Wrinkling of a Thin Film-Substrate with Non-Uniform Thickness

Wrinkling of thin films is an important issue in various fields such as skin aging, mechanics of scars, meteorology of the material properties of thin layers, coating of the surfaces, detaching and fracture of the bounded films, civil and military unmanned aerial vehicles and etc. Wrinkles lead to the failure or inappropriate operation of the system in gossamer space structures, optical mirrors, stretchable electronics and wound healing in surgery. Compressive stresses on the film may develop different patterns of wrinkles on the film‒substrate system. The wrinkling of uniform film-substrate systems has been studied by many researchers with a sinusoidal pattern along the film span; while considering the effect of the non-uniformity of the geometry or material properties of the system has not yet well understood. In this work, a thin film is modeled like a strip on an elastic foundation and the wrinkling pattern and critical loads are determined numerically by using a finite difference method. The effect of the non-uniform thickness on the wrinkling pattern is sought for a film with finite length. Unlike the film with uniform thickness, for the film with non‒uniform thickness, the wrinkles accumulate around the location with lower bending rigidity (i.e. thinner regions of the film). The results of the analysis bring more insights into the physics of wrinkling in science and provide effective tools for development of the wrinkling applications in technology.