Tensional wrinkling of thin elastic sheets with two circular holes

Journal article

A paradigm for the study of wrinkling in elastic sheet is the Lam´e configuration, in which azimuthal wrinkles form in an annular sheet subjected to tensile loads at both edges. Since wrinkles are spatially extended, this instability provides a mechanism for stress transmission over long distances. A natural extension of this problem is wrinkling in sheets with multiple holes or broken symmetry. Here, we investigate tension-induced wrinkling in thin elastic sheets containing two identical circular holes by combining analytical modeling and experiments. The pre-buckled state is solved analytically using bipolar coordinates within the framework of linear elasticity, enabling the identification of the wrinkling threshold as a function of the distance between the two holes. Near-threshold wrinkling and interactions between wrinkles are analyzed, and we validate our theoretical predictions against experimental observations obtained through video imaging of spincoated polystyrene sheets floating on liquid surfaces with controlled surface tension. Our results demonstrate that geometric symmetry breaking, such as the presence of a second hole, strongly influences wrinkle nucleation, orientation, and spatial extent. Beyond mechanics, these findings further support the idea that mechanical cues can be amplified by instabilities and might provide an analogy for long-range cellular mechanosensing.

Authors: Liu, Y; Razavi, S; Cicuta, P; Vella, D; Goriely, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of the Mechanics and Physics of Solids
• Volume: 216
• Article number: 106760
• Publication date: 2026-08-10
• Acceptance date: 2026-07-06
• DOI: 10.1016/j.jmps.2026.106760
• EISSN: 1873-4782
• ISSN: 0022-5096
• Language: English
• Keywords: Ultrathin sheets; bipolar coordinates; elasticity; asymptotic analysis; capillary wrinkling