An analytical study on the morphology of buckle-delamination under large compression and boundary undulation

Abstract

Spontaneous formation of various buckle-delamination patterns originates from complex interaction between buckles and delamination. However the impact of large compression and delamination boundary undulation on the morphology of buckle-delamination remains a challenge especially from an analytical approach. Here, a nonlinear solution based on the Föppl–von Kármán (FvK) plate theory for buckle-delamination is derived by using a coordinate transformation technique in combination with perturbation series based on Koiter expansion. The analytical results validated by finite element simulations (FEM) show that the sequential sectional profile of straight-sided (SS) blister with asymmetric secondary buckling instability exhibits a butterfly shape dependent on the compression amplitude even when the delamination boundary is straight. Besides, the wavelength for SS blister after the instability drastically changes with the compression amplitude, which is coincident with the experimental results. Our analysis further demonstrates that the elastic energy of the wavy-sided blister can be significantly lower than that of the SS blister even when the initial equi-biaxial compression is a little larger than the Euler buckling stress, significantly lower than the critical stress for secondary buckling instability of SS blisters. This result indicates an alternative mechanism that formation of telephone-cord blister may proceed first by an undulation instability of the delamination boundary.