Research Papers

Analysis of Sinusoidal Interfacial Wrinkling of an Anisotropic Film Sandwiched Between Two Compliant Layers

[+] Author and Article Information
J. W. Yang

Institute of Applied Mechanics,
School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China

G. H. Nie

Institute of Applied Mechanics,
School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China
e-mail: ghnie@tongji.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 26, 2014; final manuscript received July 6, 2014; accepted manuscript posted July 9, 2014; published online July 21, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(9), 091013 (Jul 21, 2014) (11 pages) Paper No: JAM-14-1227; doi: 10.1115/1.4027974 History: Received May 26, 2014; Revised July 06, 2014; Accepted July 09, 2014

When a stiff film is bonded to a compliant layer and meanwhile encapsulated by another compliant layer on top, the film may form wrinkles under applied compressive stress. Inspired by the recent development of foldable circuit sealed in an encapsulating layer to improve bendability, unlike the wide study of surface wrinkling in a bilayer system, this paper presents a study of possible sinusoidal interfacial wrinkling in such sandwich system. The film is assumed to be anisotropic with arbitrary orientation of elastic axis while both layers are isotropic. A linear perturbation analysis is performed to predict critical membrane stress, wave number and equilibrium amplitude for the onset of interfacial wrinkles. The effect of parameters such as elastic axis orientation of the film and moduli, thicknesses, and Poisson's ratios of the layers on the wrinkling is evaluated in detail. The results show that compared to two compliant layers, the stiffer and thinner the film is, the smaller the values of both the critical stress and wave number for wrinkling will be. Especially, we illustrate three limiting cases: two layers both reach thick-layer limit, two layers both reach thin-layer limit and one layer reaches thick-layer limit while the other layer reaches thin-layer limit. Analytical solutions are obtained for first two cases and numerical solutions are plotted for the third case. It is found that as long as the thin-layer is near incompressible, the interfacial wrinkles can be suppressed. In addition, the equilibrium wave modes for the three limiting cases are also given. The resulting solutions for the sandwich system can be reduced to the classic solutions for a bilayer system.

