Diversity of the bifurcations and deformations on films bonded to soft substrates: Robustness of the herringbone pattern and its cognate patterns. (February 2022)

• Record Type: Journal Article
• Authors: Kikuchi, Shotaro; Matsubara, Seishiro; Nagashima, So; Okumura, Dai
• Is Part Of: Journal of the mechanics and physics of solids. Volume 159(2022)
• Publication Date: 2022-02
• Subjects: Pattern evolution -- Surface instability -- Buckling -- Bifurcation -- Elastomers; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2021.104757
• Languages: English
• ISSNs: 0022-5096

Abstract

Highlights: 2nd buckling mode diagram depends on Young's modulus ratio & imperfection magnitude. Rectangular checkerboard & stripe modes give a family of herringbone patterns. Superposition of identical modes in symmetric directions generates cognate modes. Cognate modes reveal existence of diverse patterns cognate with herringbone pattern. Robustness of herringbone patterns & diversity of cognate patterns are elucidated. Abstract: In this study, we investigate the diversity of the bifurcations and deformations during evolution of periodic patterns on compressed films bonded to compliant substrates. Three-dimensional finite element analysis is performed assuming that the first bifurcation has either the hexagonal or square (i.e., checkerboard) dimple mode. Step-by-step eigenvalue buckling analysis is performed to explore sequential bifurcations on the bifurcated paths. It is found that at the second bifurcation, a rectangular checkerboard or stripe mode occurs depending not only on the Young's modulus ratio of the film and substrate, but also on the magnitude of the imperfection prescribed by the first bifurcation mode. Different bifurcation modes give a family of herringbone deformation patterns with different dimensions, i.e., the evolutional process is multiple and robust. Further, superposition of the identical modes in symmetric directions elucidates the existence of distinctive patterns cognate with the herringbone pattern, including a variety of experimentally observed patterns.