Epidermal electronic devices (EEDs) are very attractive in applications of monitoring human vital signs for diagnostic, therapeutic, or surgical functions due to their ability for integration with human skin. Thermomechanical analysis is critical for EEDs in these applications since excessive heating-induced temperature increase and stress may cause discomfort. An axisymmetric analytical thermomechanical model based on the transfer matrix method, accounting for the coupling between the Fourier heat conduction in the EED and the bio-heat transfer in human skin, the multilayer feature of human skin and the size effect of the heating component in EEDs, is established to study the thermomechanical behavior of the EED/skin system. The predictions of the temperature increase and principle stress from the analytical model agree well with those from finite element analysis (FEA). The influences of various geometric parameters and material properties of the substrate on the maximum principle stress are fully investigated to provide design guidelines for avoiding the adverse thermal effects. The thermal and mechanical comfort analyses are then performed based on the analytical model. These results establish the theoretical foundation for thermomechanical analysis of the EED/skin system.

References

References
1.
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
.
2.
Webb
,
R. C.
,
Bonifas
,
A. P.
,
Behnaz
,
A.
,
Zhang
,
Y. H.
,
Yu
,
K. J.
,
Cheng
,
H. Y.
,
Shi
,
M.
,
Bian
,
Z.
,
Liu
,
Z.
,
Kim
,
Y.-S.
,
Yeo
,
W.-H.
,
Park
,
J. S.
,
Song
,
J.
,
Li
,
Y.
,
Huang
,
Y.
,
Gorbach
,
A. M.
, and
Rogers
,
J. A.
,
2013
, “
Ultrathin Conformal Devices for Precise and Continuous Thermal Characterization of Human Skin
,”
Nat. Mater.
,
12
(10), pp.
938
944
.
3.
Lee
,
J. W.
,
Xu
,
R. X.
,
Lee
,
S.
,
Jang
,
K. I.
,
Yang
,
Y. C.
,
Banks
,
A.
,
Yu
,
K. J.
,
Kim
,
J.
,
Xu
,
S.
,
Ma
,
S. Y.
,
Jang
,
S. W.
,
Won
,
P.
,
Li
,
Y. H.
,
Kim
,
B. H.
,
Choe
,
J. Y.
,
Huh
,
S.
,
Kwon
,
Y. H.
,
Huang
,
Y. G.
,
Paik
,
U.
, and
Rogers
,
J. A.
,
2016
, “
Soft, Thin Skin-Mounted Power Management Systems and Their Use in Wireless Thermography
,”
Proc. Natl. Acad. Sci. U. S. A.
,
113
(
22
), pp.
6131
6136
.
4.
Zhang
,
Y. H.
,
Webb
,
R. C.
,
Luo
,
H. Y.
,
Xue
,
Y. G.
,
Kurniawan
,
J.
,
Cho
,
N. H.
,
Krishnan
,
S.
,
Li
,
Y. H.
,
Huang
,
Y. G.
, and
Rogers
,
J. A.
,
2016
, “
Theoretical and Experimental Studies of Epidermal Heat Flux Sensors for Measurements of Core Body Temperature
,”
Adv. Healthcare Mater.
,
5
(
1
), pp.
119
127
.
5.
Webb
,
R. C.
,
Ma
,
Y.
,
Krishnan
,
S.
,
Li
,
Y.
,
Yoon
,
S.
,
Guo
,
X.
,
Feng
,
X.
,
Shi
,
Y.
,
Seidel
,
M.
,
Cho
,
N. H.
,
Kurniawan
,
J.
,
Ahad
,
J.
,
Sheth
,
N.
,
Kim
,
J.
,
Taylor
,
J. G.
,
Darlington
,
T.
,
Chang
,
K.
,
Huang
,
W.
,
Ayers
,
J.
,
Gruebele
,
A.
,
Pielak
,
R. M.
,
Slepian
,
M. J.
,
Huang
,
Y.
,
Gorbach
,
A. M.
, and
Rogers
,
J. A.
,
2015
, “
Epidermal Devices for Noninvasive, Precise, and Continuous Mapping of Macrovascular and Microvascular Blood Flow
,”
Sci. Adv.
,
1
(
9
), p.
e1500701
.
6.
Gao
,
L.
,
Zhang
,
Y. H.
,
Malyarchuk
,
V.
,
Jia
,
L.
