Effects of pre-stretch, compressibility and material constitution on the period-doubling secondary bifurcation of a film/substrate bilayer

• Published in: International journal of non-linear mechanics 2019-10, Vol.115, p.11-19
• Main Authors: Cai, Z.X., Fu, Y.B.
• Format: Article
• Language: English
• Subjects: Bifurcation; Bifurcations; Compressibility effects; Constitution; Nonlinear elasticity; Period-doubling; Poisson's ratio; Substrates; Thin-film/substrate bilayer; Wrinkling
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2019.05.001

We refine a previously proposed semi-analytical method, and use it to study the effects of pre-stretch, compressibility and material constitution on the period-doubling secondary bifurcation of a uni-axially compressed film/substrate bilayer structure. It is found that compared with the case of incompressible neo-Hookean materials for which the critical strain is approximately 0.17 when the thin layer is much stiffer than the substrate, the critical strain when the Gent materials are used is a monotonically increasing function of the constant Jm that characterizes material extensibility, becoming as small as 0.12 when Jm is equal to 1, whereas for compressible neo-Hookean materials the critical strain is a monotonically decreasing function of Poisson’s ratio; the period-doubling secondary bifurcation seems to become impossible when Poisson’s ratio is approximately equal to 0.307. The latter result may indicate that when Poisson’s ratio is small enough there are other preferred secondary bifurcations — an example is given where a secondary bifurcation mode with 7∕4 times the original period occurs at a lower strain value. The effect of a pre-stretch (compression or extension) in the substrate is not monotonic, giving rise to a critical strain that varies between 0.15 and 0.22. •An improved semi-analytical method for studying period-doubling bifurcation is proposed.•Effects of compressibility, material constitution and a pre-stretch on the critical stretch are clarified.•It is shown that period-doubling secondary bifurcation may give way to other bifurcation modes with different periods in certain parameter regimes.