Theoretical and numerical analysis on buckling instability in a thin film sandwiched between two finite-thickness substrates under in-plane compression

• Published in: International journal of solids and structures 2024-11, Vol.304, p.113037, Article 113037
• Main Authors: Yuan, Xuebo, Zhao, Peizhi, Fan, Qiuqiu, Wang, Youshan, Li, Xiangyu
• Format: Article
• Language: English
• Subjects: Analytical model; Buckling mechanics; Layered structures; Stretchable electronics; Thin film
• ISSN: 0020-7683
• DOI: 10.1016/j.ijsolstr.2024.113037

[Display omitted] •Buckling instability of a stiff thin film embedded between two compliant substrates with finite thickness is studied.•The analytical model, considering a complete form of interfacial shear stress, shows higher accuracy than previous models.•Phase diagrams to distinguish global buckling and local wrinkling are constructed through energy analysis.•Effects of finite thicknesses and material properties on the critical condition for local wrinkling are revealed. Capturing the buckling instability mechanics of multi-layered film/substrate structures is essential for providing theoretical guidelines for designing flexible electronics (e.g., stretchable interconnects and strain-limiting structures) and understanding the morphogenesis in biology and geology. Previous buckling models of tri-layer substrate/film/substrate structures usually assumed infinite substrate thickness and incomplete forms of interfacial shear stress, failing to distinguish between local wrinkling and global buckling. In this work, we extend our previous model (Yuan et al., 2023) by accounting for both finite substrate thickness and a complete form of interfacial shear stress, without assuming uniform membrane strain in the film, to study the buckling instability of tri-layer structures. The local wrinkling versus global buckling is distinguished through energy analysis, yielding phase diagrams for a wide range of geometric parameters and material properties. The effects of finite substrate thickness and moduli on the critical compressive strain and wavelength for the onset of local wrinkling are thoroughly investigated. The high accuracy of current model is demonstrated by the excellent agreement between analytical predictions and finite element analysis. This study provides new insights into the stability analysis of substrate/film/substrate systems, and will aid in the design of flexible electronics.