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Bowden, N., Brittain, S., Evans, A. G., Hutchinson, J. W., and Whitesides, G. M., 1998, “Spontaneous Formation of Ordered Structures in Thin Films of Metals Supported on an Elastomeric Polymer,” Nature, 393(6681), pp. 146–149. [CrossRef]
Chan, E. P., and Crosby, A. J., 2006, “Spontaneous Formation of Stable Aligned Wrinkling Patterns,” Soft Matter, 2(4), pp. 324–328. [CrossRef]
Genzer, J., and Groenewold, J., 2006, “Soft Matter With Hard Skin: From Skin Wrinkles to Templating and Material Characterization,” Soft Matter, 2(4), pp. 310–323. [CrossRef]
Huck, W. T., Bowden, N., Onck, P., Pardoen, T., Hutchinson, J. W., and Whitesides, G. M., 2000, “Ordering of Spontaneously Formed Buckles on Planar Surfaces,” Langmuir, 16(7), pp. 3497–3501. [CrossRef]
Moon, M. W., Lee, S. H., Sun, J. Y., Oh, K. H., Vaziri, A., and Hutchinson, J. W., 2007, “Wrinkled Hard Skins on Polymers Created by Focused Ion Beam,” Proc. Natl. Acad. Sci. USA, 104(4), pp. 1130–1133. [CrossRef]
Li, B., Cao, Y.-P., Feng, X.-Q., and Gao, H., 2012, “Mechanics of Morphological Instabilities and Surface Wrinkling in Soft Materials: A Review,” Soft Matter, 8(21), pp. 5728–5745. [CrossRef]
Gioia, G., and Ortiz, M., 1997, “Delamination of Compressed Thin Films,” Advances in Applied Mechanics, Vol. 33, J. W.Hutchinson, and T. Y.Wu, eds., Academic Press, San Diego, CA, pp. 119–192.
Hutchinson, J. W., 2001, “Delamination of Compressed Films on Curved Substrates,” J. Mech. Phys. Solids, 49(9), pp. 1847–1864. [CrossRef]
Yin, H., Huang, R., Hobart, K. D., Suo, Z., Kuan, T. S., Inoki, C. K., Shieh, S. R., Duffy, T. S., Kub, F. J., and Sturm, J. C., 2002, “Strain Relaxation of SiGe Islands on Compliant Oxide,” J. Appl. Phys., 91(12), pp. 9716–9722. [CrossRef]
Khang, D.-Y., Rogers, J. A., and Lee, H. H., 2009, “Mechanical Buckling: Mechanics, Metrology, and Stretchable Electronics,” Adv. Funct. Mater., 19(10), pp. 1526–1536. [CrossRef]
Kim, D. H., Ahn, J. H., Choi, W. M., Kim, H. S., Kim, T. H., Song, J., Huang, Y., Liu, Z., Lu, C., and Rogers, J. A., 2008, “Stretchable and Foldable Silicon Integrated Circuits,” Science, 320(5875), pp. 507–511. [CrossRef] [PubMed]
Rogers, J. A., Someya, T., and Huang, Y., 2010, “Materials and Mechanics for Stretchable Electronics,” Science, 327(5973), pp. 1603–1607. [CrossRef] [PubMed]
Jiang, H., Khang, D.-Y., Song, J., Sun, Y., Huang, Y., and Rogers, J. A., 2007, “Finite Deformation Mechanics in Buckled Thin Films on Compliant Supports,” Proc. Natl. Acad. Sci. USA, 104(40), pp. 15607–15612. [CrossRef]
Jiang, H., Khang, D.-Y., Fei, H., Kim, H., Huang, Y., Xiao, J., and Rogers, J. A., 2008, “Finite Width Effect of Thin-Films Buckling on Compliant Substrate: Experimental and Theoretical Studies,” J. Mech. Phys. Solids, 56(8), pp. 2585–2598. [CrossRef]
Song, J., Jiang, H., Liu, Z. J., Khang, D. Y., Huang, Y., Rogers, J. A., Lu, C., and Koh, C. G., 2008, “Buckling of a Stiff Thin Film on a Compliant Substrate in Large Deformation,” Int. J. Solids Struct., 45(10), pp. 3107–3121. [CrossRef]
Song, J., Huang, Y., Xiao, J., Wang, S., Hwang, K. C., Ko, H. C., Kim, D. H., Stoykovich, M. P., and Rogers, J. A., 2009, “Mechanics of Noncoplanar Mesh Design for Stretchable Electronic Circuits,” J. Appl. Phys., 105(12), p. 123516. [CrossRef]
Breid, D., and Crosby, A. J., 2009, “Surface Wrinkling Behavior of Finite Circular Plates,” Soft Matter, 5(2), pp. 425–431. [CrossRef]
Yoo, P. J., and Lee, H. H., 2008, “Complex Pattern Formation by Adhesion-Controlled Anisotropic Wrinkling,” Langmuir, 24(13), pp. 6897–6902. [CrossRef] [PubMed]
Chan, E. P., Smith, E. J., Hayward, R. C., and Crosby, A. J., 2008, “Surface Wrinkles for Smart Adhesion,” Adv. Mater., 20(4), pp. 711–716. [CrossRef]
Chan, E. P., and Crosby, A. J., 2006, “Fabricating Microlens Arrays by Surface Wrinkling,” Adv. Mater., 18(24), pp. 3238–3242. [CrossRef]
Chung, J. Y., Nolte, A. J., and Stafford, C. M., 2011, “Surface Wrinkling: A Versatile Platform for Measuring Thin-Film Properties,” Adv. Mater., 23(3), pp. 349–368. [CrossRef] [PubMed]
Stafford, C. M., Harrison, C., Beers, K. L., Karim, A., Amis, E. J., VanLandingham, M. R., Kim, H. C., Volksen, W., Miller, R. D., and Simonyi, E. E., 2004, “A Buckling-Based Metrology for Measuring the Elastic Moduli of Polymeric Thin Films,” Nature Mater., 3(8), pp. 545–550. [CrossRef]
Chen, X., and Hutchinson, J. W., 2004, “A Family of Herringbone Patterns in Thin Films,” Scr. Mater., 50(6), pp. 797–801. [CrossRef]
Chen, X., and Hutchinson, J. W., 2004, “Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates,” ASME J. Appl. Mech., 71(5), pp. 597–603. [CrossRef]
Yoo, P., and Lee, H., 2003, “Evolution of a Stress-Driven Pattern in Thin Bilayer Films: Spinodal Wrinkling,” Phys. Rev. Lett., 91(15), p. 154502. [CrossRef] [PubMed]
Yoo, P., Suh, K., Kang, H., and Lee, H., 2004, “Polymer Elasticity-Driven Wrinkling and Coarsening in High Temperature Buckling of Metal-Capped Polymer Thin Films,” Phys. Rev. Lett., 93(3), p. 034301. [CrossRef] [PubMed]
Cai, S., Breid, D., Crosby, A. J., Suo, Z., and Hutchinson, J. W., 2011, “Periodic Patterns and Energy States of Buckled Films on Compliant Substrates,” J. Mech. Phys. Solids, 59(5), pp. 1094–1114. [CrossRef]
Audoly, B., and Boudaoud, A., 2008, “Buckling of a Stiff Film Bound to a Compliant Substrate—Part I,” J. Mech. Phys. Solids, 56(7), pp. 2401–2421. [CrossRef]
Cerda, E., and Mahadevan, L., 2003, “Geometry and Physics of Wrinkling,” Phys. Rev. Lett., 90(7), p. 074302. [CrossRef] [PubMed]
Cerda, E., Ravi-Chandar, K., and Mahadevan, L., 2002, “Thin Films—Wrinkling of an Elastic Sheet Under Tension,” Nature, 419(6907), pp. 579–580. [CrossRef] [PubMed]
Huang, R., and Suo, Z., 2002, “Wrinkling of a Compressed Elastic Film on a Viscous Layer,” J. Appl. Phys., 91(3), pp. 1135–1142. [CrossRef]
Huang, R., and Suo, Z., 2002, “Instability of a Compressed Elastic Film on a Viscous Layer,” Int. J. Solids Struct., 39(7), pp. 1791–1802. [CrossRef]
Im, S., and Huang, R., 2008, “Wrinkle Patterns of Anisotropic Crystal Films on Viscoelastic Substrates,” J. Mech. Phys. Solids, 56(12), pp. 3315–3330. [CrossRef]
Im, S. H., and Huang, R., 2005, “Evolution of Wrinkles in Elastic-Viscoelastic Bilayer Thin Films,” ASME J. Appl. Mech., 72(6), pp. 955–961. [CrossRef]
Huang, R., 2005, “Kinetic Wrinkling of an Elastic Film on a Viscoelastic Substrate,” J. Mech. Phys. Solids, 53(1), pp. 63–89. [CrossRef]
Cheng, H., Zhang, Y., Hwang, K.-C., Rogers, J. A., and Huang, Y., “Buckling of a Stiff Thin Film on a Pre-Strained Bi-Layer Substrate,” Int. J. Solids Struct., 51(18), pp. 3113–3118. [CrossRef]
Allen, H. G., 1969, Analysis and Design of Structured Sandwich Panels, Pergamon, New York.
Niu, K., and Talreja, R., 1999, “Modeling of Wrinkling in Sandwich Panels Under Compression,” J. Eng. Mech., 125(8), pp. 875–883. [CrossRef]
Birman, V., 2004, “Wrinkling of Composite-Facing Sandwich Panels Under Biaxial Loading,” J. Sandwich Struct. Mater., 6(3), pp. 217–237. [CrossRef]
Laudau, L. D., and Lifshitz, E. M., 1959, Theory of Elasticity, Pergamon, London.
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]


