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.

Copyright © 2016 by ASME
Topics: Membranes , Adhesion
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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.



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