Wrinkling of a film/substrate bilayer with periodic material properties: An assessment of the Winkler foundation model

Fu, Yuxin; Wang, Yue-Sheng; Fu, Yibin

Abstract

The Winkler foundation model is often used to analyze the wrinkling of a film/substrate bilayer under compression, and it can be rigorously justified when both the film and substrate are homogeneous and the film is much stiffer than the substrate. We assess the validity of this model when the substrate is still homogeneous but the film has periodic material properties in the direction parallel to the interface. More precisely, we assume that each unit cell is piecewise homogeneous, and each piece can be described by the Euler-Bernoulli beam theory. We provide analytical results for the critical compression when the substrate is viewed as a Winkler foundation with stiffness modeled either approximately (as in some previous studies) or exactly (using the Floquet theory). The analytical results are then compared with those from Abaqus simulations based on the three-dimensional nonlinear elasticity theory in order to assess the validity of the Euler-Bernoulli beam theory and the Winkler foundation model in the current context.

Citation

Fu, Y., Wang, Y.-S., & Fu, Y. (2024). Wrinkling of a film/substrate bilayer with periodic material properties: An assessment of the Winkler foundation model. International Journal of Non-Linear Mechanics, 166, 1-12. https://doi.org/10.1016/j.ijnonlinmec.2024.104815

• Journal Article Type: Article
• Acceptance Date: Jun 19, 2024
• Online Publication Date: Jun 24, 2024
• Publication Date: 2024-11
• Deposit Date: Jul 4, 2024
• Publicly Available Date: Jul 4, 2024
• Journal: International Journal of Non-Linear Mechanics
• Print ISSN: 0020-7462
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 166
• Article Number: 104815
• Pages: 1-12
• DOI: https://doi.org/10.1016/j.ijnonlinmec.2024.104815
• Keywords: Thin-film/substrate bilayer; Periodic structure; Surface wrinkling; Bifurcation; Nonlinear elasticity
• Public URL: https://keele-repository.worktribe.com/output/870839
• Additional Information: This article is maintained by: Elsevier; Article Title: Wrinkling of a film/substrate bilayer with periodic material properties: An assessment of the Winkler foundation model; Journal Title: International Journal of Non-Linear Mechanics; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.ijnonlinmec.2024.104815; Content Type: article; Copyright: © 2024 The Author(s). Published by Elsevier Ltd.