,
Jang
,
K. I.
,
Webb
,
R. C.
,
Fu
,
H. R.
,
Shi
,
Y.
,
Zhou
,
G. Y.
,
Shi
,
L. K.
,
Shah
,
D.
,
Huang
,
X.
,
Xu
,
B. X.
,
Yu
,
C. J.
,
Huang
,
Y. G.
, and
Rogers
,
J. A.
,
2014
, “
Epidermal Photonic Devices for Quantitative Imaging of Temperature and Thermal Transport Characteristics of the Skin
,”
Nat. Commun.
,
5
, p.
4938
.
7.
Lee
,
H.
,
Choi
,
T. K.
,
Lee
,
Y. B.
,
Cho
,
H. R.
,
Ghaffari
,
R.
,
Wang
,
L.
,
Choi
,
H. J.
,
Chung
,
T. D.
,
Lu
,
N. S.
,
Hyeon
,
T.
,
Choi
,
S. H.
, and
Kim
,
D. H.
,
2016
, “
A Graphene-Based Electrochemical Device With Thermoresponsive Microneedles for Diabetes Monitoring and Therapy
,”
Nat. Nanotechnol.
,
11
(
6
), pp. 566–572.
8.
Gao
,
W.
,
Emaminejad
,
S.
,
Nyein
,
H. Y. Y.
,
Challa
,
S.
,
Chen
,
K. V.
,
Peck
,
A.
,
Fahad
,
H. M.
,
Ota
,
H.
,
Shiraki
,
H.
,
Kiriya
,
D.
,
Lien
,
D. H.
,
Brooks
,
G. A.
,
Davis
,
R. W.
, and
Javey
,
A.
,
2016
, “
Fully Integrated Wearable Sensor Arrays for Multiplexed In Situ Perspiration Analysis
,”
Nature
,
529
(
7587
), p.
509
.
9.
Li
,
H.
,
Xu
,
Y.
,
Li
,
X.
,
Chen
,
Y.
,
Jiang
,
Y.
,
Zhang
,
C.
,
Lu
,
B.
,
Wang
,
J.
,
Ma
,
Y.
,
Chen
,
Y.
,
Huang
,
Y.
,
Ding
,
M.
,
Su
,
H.
,
Song
,
G.
,
Luo
,
Y.
, and
Feng
,
X.
,
2017
, “
Epidermal Inorganic Optoelectronics for Blood Oxygen Measurement
,”
Adv. Healthcare Mater.
,
6
(9), p.
1601013
.
10.
Dagdeviren
,
C.
,
Su
,
Y. W.
,
Joe
,
P.
,
Yona
,
R.
,
Liu
,
Y. H.
,
Kim
,
Y. S.
,
Huang
,
Y. A.
,
Damadoran
,
A. R.
,
Xia
,
J.
,
Martin
,
L. W.
,
Huang
,
Y. G.
, and
Rogers
,
J. A.
,
2014
, “
Conformable Amplified Lead Zirconate Titanate Sensors With Enhanced Piezoelectric Response for Cutaneous Pressure Monitoring
,”
Nat. Commun.
,
5
, p.
4496
.
11.
Wang
,
C.
,
Hwang
,
D.
,
Yu
,
Z. B.
,
Takei
,
K.
,
Park
,
J.
,
Chen
,
T.
,
Ma
,
B. W.
, and
Javey
,
A.
,
2013
, “
User-Interactive Electronic Skin for Instantaneous Pressure Visualization
,”
Nat. Mater.
,
12
(
10
), pp.
899
904
.
12.
Shi
,
Y.
,
Dagdeviren
,
C.
,
Rogers
,
J. A.
,
Gao
,
C. F.
, and
Huang
,
Y.
,
2015
, “
An Analytical Model for Skin Modulus Measurement Via Conformal Piezoelectric Systems
,”
ASME J. Appl. Mech.
,
82
(
9
), p.
091007
.
13.
Yuan
,
J. H.
,
Shi
,
Y.
,
Pharr
,
M.
,
Feng
,
X.
,
Rogers
,
J. A.
, and
Huang
,
Y.
,
2016
, “
A Mechanics Model for Sensors Imperfectly Bonded to the Skin for Determination of the Young’s Moduli of Epidermis and Dermis
,”
ASME J. Appl. Mech.
,
83
(
8
), p.
084501
.
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.
Liu
,
W.
, 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.
Lu
,
N. S.
,
Zhang
,
Z.
