Conformability of bio-integrated electronics to soft and microscopically rough biotissues can enhance effective electronics–tissue interface adhesion and can facilitate signal/heat/mass transfer across the interface. When biotissues deform, for example, when skin stretches or heart beats, the deformation may lead to changes in conformability. Although a theory concerning just full conformability (FC) under deformation has been developed (i.e., the FC theory), there is no available theory for partially conformable (PC) systems subjected to deformation. Taking advantage of the path-independent feature of elastic deformation, we find that the total energy of a PC system subjected to stretching or compression can be analytically expressed and minimized. We discover that the FC theory is not sufficient in predicting FC and a full energy landscape obtained by our PC theory is needed for searching for the equilibrium. Our results reveal that stretching enhances conformability while compression degrades it. In addition to predicting the critical parameters to maintain FC under deformation, our PC theory can also be applied to predict the critical compressive strain beyond which FC is lost. Our theory has been validated by laminating poly(methyl methacrylate) (PMMA) membranes of different thicknesses on human skin and inducing skin deformation.
Issue Section:
Research Papers
References
1.
Kim
, D.-H.
, Ghaffari
, R.
, Lu
, N.
, and Rogers
, J. A.
, 2012
, “Flexible and Stretchable Electronics for Biointegrated Devices
,” Annu. Rev. Biomed. Eng.
, 14
, pp. 113
–128
.2.
Lu
, N.
, and Kim
, D.-H.
, 2014
, “Flexible and Stretchable Electronics Paving the Way for Soft Robotics
,” Soft Rob.
, 1
(1
), pp. 53
–62
.3.
Rogers
, J. A.
, Someya
, T.
, and Huang
, Y. G.
, 2010
, “Materials and Mechanics for Stretchable Electronics
,” Science
, 327
(5973
), pp. 1603
–1607
.4.
Lu
, N. S.
, and Yang
, S. X.
, 2015
, “Mechanics for Stretchable Sensors
,” Curr. Opin. Solid State Mater. Sci.
, 19
(3
), pp. 149
–159
.5.
Suo
, Z. G.
, 2012
, “Mechanics of Stretchable Electronics and Soft Machines
,” MRS Bull.
, 37
(3
), pp. 218
–225
.6.
Forrest
, S. R.
, 2004
, “The Path to Ubiquitous and Low-Cost Organic Electronic Appliances on Plastic
,” Nature
, 428
(6986
), pp. 911
–918
.7.
Oh
, J. Y.
, Rondeau-Gagne
, S.
, Chiu
, Y. C.
, Chortos
, A.
, Lissel
, F.
, Wang
, G. J. N.
, Schroeder
, B. C.
, Kurosawa
, T.
, Lopez
, J.
, Katsumata
, T.
, Xu
, J.
, Zhu
, C. X.
, Gu
, X. D.
, Bae
, W. G.
, Kim
, Y.
, Jin
, L. H.
, Chung
, J. W.
, Tok
, J. B. H.
, and Bao
, Z. N.
, 2016
, “Intrinsically Stretchable and Healable Semiconducting Polymer for Organic Transistors
,” Nature
, 539
(7629
), pp. 411
–415
.8.
Akinwande
, D.
, Petrone
, N.
, and Hone
, J.
, 2014
, “Two-Dimensional Flexible Nanoelectronics
,” Nat. Commun.
, 5
, p. 5678.9.
Carlson
, A.
, Bowen
, A. M.
, Huang
, Y. G.
, Nuzzo
, R. G.
, and Rogers
, J. A.
, 2012
, “Transfer Printing Techniques for Materials Assembly and Micro/Nanodevice Fabrication
,” Adv. Mater.
, 24
(39
), pp. 5284
–5318
.10.
Yang
, S.
, Chen
, Y. C.
, Nicolini
, L.
, Pasupathy
, P.
, Sacks
, J.
, Becky
, S.
, Yang
, R.
, Daniel
, S.
, Chang
, Y. F.
, Wang
, P.
, Schnyer
, D.
, Neikirk
, D.
, and Lu
, N.
, 2015
, “ ‘Cut-and-Paste’ Manufacture of Multiparametric Epidermal Sensor Systems
,” Adv. Mater.
, 27
(41
), pp. 6423
–6430
.11.
Fukuda
, K.
, and Someya
, T.
