0
Research Papers

Conformability of a Thin Elastic Membrane Laminated on a Soft Substrate With Slightly Wavy Surface

[+] Author and Article Information
Liu Wang

Center for Mechanics of Solids,
Structures and Materials,
Department of Aerospace Engineering
and Engineering Mechanics,
The University of Texas at Austin,
Austin, TX 78712

Nanshu Lu

Center for Mechanics of Solids,
Structures and Materials,
Department of Aerospace Engineering
and Engineering Mechanics,
The University of Texas at Austin,
Austin, TX 78712;
Department of Biomedical Engineering,
The University of Texas at Austin,
Austin, TX 78712;
Texas Materials Institute,
The University of Texas at Austin,
Austin, TX 78712
e-mail: nanshulu@utexas.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 8, 2015; final manuscript received January 5, 2016; published online January 27, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(4), 041007 (Jan 27, 2016) (9 pages) Paper No: JAM-15-1662; doi: 10.1115/1.4032466 History: Received December 08, 2015; Revised January 05, 2016

When laminating a thin elastic membrane on a substrate with surface roughness, three scenarios can happen: fully conformed (FC), i.e., the membrane completely follows the surface morphology of the substrate without any interfacial gap, nonconformed (NC), i.e., the membrane remains flat if gravity is not concerned, and partially conformed (PC). Good conformability can enhance effective membrane-to-substrate adhesion strength and can facilitate signal/heat/mass transfer across the interface, which are of great importance to soft electronics laminated on rough bio-tissues. To reveal governing parameters in this problem and to predict conformability, energy minimization is implemented after successfully finding the substrate elastic energy under partially conformable contact. Four dimensionless governing parameters involving the substrate roughness, membrane thickness, membrane and substrate elastic moduli, and membrane-to-substrate intrinsic work of adhesion have been identified to analytically predict the conformability status and the area of contact. The analytical prediction has found excellent agreement with experimental observations. In summary, an experimentally validated quantitative guideline for the conformability of elastic membrane on soft corrugated substrate has been established in the four-parameter design space.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Topics: Membranes , Adhesion
Your Session has timed out. Please sign back in to continue.

