Mode jumping analysis of thin film secondary wrinkling

• Membrane secondary wrinkling leads to local mode jumping in post-wrinkling stage.
• Wave pattern splitting and equilibrium path reversal are described by maths form.
• Double eigenvalues bifurcate as wrinkling wavelength ratio equals to a critical value.
• Stresses at critical point of primary wrinkling relate to secondary wrinkling directly.
• Secondary wrinkling load is accurately predicted and verified by our non-contact test.

In this paper, a mathematic expression is presented to describe the mode jumping and the equilibrium path reversal characteristics of thin film secondary wrinkling based on the non-linear bifurcation buckling theory. With the usage of variable transformation and the introduction of dimensionless parameters, the non-linear Von-Karman equilibrium equation considering the two-direction loading characteristics, is transformed into a non-linear boundary value problem with zero trivial solution. Based on the bifurcation theory, the eigenvalue problem is addressed through the linearization of non-linear boundary value problem. An approach to critical load prediction of thin film secondary wrinkling is proposed by introducing a critical aspect ratio parameter, since the mechanism of thin film secondary wrinkling is double eigenvalues splitting. Furthermore, this paper presents an analysis in detail on the critical load of the rectangular thin film secondary wrinkling under shear, indicating that the critical load is linearly proportional to the initial stretching displacement, while its relationship with the size of the free edge is nonlinear. The validity of this critical load prediction approach is verified via the digital image correlation experiment. The results provide strong supports for the controlling and tuning of the wrinkles for high precision pre-tensioned thin film structures.

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