, 2017
, “Recent Progress in the Development of Printed Thin‐Film Transistors and Circuits With High‐Resolution Printing Technology
,” Adv. Mater.
, 29
(25
), p. 1602736.12.
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
.13.
Hammock
, M. L.
, Chortos
, A.
, Tee
, B. C. K.
, Tok
, J. B. H.
, and Bao
, Z. A.
, 2013
, “25th Anniversary Article: The Evolution of Electronic Skin (E-Skin): A Brief History, Design Considerations, and Recent Progress
,” Adv. Mater.
, 25
(42
), pp. 5997
–6037
.14.
Park
, S. I.
, Brenner
, D. S.
, Shin
, G.
, Morgan
, C. D.
, Copits
, B. A.
, Chung
, H. U.
, Pullen
, M. Y.
, Noh
, K. N.
, Davidson
, S.
, and Oh
, S. J.
, 2015
, “Soft, Stretchable, Fully Implantable Miniaturized Optoelectronic Systems for Wireless Optogenetics
,” Nat. Biotechnol.
, 33
(12
), p. 1280
.15.
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
.16.
Jeong
, J.-W.
, Yeo
, W.-H.
, Akhtar
, A.
, Norton
, J. J. S.
, Kwack
, Y.-J.
, Li
, S.
, Jung
, S.-Y.
, Su
, Y.
, Lee
, W.
, Xia
, J.
, Cheng
, H.
, Huang
, Y.
, Choi
, W.-S.
, Bretl
, T.
, and Rogers
, J. A.
, 2013
, “Materials and Optimized Designs for Human-Machine Interfaces Via Epidermal Electronics
,” Adv. Mater.
, 25
(47
), pp. 6839
–6846
.17.
Cheng
, H.
, and Wang
, S.
, 2013
, “Mechanics of Interfacial Delamination in Epidermal Electronics Systems
,” ASME J. Appl. Mech.
, 81
(4
), p. 044501
.18.
Wang
, L.
, and Lu
, N.
, 2016
, “Conformability of a Thin Elastic Membrane Laminated on a Soft Substrate With Slightly Wavy Surface
,” ASME J. Appl. Mech.
, 83
(4
), p. 041007
.19.
Kim
, D.-H.
, Viventi
, J.
, Amsden
, J. J.
, Xiao
, J.
, Vigeland
, L.
, Kim
, Y.-S.
, Blanco
, J. A.
, Panilaitis
, B.
, Frechette
, E. S.
, Contreras
, D.
, Kaplan
, D. L.
, Omenetto
, F. G.
, Huang
, Y.
, Hwang
, K.-C.
, Zakin
, M. R.
, Litt
, B.
, and Rogers
, J. A.
, 2010
, “Dissolvable Films of Silk Fibroin for Ultrathin Conformal Bio-Integrated Electronics
,” Nat. Mater.
, 9
(6
), pp. 511
–517
.20.
Xu
, L.
, Gutbrod
, S. R.
, Bonifas
, A. P.
, Su
, Y.
, Sulkin
, M. S.
, Lu
, N.
, Chung
, H.-J.
, Jang
, K.-I.
, Liu
, Z.
, Ying
, M.
, Lu
, C.
, Webb
, R. C.
, Kim
, J.-S.
, Laughner
, J. I.
, Cheng
, H.
, Liu
, Y.
, Ameen
, A.
, Jeong
, J.-W.
, Kim
, G.-T.
, Huang
, Y.
, Efimov
, I. R.
, and Rogers
, J. A.
, 2014
, “3D Multifunctional Integumentary Membranes for Spatiotemporal Cardiac Measurements and Stimulation Across the Entire Epicardium
,” Nat. Commun.
, 5
, p. 3329.21.
Kim
, D.-H.
, Ghaffari
, R.
, Lu
, N.
, Wang
, S.
, Lee
, S. P.
, Keum
, H.
, D’Angelo
, R.
, Klinker
, L.
, Su
, Y.
, and Lu
, C.
, 2012
, “Electronic Sensor and Actuator Webs for Large-Area Complex Geometry Cardiac Mapping and Therapy
,” Proc. Natl. Acad. Sci.
, 109
(49
), pp. 19910
–19915
.22.
Jeong
, J. W.
, Kim
, M. K.
, Cheng
, H.
, Yeo
, W. H.
, Huang
, X.
, Liu
, Y.
, Zhang
, Y.
, Huang
, Y.
, and Rogers
, J. A.
