Toward new scaling laws for wrinkling in biologically relevant fiber-reinforced bilayers

Wrinkling, creasing, and folding are frequent phenomena encountered in biological and man-made bilayers made by thin films bonded to thicker and softer substrates often containing fibers. Paradigmatic examples of the latter are the skin, the brain, and arterial walls, for which wiggly cross sections are detected. Although experimental investigations on corrugation of these and analog bilayers would greatly benefit from scaling laws for prompt comparison of the wrinkling features, neither are they available nor have systematic approaches yielding to such laws ever been provided before. This gap is filled in this paper, where a uniaxially compressed bilayer formed by a thin elastic film bonded on a hyperelastic fiber-reinforced substrate is considered. The force balance at the film-substrate interface is here analytically and numerically investigated for highly mismatched film-substrates. The onset of wrinkling is then characterized in terms of both the critical strain and its corresponding wavenumber. Inspired by the asymptotic laws available for neo-Hookean bilayers, the paper then provides a systematic way to achieve novel scaling laws for the wrinkling features for fiber-reinforced highly mismatched hyperelastic bilayers. Such novel scaling laws shed light on the key contributions defining the response of the bilayer, as it is characterized by a fiber-induced complex anisotropy. Results are compared with finite element analyses and also with outcomes of both existing linear models and available ad hoc scalings. Furthermore, the amplitude, the global maximum and minimum of ruga occurring under increasing compression spanning the wrinkling, period doubling, and folding regimes are also obtained.