,
Yoon
,
J.
, and
Suo
,
Z. G.
,
2012
, “
Singular Stress Fields at Corners in Flip-Hip Packages
,”
Eng. Fract. Mech.
,
86
, pp.
38
47
.
17.
Huang
,
Y.
,
Yuan
,
J.
,
Zhang
,
Y.
, and
Feng
,
X.
,
2016
, “
Interfacial Delamination of Inorganic Films on Viscoelastic Substrates
,”
ASME J. Appl. Mech.
,
83
(
10
), p.
101005
.
18.
Xu
,
F.
,
Lu
,
T. J.
, and
Steffen
,
K. A.
,
2008
, “
Biothermomechanics of Skin Tissues
,”
J. Mech. Phys. Solids
,
56
(
5
), pp.
1852
1884
.
19.
Xu
,
F.
,
Lu
,
T. J.
,
Steffen
,
K. A.
, and
Ng
,
E. Y. K.
,
2009
, “
Mathematical Modeling of Skin Bioheat Transfer
,”
Appl. Mech. Rev.
,
62
(
5
), p.
050801
.
20.
Song
,
J.
,
Feng
,
X.
, and
Huang
,
Y.
,
2016
, “
Mechanics and Thermal Management of Stretchable Inorganic Electronics
,”
Natl. Sci. Rev.
,
3
(
1
), p.
128
.
21.
Cui
,
Y.
,
Li
,
Y. H.
,
Xing
,
Y. F.
,
Yang
,
T. Z.
, and
Song
,
J. Z.
,
2016
, “
One-Dimensional Thermal Analysis of the Flexible Electronic Devices Integrated With Human Skin
,”
Micromachines
,
7
(
11
), p.
210
.
22.
Cui
,
Y.
,
Li
,
Y. H.
,
Xing
,
Y. F.
,
Ji
,
Q. G.
, and
Song
,
J. Z.
,
2017
, “
Thermal Design of Rectangular Microscale Inorganic Light-Emitting Diodes
,”
Appl. Therm. Eng.
,
122
, pp.
653
660
.
23.
,
C.
,
Li
,
Y.
,
Song
,
J.
,
Kim
,
H. S.
,
Brueckner
,
E.
,
Fang
,
B.
,
Hwang
,
K. C.
,
Huang
,
Y.
,
Nuzzo
,
R. G.
, and
Rogers
,
J. A.
,
2012
, “
A Thermal Analysis of the Operation of Microscale, Inorganic Light-Emitting Diodes
,”
Proc. R. Soc. London A
,
468
(2146), pp.
3215
3223
.
24.
Li
,
Y.
,
Shi
,
Y.
,
Song
,
J.
,
,
C.
,
Kim
,
T.
,
Rogers
,
J. A.
, and
Huang
,
Y.
,
2013
, “
Thermal Properties of Microscale Inorganic Light-Emitting Diodes in a Pulsed Operation
,”
J. Appl. Phys.
,
113
(14), p.
144505
.
25.
Xu
,
F.
,
Seffen
,
K. A.
, and
Lu
,
T. J.
,
2008
, “
Non-Fourier Analysis of Skin Biothermomechanics
,”
Int. J. Heat Mass Transfer
,
51
(9–10), pp.
2237
3704
.
26.
Carslaw
,
H. S.
, and
Jaeger
,
J. C.
,
1959
,
Conduction of Heat in Solids
,
2nd ed.
,
Carendon Press
,
Oxford, UK
.
27.
Lee
,
C. H.
,
Ma
,
Y.
,
Jang
,
K. I.
,
Banks
,
A.
,
Pan
,
T.
,
Feng
,
X.
,
Kim
,
J. S.
,
Kang
,
D.
,
Raj
,
M. S.
,
McGrane
,
B. L.
,
Morey
,
B.
,
Wang
,
X.
,
Ghaffari
,
R.
,
Huang
,
Y.
, and
Rogers
,
J. A.
,
2015
, “
Soft Core/Shell Packages for Stretchable Electronics
,”
Adv. Funct. Mater.
,
25
(24), pp.
3698
3704
.
28.
Xu
,
F.
,
Wen
,
T.
,
Seffen
,
K.
, and
Lu
,
T.
,
2008
, “
Modeling of Skin Thermal Pain: A Preliminary Study
,”
Appl. Math. Comput.
,
205
(1), pp.
37
46
.
You do not currently have access to this content.