Buckling of a coated elastic half-space when the coating and substrate have similar material properties

Fu, YB; Ciarletta, P

Abstract

This study investigates the buckling of a uni-axially compressed neo-Hookean thin film bonded to a neo-Hookean substrate. Previous studies have shown that the elastic bifurcation is supercritical if r=µf/µs>1.74 and subcritical if r<1.74, where µf and µs are the shear moduli of the film and substrate, respectively. Moreover, existing numerical simulations of the fully nonlinear post-buckling behaviour have all been focused on the regime r>1.74. In this paper, we consider instead a subset of the regime r<1.74, namely when r is close to unity. Four near-critical regimes are considered. In particular, it is shown that, when r>1 and the stretch is greater than the critical stretch (the subcritical regime), there exists a localized solution that arises as the limit of modulated periodic solutions with increasingly longer and longer decaying tails. The evolution of each modulated periodic solution is followed as r is decreased, and it is found that there exists a critical value of r at which the deformation gradient develops a discontinuity and the solution becomes a static shock. The semi-analytical results presented could help future numerical simulations of the fully nonlinear post-buckling behaviour.

Citation

Fu, Y., & Ciarletta, P. (2015). Buckling of a coated elastic half-space when the coating and substrate have similar material properties. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. https://doi.org/10.1098/rspa.2014.0979

• Acceptance Date: Apr 1, 2015
• Publication Date: Jun 8, 2015
• Journal: Proceedings Of The Royal Society A-mathematical Physical And Engineering Sciences
• Print ISSN: 1364-5021
• Electronic ISSN: 1471-2946
• Publisher: The Royal Society
• DOI: https://doi.org/10.1098/rspa.2014.0979
• Keywords: soft materials, bifurcation, film-wrinkling, pattern formation
• Public URL: https://keele-repository.worktribe.com/output/405208
• Publisher URL: https://doi.org/10.1098/rspa.2014.0979