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Research Papers

Analytical and Experimental Studies of the Mechanics of Deformation in a Solid With a Wavy Surface Profile

[+] Author and Article Information
J. Xiao

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

A. Carlson

Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL 61801

Z. J. Liu

 Institute of High Performance Computing, 1 Fusionopolis Way, No. 16-16 Connexis, Singapore 138632, Singapore

Y. Huang

Department of Mechanical Engineering, and Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208

J. A. Rogers

Department of Materials Science and Engineering and Beckman Institute, and Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL 61801

J. Appl. Mech. 77(1), 011003 (Sep 23, 2009) (6 pages) doi:10.1115/1.3132184 History: Received May 27, 2008; Revised December 01, 2008; Published September 23, 2009

The analytical solution is obtained for a semi-infinite linear elastic solid with a sinusoidal, “wavy” surface profile subject to applied strain. The amplitude A of a deformed wavy surface is related to the initial amplitude A0 and the applied strain εa through the simple expression A=A0(1εa). This relation is confirmed independently by finite element analyses and experimental measurements of strained wavy poly(dimethylsiloxane) surfaces. Analytical solutions are also obtained for a wavy solid subject to stretch and lateral displacement.

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Figures

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Figure 1

A solid with wavy surface subject to the applied strain εa. The wavelength is λ and initial amplitude is A0.

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Figure 2

Critical fabrication steps for generating wavy surface profiles in PDMS, (a). Anisotropic etching of a Si (100) wafer yields a saw-tooth surface relief, which after partial smoothing can be replicated through sequential imprinting into layers of PDMS prepolymer (i). The approximately sinusoidal relief can be molded into a layer of SU-8 supported on a plastic substrate (ii), cured, and undergone a final smoothing step. The molded SU-8 is then used as a template for a final PDMS imprinting step, (iii). The resulting PDMS substrate has a sinusoidal profile like that in (b), with a wavelength of 49 μm and tunable peak to valley amplitude.

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Figure 3

The analytical, experimental, and numerical results of amplitude A versus the applied strain εa for a wavy PDMS (E=2 MPa, ν=0.48), with wavelength λ=49 μm and initial amplitudes A0=6.7, 8.4, and 9.7 μm.

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Figure 4

Finite element mesh for the solid with the wavy surface

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Figure 5

Distribution of tangential strain εtt of the wavy surface up to the zeroth-, first-, and second-order normalized by the applied strain εa. The wavelength is λ=49 μm, and initial amplitudes are (a) A0=3 μm and (b) A0=9.7 μm. The results from the finite element analysis are also shown.

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Figure 6

Strain energy/wavelength versus the ratio B/A0 with applied strain εa=0, for the wavelength λ=49 μm and amplitude A0=3 μm

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