, 2014
, “Epidermal Electronics: Capacitive Epidermal Electronics for Electrically Safe, Long‐Term Electrophysiological Measurements
,” Adv. Healthcare Mater.
, 3
(5
), p. 621.23.
Dong
, W.
, Xiao
, L.
, Zhu
, C.
, Ye
, D.
, Wang
, S.
, Huang
, Y.
, and Yin
, Z.
, 2017
, “Theoretical and Experimental Study of 2D Conformability of Stretchable Electronics Laminated Onto Skin
,” Sci. China Technol. Sci.
, 60
, pp. 1
–8
.24.
Xiao
, J.
, Carlson
, A.
, Liu
, Z.
, Huang
, Y.
, Jiang
, H.
, and Rogers
, J.
, 2008
, “Stretchable and Compressible Thin Films of Stiff Materials on Compliant Wavy Substrates
,” Appl. Phys. Lett.
, 93
(1
), p. 013109
.25.
Xiao
, J.
, Carlson
, A.
, Liu
, Z. J.
, Huang
, Y.
, and Rogers
, J. A.
, 2010
, “Analytical and Experimental Studies of the Mechanics of Deformation in a Solid With a Wavy Surface Profile
,” ASME J. Appl. Mech.
, 77
(1
), p. 011003
.26.
Huang
, Z. Y.
, Hong
, W.
, and Suo
, Z.
, 2005
, “Nonlinear Analyses of Wrinkles in a Film Bonded to a Compliant Substrate
,” J. Mech. Phys. Solids
, 53
(9
), pp. 2101
–2118
.27.
Tchvialeva
, L.
, Zeng
, H.
, Markhvida
, I.
, McLean
, D. I.
, Lui
, H.
, and Lee
, T. K.
, 2010
, “Skin Roughness Assessment
,” New Developments in Biomedical Engineering
, D.
Campolo
, ed., InTech, Rijeka, Croatia
, pp. 341
–358
.28.
Pailler-Mattei
, C.
, Bec
, S.
, and Zahouani
, H.
, 2008
, “In Vivo Measurements of the Elastic Mechanical Properties of Human Skin by Indentation Tests
,” Med. Eng. Phys.
, 30
(5
), pp. 599
–606
.29.
Meitl
, M. A.
, Zhu
, Z.-T.
, Kumar
, V.
, Lee
, K. J.
, Feng
, X.
, Huang
, Y. Y.
, Adesida
, I.
, Nuzzo
, R. G.
, and Rogers
, J. A.
, 2006
, “Transfer Printing by Kinetic Control of Adhesion to an Elastomeric Stamp
,” Nat. Mater.
, 5
(1
), pp. 33
–38
.30.
Ameri
, S.
, Ho
, R.
, Jang
, H.
, Wang
, Y.
, Schnyer
, D.
, Akinwande
, D.
, and Lu
, N.
, 2016
, “Thinnest Transparent Epidermal Sensor System Based on Graphene
,” IEEE International Electron Devices Meeting
(IEDM
), San Francisco, CA, Dec. 3–7.31.
Kabiri Ameri
, S.
, Ho
, R.
, Jang
, H.
, Tao
, L.
, Wang
, Y.
, Wang
, L.
, Schnyer
, D. M.
, Akinwande
, D.
, and Lu
, N.
, 2017
, “Graphene Electronic Tattoo Sensors
,” ACS Nano
, 11
(8
), pp. 7634
–7641
.32.
Brennan
, C. J.
, Nguyen
, J.
, Yu
, E. T.
, and Lu
, N.
, 2015
, “Interface Adhesion Between 2D Materials and Elastomers Measured by Buckle Delaminations
,” Adv. Mater. Interfaces
, 2
(16
), p. 1500176.33.
Wagner
, T. J.
, and Vella
, D.
, 2012
, “The Sensitivity of Graphene “Snap-Through” to Substrate Geometry
,” Appl. Phys. Lett.
, 100
(23
), p. 233111
.34.
Qiao
, S. T.
, Gratadour
, J. B.
, Wang
, L.
, and Lu
, N. S.
, 2015
, “Conformability of a Thin Elastic Membrane Laminated on a Rigid Substrate With Corrugated Surface
,” IEEE Trans. Compon., Packag., Manuf. Technol.
, 5
(9
), pp. 1237
–1243
.Copyright © 2017 by ASME
You do not currently have access to this content.
