanogenerators as Tactile Sensors for Epidermal Electronics
,”
Nano Energy
,
81
, p.
105590
.
4.
Hua
,
Q.
,
Sun
,
J.
,
Liu
,
H.
,
Bao
,
R.
,
Yu
,
R.
,
Zhai
,
J.
,
Pan
,
C.
, and
Wang
,
Z. L.
,
2018
, “
Skin-Inspired Highly Stretchable and Conformable Matrix Networks for Multifunctional Sensing
,”
Nat. Commun.
,
9
(
1
), p.
244
.
5.
Zhou
,
Z. H.
,
Chen
,
K.
,
Li
,
X. S.
,
Zhang
,
S. L.
,
Wu
,
Y. F.
,
Zhou
,
Y. H.
,
Meng
,
K. Y.
,
Sun
,
C. C.
,
He
,
Q.
,
Fan
,
W. J.
,
Fan
,
E. D.
,
Lin
,
Z. W.
,
Tan
,
X. L.
,
Deng
,
W. L.
,
Yang
,
J.
, and
Chen
,
J.
,
2020
, “
Sign-to-Speech Translation Using Machine-Learning-Assisted Stretchable Sensor Arrays
,”
Nat. Electron.
,
3
(
9
), pp.
571
578
.
6.
Fastier-Wooller
,
J. W.
,
Dau
,
V.
,
Dinh
,
T.
,
Tran
,
C. D.
, and
Dao
,
D. V.
,
2021
, “
Pressure and Temperature Sensitive e-Skin for In situ Robotic Applications
,”
Mater. Des.
,
208
, p.
109886
.
7.
Wang
,
Y.
,
Qiu
,
L.
,
Luo
,
Y. J.
, and
Ding
,
R.
,
2019
, “
A Stretchable and Large-Scale Guided Wave Sensor Network for Aircraft Smart Skin of Structural Health Monitoring
,”
Struct. Health Monit.
,
20
(
3
), pp.
861
876
.
8.
Huang
,
Y. A.
,
Zhu
,
C.
,
Xiong
,
W. N.
,
Wang
,
Y.
,
Jiang
,
Y. G.
,
Qiu
,
L.
,
Guo
,
D. L.
,
Hou
,
C.
,
Jiang
,
S.
,
Yang
,
Z. X.
,
Wang
,
B.
,
Wang
,
L.
, and
Yin
,
Z. P.
,
2021
, “
Flexible Smart Sensing Skin for “Fly-by-Feel” Morphing Aircraft
,”
Sci. China Technol. Sci.
,
64
, pp.
1
29
.
9.
Xiong
,
W. N.
,
Zhu
,
C.
,
Guo
,
D. L.
,
Hou
,
C.
,
Yang
,
Z. X.
,
Xu
,
Z. Y.
,
Qiu
,
L.
,
Yang
,
H.
,
Li
,
K.
, and
Huang
,
Y. A.
,
2021
, “
Bio-inspired, Intelligent Flexible Sensing Skin for Multifunctional Flying Perception
,”
Nano Energy
,
90
(
Part A
), pp.
106550
.
10.
Sim
,
K.
,
Chen
,
S.
,
Li
,
Z. W.
,
Rao
,
Z. Y.
,
Liu
,
J. S.
,
Lu
,
Y. T.
,
Jang
,
S.
, et al
,
2019
, “
Three-Dimensional Curvy Electronics Created Using Conformal Additive Stamp Printing
,”
Nat. Electron.
,
2
(
10
), pp.
471
479
.
11.
Ko
,
H. C.
,
Shin
,
G.
,
Wang
,
S.
,
Stoykovich
,
M. P.
,
Lee
,
J. W.
,
Kim
,
D. H.
,
Ha
,
J. S.
,
Huang
,
Y.
,
Hwang
,
K. C.
, and
Rogers
,
J. A.
,
2009
, “
Curvilinear Electronics Formed Using Silicon Membrane Circuits and Elastomeric Transfer Elements
,”
Small
,
5
(
23
), pp.
2703
2709
.
12.
Park
,
S.-I.
,
Xiong
,
Y.
,
Kim
,
R.-H.
,
Elvikis
,
P.
,
Meitl
,
M.
,
Kim
,
D.-H.
,
Wu
,
J.
,
Yoon
,
J. S.
,
Yu
,
C. -J.
,
Liu
,
Z. J.
,
Huang
,
Y. G.
,
Hwang
,
K. -C.
,
Ferreira
,
P.
,
Li
,
X. L.
,
Choquette
,
K.
, and
Rogers
,
J. A.
,
2009
, “
Printed Assemblies of Inorganic Light-Emitting Diodes for Deformable and Semitransparent Displays
,”
Science
,
325
(
5943
), pp.
977
981
.
13.
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
.
14.
