From period-doubling to folding in stiff film/soft substrate system: The role of substrate nonlinearity

• The neo-Hookean model is used to describe the nonlinear effect of a substrate, which depends on both the pre-stretch and the external nominal strain.
• The key parameter as called K2K2 in the paper, which is associated with the substrate quadratic nonlinearity, is identified and thoroughly studied; and its role in the formation of post-buckling modes of stiff film/soft substrate system is also revealed.
• That the onset of period-doubling instability is linearly dependent on the substrate pre-stretch, is presented as a major conclusion of our study.

Uniaxial compressed stiff films on soft substrates can evolve into the period-doubling and folding instabilities, beyond the onset of sinusoidal wrinkling. The substrate is modeled as a neo-Hookean solid with a pre-stretch prior to film attachment, and its nonlinearity is obtained. Both the pre-stretch and the external nominal strain imposed on the film/substrate system can induce different substrate nonlinearity, and thus have different effects on the post-buckling mode evolution of the system. This study shows that the critical strain of period-doubling instability is linear to the pre-stretch. As the compressive nominal strain increases, the folding mode occurs beyond the onset of period-doubling in both the pre-tension and the pre-compression case, due to the softening/hardening effects for the inward/outward displacements generated by the positive substrate nonlinearity.