Wang, G, Liu, Y and Fu, Y (2022) A refined model for the buckling of film/substrate bilayers. Mathematics and Mechanics of Solids. ISSN 1081-2865

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The classical reduced model for film/substrate bilayers is the one in which the film is governed by the Euler–Bernoulli beam equation, and the substrate is replaced by an array of springs (the so-called Winkler foundation assumption). We derive a refined model in which the normal and shear tractions at the bottom of the film are expressed in terms of the corresponding horizontal and vertical displacements, and the response of the half-space is described by the exact theory. The self-consistency of the refined model is confirmed by showing that it yields a four-term (in the incompressible case) or six-term (in the compressible case) expansion for the critical strain that agrees with the expansion given by the exact theory.

Item Type: Article
Additional Information: article is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 License ( which permits non-commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (
Subjects: Q Science > Q Science (General)
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 08 Sep 2022 13:29
Last Modified: 08 Sep 2022 13:29

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