Cheng
,
H. Y.
, and
Wang
,
S. D.
,
2014
, “
Mechanics of Interfacial Delamination in Epidermal Electronics Systems
,”
ASME J. Appl. Mech.
,
81
(
4
), p.
044501
.
15.
Wang
,
L.
, and
Lu
,
N. S.
,
2016
, “
Conformability of a Thin Elastic Membrane Laminated on a Soft Substrate With Slightly Wavy Surface
,”
ASME J. Appl. Mech.
,
83
(
4
), p.
041007
.
16.
Wang
,
L.
,
Qiao
,
S. T.
,
Ameri
,
S. K.
,
Jeong
,
H.
, and
Lu
,
N. S.
,
2017
, “
A Thin Elastic Membrane Conformed to a Soft and Rough Substrate Subjected to Stretching/Compression
,”
ASME J. Appl. Mech.
,
84
(
11
), p.
111003
.
17.
Cai
,
S. S.
,
Li
,
H. F.
,
Ma
,
Y. J.
, and
Feng
,
X.
,
2019
, “
Conformal Analysis of Epidermal Electronics Bonded Onto Wavy Bio-tissue by Moderately Large Deflection Theory
,”
Mech. Mater.
,
134
(
11
), pp.
61
68
18.
Dong
,
W. T.
,
Xiao
,
L.
,
Zhu
,
C.
,
Ye
,
D.
,
Wang
,
S. D.
,
Huang
,
Y. A.
, and
Yin
,
Z. P.
,
2017
, “
Theoretical and Experimental Study of 2D Conformability of Stretchable Electronics Laminated Onto Skin
,”
Sci. China Technol. Sci.
,
60
(
9
), pp.
1415
1422
.
19.
Majidi
,
C.
, and
Fearing
,
R. S.
,
2008
, “
Adhesion of an Elastic Plate to a Sphere
,”
Proc. R. Soc. London, Ser. A
,
464
(
2093
), pp.
1309
1317
.
20.
Hure
,
J.
, and
Audoly
,
B.
,
2013
, “
Capillary Buckling of a Thin Film Adhering to a Sphere
,”
J. Mech. Phys. Solids
,
61
(
2
), pp.
450
471
.
21.
Zhou
,
Y. G.
,
Chen
,
Y. L.
,
Liu
,
B.
,
Wang
,
S. T.
,
Yang
,
Z. Y.
, and
Hu
,
M.
,
2015
, “
Mechanics of Nanoscale Wrinkling of Graphene on a Non-developable Surface
,”
Carbon
,
84
, pp.
263
271
.
22.
Chen
,
Y. L.
,
Ma
,
Y.
,
Wang
,
S. T.
,
Zhou
,
Y. G.
, and
Liu
,
H.
,
2016
, “
The Morphology of Graphene on a Non-developable Concave Substrate
,”
Appl. Phys. Lett.
,
108
(
3
), p.
031905
.
23.
Wagner
,
S.
, and
Bauer
,
S.
,
2012
, “
Materials for Stretchable Electronics
,”
MRS Bull.
,
37
(
3
), pp.
207
217
.
24.
Besl
,
P. J.
, and
Jain
,
R. C.
,
1988
, “
Segmentation Through Variable-Order Surface Fitting
,”
ITPAM
,
10
(
2
), pp.
167
192
.
25.
Besl
,
P. J.
, and
Jain
,
R. C.
,
1986
, “
Invariant Surface Characteristics for 3D Object Recognition in Range Images
,”
CVGIP
,
33
(
1
), pp.
33
80
.
26.
Song
,
J.
,
Jiang
,
H.
,
Choi
,
W. M.
,
Khang
,
D. Y.
,
Huang
,
Y.
, and
Rogers
,
J. A.
,
2008
, “
An Analytical Study of Two-Dimensional Buckling of Thin Films on Compliant Substrates
,”
J. Appl. Phys.
,
103
(
1
), p.
014303
.
27.
Grason
,
G. M.
, and
Davidovitch
,
B.
,
2013
, “
Universal Collapse of Stress and Wrinkle-to-Scar Transition in Spherically Confined Crystalline Sheets
,”
Proc. Natl. Acad. Sci. U. S. A.
,
110
(
32
), pp.
12893
12898
.
28.
Mitchell
,
N. P.
,
Koning
,
V.
,
Vitelli
,
V.
, and
Irvine
,
W. T. M.
,
2017
, “
Fracture in Sheets Draped on Curved Surfaces
,”
Nat. Mater.
,
16
(
1
), pp.
89
93
.
29.
Liu
,
G. D.
,
Sun
,
L. J.
, and
Su
,
Y. W.
,
2020
, “
Scaling Effects in the Mechanical System of the Flexible Epidermal Electronics and the Human Skin
,”
ASME J. Appl. Mech.
,
87
(
8
), p.
081007
.
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