A variational approach to the fracture of brittle thin films subject to out-of-plane loading

•Variational approach to fracture mechanics is extended to thin-film fracture.•Fracture of thin-films subject to out-of-plane loading is studied.•Crack patterns corresponding to experimental observations are predicted.

We address the problem of fracture in homogenous linear elastic thin films using a variational model. We restrict our attention to quasi-static problems assuming that kinetic effects are minimal. We focus on out-of-plane displacement of the film and investigate the effect of bending on fracture. Our analysis is based on a two-dimensional model where the thickness of the film does not need to be resolved. We derive this model through a formal asymptotic analysis. We present numerical simulations in a highly idealized setting for the purpose of verification, as well as more realistic micro-indentation experiments.