Grahic Jump Location
Fig. 1

(a) Schematics of undeformed sandwich system that a stiff film is in between of two finite-thickness compliant layers which in turn are bonded to rigid supports. (b) Deformed sandwich system that film forms interfacial wrinkles with wavelength described as λ and the wave number can be calculated as k = 2π/λ.

Grahic Jump Location
Fig. 2

(a) Schematics of in-plane elastic axis of anisotropic material labeled as 1,2 and Cartesian coordinates as global coordinates labeled as x,y. The rotate angle between the two set of coordinates is θ, which is also defined as elastic axis orientation angle. (b) The in-plane modulus of film in x direction with variation of θ.

Grahic Jump Location
Fig. 3

The normalized membrane stress as a function of normalized wave number with variations of two layers' (a) moduli, (b) thicknesses, (c) Poisson's ratios, and (d) elastic axis orientation angle of the film

Grahic Jump Location
Fig. 4

The critical normalized membrane stress, wave number and the equilibrium amplitude as a function of thicknesses ratio of the layers and film with variations of both layers' moduli. Left column shows νu = νl = 0.3 and right column shows νu = 0.1,νl = 0.49. The insets show the close-up view of rectangular region in the figure.

Grahic Jump Location
Fig. 5

The effects of elastic axis orientation angle of film on the critical membrane stress and wave number with variations of moduli, thicknesses, and Poisson's ratios of both layers

Grahic Jump Location
Fig. 6

The normalized critical membrane stress and wave number as a function of elastic axis orientation angle of film with variations of moduli and Poisson's ratios of both layers for a film sandwiched between a thick layer and a thin layer

Grahic Jump Location
Fig. 7

The equilibrium wave modes for the three limiting cases when E¯u/C¯¯11 = E¯l/C¯¯11 = 0.01, t/Hu = t/Hl = 10, νu = νl = 0.3, σxx0/C¯¯11 = -0.5




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