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Structural Engineering and Mechanics
  Volume 74, Number 2, April25 2020, pages 215-225
DOI: http://dx.doi.org/10.12989/sem.2020.74.2.215
 


Wrinkling of a homogeneous thin solid film deposited on a functionally graded substrate
Masoud Noroozi

 
Abstract
    Thin films easily wrinkle under compressive loading due to their small bending stiffness resulting from their tiny thickness. For a thin film deposited on a functionally graded substrate with non–uniform stiffness exponentially changes along the length span in this paper, the uniaxial wrinkling problem is solved analytically in terms of hyper–Bessel functions. For infinite, semi–infinite and finite length systems the wrinkling load and wrinkling wavenumber are determined and compared with those in literature. In comparison with a homogeneous substrate–bounded film in which the wrinkling pattern is uniform along the length span, for a functionally graded substrate–film system the wrinkles accumulate around the softer location of the functionally graded substrate. Therefore, the effective length of the film influenced by the wrinkles decreases, the amplitude of the wrinkles on softer regions of the functionally graded substrate grows and the wrinkling load of the functionally graded substrates with higher softening rate decreases more. The results of the current research are expected to be useful in science and technology of thin films and wrinkling of the structures especially living tissues.
 
Key Words
    thin film; substrate; wrinkling; functionally graded materials; hypergeometric function
 
Address
Faculty of Mechatronics, Islamic Azad University (Karaj Branch), Karaj, Iran
 

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