The Role of Material Parameters in the Buckling Behavior of Stiff/Soft Bilayer Films

Abstract

A stiff/soft bilayer film is prone to losing surface stability under compression, resulting in various buckling patterns, including wrinkles and period-doubling folds. This phenomenon has attracted considerable attention over the past two decades owing to its potential applications in flexible electronics, strain control, and thin-film property tuning. However, theoretically studying the post-buckling behavior beyond period-doubling folds is a major challenge due to strong nonlinearity, highlighting the need for new models based on alternative approaches. This study clarifies how material parameters control the buckling and post-buckling behavior of stiff/soft bilayer films, with particular emphasis on the thickness ratio, modulus ratio, Poisson’s ratio, and the scaling law for higher-order instability. Rather than treating applied compression as the primary determinant of pattern evolution, we identify the intrinsic geometric and elastic parameters of the bilayer as the main controlling factors. The thickness ratio is highlighted as the dominant geometric parameter governing the onset of local wrinkling, the suppression or delay of secondary period-doubling instability, and the transition between local and global buckling. The modulus ratio and Poisson’s ratio further tune the critical wavelength and critical strain through the effective plane-strain modulus contrast and, together with the thickness ratio, define the equivalent thickness ratio used in the scaling description of the post-buckling instabilities.



Received: 20 January 2026 | Revised: 15 July 2026 | Accepted: 27 July 2026



Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.



Data Availability Statement

Data are available from the corresponding author upon reasonable request.



Author Contribution Statement

Hui He: Conceptualization, Formal analysis, Investigation, Writing – original draft. Yufeng Chen: Methodology, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Writing – review & editing. Xintong Shen: Methodology, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Writing – review & editing. Feng Chen: Resources, Data curation. Zhixiang Wang: Resources, Data curation. Yancheng Meng: Conceptualization, Methodology, Validation, Investigation, Data curation, Writing – original draft, Writing – review & editing, Supervision, Project administration, Funding acquisition.