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Abstract In this paper, the governing equations for the wrinkling of a film sandwiched between two compliant layers are derived based on classical plate theory, first-order shear deformation theory and high-order shear deformation theory, respectively. The two compliant layers are treated as elastic bodies with finite thickness under plane strain condition along one inplane direction. The Airy stress function is then employed to solve the stress field in the two compliant layers subject to clamped and free boundary conditions. With the calculated pressure difference between the upper and lower layers, the governing equations are solved by the linear perturbation method and the critical load expression is thus obtained, which determines the periodic sinusoidal wrinkling of the film. As a validation, the finite element method is also employed to solve the wrinkling of the sandwich structure and the results are compared with our analytical solutions. Good agreement is achieved between the finite element and analytical results. It is shown that, albeit small differences exist, the results obtained based on the classical plate theory can provide sufficient accuracy compared with the shear deformation theories of different orders. Finally, the parameter analysis is conducted to illustrate the influences of boundary conditions, material properties and thicknesses of the film and the compliant layers on the critical loading. The limiting cases, where the thickness of the compliant layers is set to be zero or infinite, are also discussed. The results can serve as guidelines for the optimal designs of various substrate/film structures such as stretchable electronics.
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Received: 22 June 2020
Published: 22 February 2021
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2021, Vol. 42 
