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Research Papers

A Thin Elastic Membrane Conformed to a Soft and Rough Substrate Subjected to Stretching/Compression

[+] Author and Article Information
Liu Wang, Shutao Qiao

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

Shideh Kabiri Ameri, Hyoyoung Jeong

Department of Electrical and
Computer Engineering,
The University of Texas at Austin,
Austin, TX 78712

Nanshu Lu

Department of Aerospace Engineering and
Engineering Mechanics,
Center for Mechanics of Solids,
Structures and Materials,
The University of Texas at Austin,
210 E. 24th Street,
Austin, TX 78712;
Department of Electrical and
Computer Engineering,
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 July 24, 2017; final manuscript received August 20, 2017; published online September 12, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(11), 111003 (Sep 12, 2017) (9 pages) Paper No: JAM-17-1401; doi: 10.1115/1.4037740 History: Received July 24, 2017; Revised August 20, 2017

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.

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Figures

Grahic Jump Location
Fig. 1

Schematics of a thin elastic membrane fully conformed to a soft corrugated substrate following two different loading paths: (a) The laminate-stretching path: the membrane first laminates on the substrate and the system is then subjected to lateral strain ϵ0. At equilibrium, the substrate surface is characterized by its semi-amplitude and wavelength, i.e., (h0,λ0) at state 0; (h1,λ1) at state 1; (h2,λ2) at state 2. (b) The stretch-laminating path: the membrane and substrate are first subjected to ϵ0 and then laminated together with ϵ0 still applied. At equilibrium, the substrate surface is characterized by (h0,λ0) at state 0; (H1,λ1) at state 1; (H2,λ2) at state 2.

Grahic Jump Location
Fig. 2

Schematics of a thin elastic membrane partially conformed to a soft corrugated substrate following two different loading paths similar to Fig. 1. (a) The laminate-stretching path: at equilibrium, the substrate is characterized by (xc1,h1,λ1) at state 1; (xc2,h2,λ2) at state 2 where xc reflects the contact zone size. (b) At equilibrium, the substrate is characterized by (H1,λ1) at state 1; (Xc2,H2,λ2) at state 2.

Grahic Jump Location
Fig. 3

(a) Normalized total energy of the system as a function of contact zone variable x̂c1 atstate 1 of Fig. 2(a) with β=0.8,α=15.4, and μ=0.011 fixed. Six different η=0.11,0.12,0.13,0.14,0.15, and 0.21 are plotted where η=0.14 (magenta curve) is the critical membrane thickness for FC. (b) Normalized total energy of the system as a function of contact zone variable x̂c2 at state 2 of Fig. 2(a) with β=0.8,α=15.4, μ=0.011, and η=0.14 fixed. Five different applied strains ϵ0=−0.1,−0.05,0,0.05, and 0.1 are plotted. (c) Critical combinations of η and α for FC according to the FC theory (red curve) and the PC theory (blue, magenta, and black) with β=0.8 and μ=0.011 fixed. (d) Critical membrane thickness for FC as a function of applied strain ϵ0 (The reader is referred to the web version of this paper for the color representation of this figure.)

Grahic Jump Location
Fig. 4

Experimental pictures of PMMA membranes on human skin: (a) membrane of thickness t= 500 nm can fully conform to the skin with or without skin compression, (b) membrane of thickness t = 550 nm fully conforms to relaxed skin but experiences partial delamination under a compression of 10%, and (c) membrane of thickness t = 700 nm cannot form FC even with relaxed skin and more delaminations appear after a compression of 10%. Scale bar indicates 1 mm.

Grahic Jump Location
Fig. 5

Analytical prediction of conformability of PMMA membrane. (a) Normalized total energy of the system as a function of contact zone variable x̂c with β=0.8,α=25384, and μ=0.00092 fixed. At state 1, three thicknesses of PMMA t=500,550, and 700 nm are plotted as solid curves; at state 2 (e.g., ϵ0=−0.25), t=500, and 550 nm are plotted as dashed curves. (b) Conformability as a function of ϵ0 for PMMAs of thicknesses t=500 nm (red) and 550 nm (blue). Snap-through transition from FC to PC is predicted at ϵ0=−0.08 when t=550 nm while PMMA with t=500 nm remains FC throughout the compression up to ϵ0=−0.25 (The reader is referred to the web version of this paper for the color representation of this figure.)

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