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Modelling and Simulation in Engineering
Volume 2016 (2016), Article ID 5393621, 11 pages
Research Article

Finite Thin Cover on an Orthotropic Elastic Half Plane

1DIEF, Department of Engineering Enzo Ferrari, University of Modena and Reggio Emilia, Via P. Vivarelli 10 Int. 27, 41125 Modena, Italy
2DISMI, Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via Amendola 2, 42122 Reggio Emilia, Italy

Received 24 December 2015; Accepted 5 October 2016

Academic Editor: Julius Kaplunov

Copyright © 2016 Federico Oyedeji Falope and Enrico Radi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present work deals with the mechanical behaviour of thin films bonded to a homogeneous elastic orthotropic half plane under plain strain condition and infinitesimal strain. Both the film and semi-infinite substrate display linear elastic orthotropic behaviour. By assuming perfect adhesion between film and half plane together with membrane behaviour of the film, the compatibility condition between the coating and substrate leads to a singular integral equation with Cauchy kernel. Such an equation is straightforwardly solved by expanding the unknown interfacial stress in series of Chebyshev polynomials displaying square-root singularity at the film edges. This approach allows handling the singular behaviour of the shear stress and, in turn, reducing the problem to a linear algebraic system of infinite terms. Results are found for two loading cases, with particular reference to concentrated axial forces acting at the edges of the film. The corresponding mode II stress intensity factor has been assessed, thus providing the stress concentrations at both ends of the covering. Possible applications of the results here obtained range from MEMS, NEMS, and solar Silicon cell for energy harvesting to welded joint and building foundation.