References

Na, S. R. , Suk, J. W. , Ruoff, R. S. , Huang, R. , and Liechti, K. M. , 2014, “ Ultra Long-Range Interactions Between Large Area Graphene and Silicon,” ACS Nano, 8(11), pp. 11234–11242. [CrossRef] [PubMed]
Hendriks, C. , and Franklin, S. , 2010, “ Influence of Surface Roughness, Material and Climate Conditions on the Friction of Human Skin,” Tribol. Lett., 37(2), pp. 361–373. [CrossRef]
Koenig, S. P. , Boddeti, N. G. , Dunn, M. L. , and Bunch, J. S. , 2011, “ Ultrastrong Adhesion of Graphene Membranes,” Nat. Nanotechnol., 6(9), pp. 543–546. [CrossRef] [PubMed]
Gao, W. , and Huang, R. , 2011, “ Effect of Surface Roughness on Adhesion of Graphene Membranes,” J. Phys. D: Appl. Phys., 44(45), p. 452001. [CrossRef]
Persson, B. , 2003, “ On the Mechanism of Adhesion in Biological Systems,” J. Chem. Phys., 118(16), pp. 7614–7621. [CrossRef]
Persson, B. , and Gorb, S. , 2003, “ The Effect of Surface Roughness on the Adhesion of Elastic Plates With Application to Biological Systems,” J. Chem. Phys., 119(21), pp. 11437–11444. [CrossRef]
Scharfenberg, S. , Rocklin, D. , Chialvo, C. , Weaver, R. L. , Goldbart, P. M. , and Mason, N. , 2011, “ Probing the Mechanical Properties of Graphene Using a Corrugated Elastic Substrate,” Appl. Phys. Lett., 98(9), p. 091908. [CrossRef]
Kim, D.-H. , Ghaffari, R. , Lu, N. , and Rogers, J. A. , 2012, “ Flexible and Stretchable Electronics for Biointegrated Devices,” Annu. Rev. Biomed. Eng., 14(1), pp. 113–128. [CrossRef] [PubMed]
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. [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
Kim, D. H. , Lu, N. , Ma, R. , Kim, Y. S. , Kim, R. H. , Wang, S. , Wu, J. , Won, S. M. , Tao, H. , Islam, A. , Yu, K. J. , Kim, T. I. , Chowdhury, R. , Ying, M. , Xu, L. , Li, M. , Chung, H. J. , Keum, H. , McCormick, M. , Liu, P. , Zhang, Y. W. , Omenetto, F. G. , Huang, Y. , Coleman, T. , and Rogers, J. A. , 2011, “ Epidermal Electronics,” Science, 333(6044), pp. 838–843. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Yeo, W. H. , Kim, Y. S. , Lee, J. , Ameen, A. , Shi, L. , Li, M. , Wang, S. , Ma, R. , Jin, S. H. , and Kang, Z. , 2013, “ Multi-Functional Electronics: Multifunctional Epidermal Electronics Printed Directly Onto the Skin,” Adv. Mater., 25(20), p. 2778.
Huang, X. , Cheng, H. , Chen, K. , Zhang, Y. , Zhang, Y. , Liu, Y. , Zhu, C. , Ouyang, S.-C. , Kong, G.-W. , Yu, C. , Huang, Y. , and Rogers, J. A. , 2013, “ Epidermal Impedance Sensing Sheets for Precision Hydration Assessment and Spatial Mapping,” IEEE Trans. Biomed. Eng., 60(10), pp. 2848–2857. [CrossRef] [PubMed]
Webb, R. C. , Bonifas, A. P. , Behnaz, A. , Zhang, Y. H. , Yu, K. J. , Cheng, H. Y. , Shi, M. X. , Bian, Z. G. , Liu, Z. J. , Kim, Y. S. , Yeo, W. H. , Park, J. S. , Song, J. Z. , Li, Y. H. , Huang, Y. G. , 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. [CrossRef] [PubMed]
Choi, S. , Park, J. , Hyun, W. , Kim, J. , Kim, J. , Lee, Y. B. , Song, C. , Hwang, H. J. , Kim, J. H. , Hyeon, T. , and Kim, D. H. , 2015, “ Stretchable Heater Using Ligand-Exchanged Silver Nanowire Nanocomposite for Wearable Articular Thermotherapy,” ACS Nano, 9(6), pp. 6626–6633. [CrossRef] [PubMed]
Hong, S. , Lee, H. , Lee, J. , Kwon, J. , Han, S. , Suh, Y. D. , Cho, H. , Shin, J. , Yeo, J. , and Ko, S. H. , 2015, “ Highly Stretchable and Transparent Metal Nanowire Heater for Wearable Electronics Applications,” Adv. Mater., 27(32), pp. 4744–4751. [CrossRef] [PubMed]
Bandodkar, A. J. , Molinnus, D. , Mirza, O. , Guinovart, T. , Windmiller, J. R. , Valdes-Ramirez, G. , Andrade, F. J. , Schoning, M. J. , and Wang, J. , 2014, “ Epidermal Tattoo Potentiometric Sodium Sensors With Wireless Signal Transduction for Continuous Non-Invasive Sweat Monitoring,” Biosens. Bioelectron., 54, pp. 603–609. [CrossRef] [PubMed]
Huang, X. , Liu, Y. H. , Chen, K. L. , Shin, W. J. , Lu, C. J. , Kong, G. W. , Patnaik, D. , Lee, S. H. , Cortes, J. F. , and Rogers, J. A. , 2014, “ Stretchable, Wireless Sensors and Functional Substrates for Epidermal Characterization of Sweat,” Small, 10(15), pp. 3083–3090. [CrossRef] [PubMed]
Son, D. , Lee, J. , Qiao, S. , Ghaffari, R. , Kim, J. , Lee, J. E. , Song, C. , Kim, S. J. , Lee, D. J. , Jun, S. W. , Yang, S. , Park, M. , Shin, J. , Do, K. , Lee, M. , Kang, K. , Hwang, C. S. , Lu, N. S. , Hyeon, T. , and Kim, D. H. , 2014, “ Multifunctional Wearable Devices for Diagnosis and Therapy of Movement Disorders,” Nat. Nanotechnol., 9(5), pp. 397–404. [CrossRef] [PubMed]
Wagner, T. J. , and Vella, D. , 2012, “ The Sensitivity of Graphene ‘Snap-Through’ to Substrate Geometry,” Appl. Phys. Lett., 100(23), p. 233111. [CrossRef]
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. [CrossRef]
Carbone, G. , Mangialardi, L. , and Persson, B. , 2004, “ Adhesion Between a Thin Elastic Plate and a Hard Randomly Rough Substrate,” Phys. Rev. B, 70(12), p. 125407. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Cheng, H. , and Wang, S. , 2013, “ Mechanics of Interfacial Delamination in Epidermal Electronics Systems,” ASME J. Appl. Mech., 81(4), p. 044501. [CrossRef]
Tchvialevaa, L. , Zenga, H. , Markhvidaa, I. , McLeana, D. I. , Luia, H. , and Leea, T. K. , 2010, “ Skin Roughness Assessment,” New Developments in Biomedical Engineering, D. Campolo ed., InTech, Vukovar, Croatia, pp. 341–358.
Johnson, K. L. , 1995, “ The Adhesion of Two Elastic Bodies With Slightly Wavy Surfaces,” Int. J. Solids Struct., 32(3–4), pp. 423–430. [CrossRef]
Westergaard, H. , 1939, “ Bearing Pressures and Cracks,” ASME J. Appl. Mech., 66, pp. 49–53.
Koiter, W. , 1959, “ An Infinite Row of Collinear Cracks in an Infinite Elastic Sheet,” Arch. Appl. Mech., 28(1), pp. 168–172.
Zilberman, S. , and Persson, B. , 2002, “ Adhesion Between Elastic Bodies With Rough Surfaces,” Solid State Commun., 123(3), pp. 173–177. [CrossRef]
Jeong, J. W. , Kim, M. K. , Cheng, H. Y. , Yeo, W. H. , Huang, X. , Liu, Y. H. , Zhang, Y. H. , Huang, Y. G. , and Rogers, J. A. , 2014, “ Capacitive Epidermal Electronics for Electrically Safe, Long-Term Electrophysiological Measurements,” Adv. Healthcare Mater., 3(5), pp. 642–648. [CrossRef]
Yu, Y. L. , Sanchez, D. , and Lu, N. S. , 2015, “ Work of Adhesion/Separation Between Soft Elastomers of Different Mixing Ratios,” J. Mater. Res., 30(18), pp. 2702–2712. [CrossRef]
Scharfenberg, S. , Mansukhani, N. , Chialvo, C. , Weaver, R. L. , and Mason, N. , 2012, “ Observation of a Snap-Through Instability in Graphene,” Appl. Phys. Lett., 100(2), p. 021910. [CrossRef]
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. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Three possible conformability status when a thin elastic membrane is laminated on a sinusoidally corrugated substrate: (a) FC, (b) PC, and (c) NC. (d) Schematic of PC scenario with geometric parameters and characteristic points labeled: the initial amplitude and wavelength of the substrate are 2h0 and λ, respectively; after membrane lamination, the substrate surface within the contact zone deforms to a new sinusoidal shape with amplitude 2h1 (not labeled in the figure) and unchanged wavelength; xc is the horizontal projection of the contact zone; and point B denotes the delaminating point.

