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Physical Review E

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Contact instabilities of anisotropic and inhomogeneous soft elastic films

Gaurav Tomar^1,* and Ashutosh Sharma²

¹Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
²Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208 016, India

^*gtom@mecheng.iisc.ernet.in

Phys. Rev. E 85, 021603 – Published 15 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.021603

Abstract

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

Article Text

References (28)

H. Hertz, Reine Angew. Math. 92, 156 (1882).
K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London, Ser. A 324, 301 (1971).
B. V. Derjaguin, V. M. Muller, and Y. P. Toporov, J. Colloid Interface Sci. 53, 314 (1975).
W. Mönch and S. Herminghaus, Europhys. Lett. 53, 525 (2001).
V. Shenoy and A. Sharma, Phys. Rev. Lett. 86, 119 (2001).
V. Shenoy and A. Sharma, J. Mech. Phys. Solids 50, 1115 (2002).
C. Q. Ru, ASME J. Appl. Mech. 71, 138 (2004).
S. Q. Huang, Q. Y. Li, X. Q. Feng, and S. W. Yu, Mech. Mater. 38, 88 (2006).
A. Ghatak and M. K. Chaudhury, Langmuir 19, 2621 (2003).
J. Sarkar, A. Sharma, and V. B. Shenoy, Phys. Rev. E. 77, 031604 (2008).
J. Sarkar, A. Sharma, and V. Shenoy, Langmuir 21, 1457 (2005).
J. Sarkar, V. Shenoy, and A. Sharma, Phys. Rev. Lett. 93, 018302 (2004).
R. Mukherjee, A. Sharma, M. Gonuguntla, and G. Patil, J. Nanosci. Nanotech. 8, 3406 (2008).
A. Sharma, M. Gonuguntla, R. Mukherjee, S. A. Subramanian, and R. K. Pangule, J. Nanosci. Nanotech. 7, 1744 (2007).
D. E. Discher, P. Janmey, and Y. Wang, Science 310, 1139 (2005).
N. Arun, J. Sarkar, A. Sharma, V. Shenoy, and K. S. Narayan, J. Adhesion 83, 513 (2007).
A. Oron, S. H. Davis, and S. G. Bankoff, Rev. Mod. Phys. 69, 931 (1997).
A. Sharma, Eur. Phys. J. E 12, 397 (2003).
J. Sarkar and A. Sharma, Langmuir 26, 8464 (2010).
G. Tomar, A. Sharma, V. Shenoy, and G. Biswas, Phys. Rev. E 76, 011607 (2007).
R. Mukherjee, R. Pangule, A. Sharma, and G. Tomar, Adv. Func. Mater. 17, 2356 (2007).
J. Yoon, C. Q. Ru, and A. Mioduchowski, J. Appl. Phys. 98, 113503 (2005).
A. D. Kerr, Ing. Arch. 54, 455 (1984).
X.-H. Pan, S.-Q. Huang, S.-W. Yu, and X.-Q. Feng, J. Phys. D 42, 055302 (2009).
A. Majumdar, A. Ghatak, and A. Sharma, Science 318, 258 (2007).
H. Yao and H. Gao, J. Mech. Phys. Solids 54, 1120 (2006).
X. Wang, Mech. Res. Commun. 35, 181 (2008).
P. Chadwick, Proc. R. Ir. Acad. 93A, 231 (1993).