Wrinkling of a thin film-substrate with a shear-lag model at the interface

Abstract

Wrinkling of a thin film-bonded substrate under compressive loading has attracted great attention of many researchers due to various applications in soft tissues, polymer industry, engineering, and medical science. The interaction between the film and its substrate at the interface has been modeled with different mechanical loading patterns defined by shear-lag theory. For a continuous in-plane loading with an exponential profile along the length span in this paper, the uniaxial wrinkling problem is solved analytically in terms of hypergeometric functions. The results are verified numerically using a finite difference code. For systems with infinite and finite length, the wrinkling loads and wrinkling patterns are determined and compared with those in the literature. In comparison with a constant in-plane loading on the film in which the wrinkling pattern is uniform along the length span, for a variable loading the wrinkles accumulate around the location with greater loads; so the effective length of the film which is impacted by the wrinkling decreases. The results of the current work bring more insights into the wrinkling mechanism of thin-film structures in science, technology, and medicine.