Grahic Jump Location
Fig. 2

Schematic of traction over the contact area in the presence of adhesion by superposition P(x)=P1(x)+P2(x), where P1(x) is given by Eq. (18) and P2(x) is given by Eq. (19)

Grahic Jump Location
Fig. 3

(a) Schematic of a rigid, slightly wavy surface with periodicity λ touching a flat elastic surface before any deformation. (b) When subjected to uniform external pressure periodic, sinusoidal displacement is induced in the contact zone (−xc < x < xc). (c) Distribution of the bearing pressure, P1(x) as given by Eq. (18), within the contact zone.

Grahic Jump Location
Fig. 4

(a) A row of collinear cracks in an infinite elastic sheet with crack length 2a and interval 2b, subjected to remote tensile stress σ0. (b) Stress distribution over the ligament represents the adhesion stress P2(x) as given by Eq. (19).

Grahic Jump Location
Fig. 5

Normalized total energy landscape of Ecoflex membrane of four different thicknesses (four different η's) laminating on Ecoflex skin replica, where α=1, β=1.2, and μ=0.003. Global minima are labeled by red dots. (a) When η=0.02, x̂c=1, and ξ=0.88, it indicates FC. (b) When η=0.0144, x̂c=0.09, ξ=0.65, it predicts PC. (c) When η=0.4 and (d) when η=2, x̂c=0, and ξ=1, it suggests NC.

Grahic Jump Location
Fig. 6

(a) Surfaces dividing FC/PC and PC/NC when β = 1.2 (i.e., h0=50 μm and λ=250 μm) is fixed. (b) Contact area x̂c versus η on the top or t in the bottom when β=1.2,α=1, and μ=0.003. (c) Contact area x̂c versus μ when β=1.2, α=1, and η=0.12. (d) Contact area  x̂c versus α when β=1.2, μ=0.003, and η=0.12.

Grahic Jump Location
Fig. 7

(a)–(c) Normalized total energy landscape of PI supported electrodes of three different thicknesses (i.e., three different η's) laminated on feline cortex when β=0.13,α=56,000,and μ=2.4×10−4. (a) When η=0.0002, x̂c=1, and ξ=0.9, it indicates FC. (b) When η=0.001, x̂c=0.12, and ξ=0.86, it predicts PC. (c) When η=0.006, x̂c=0, and ξ=1, it suggests NC.(d) Contact area  x̂c versus η on the top or t in the bottom when β=0.06,α=56,000, and μ=2.4×10−4.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In