Wrinkling of a stiff film resting on a fiber-filled soft substrate and its potential application as tunable metamaterials

Abstract

Mechanical self-assembly of ordered patterns via spontaneous buckling of thin-film/soft-substrate systems has received considerable interests in recent years. Here we study the wrinkling of a stiff film resting on a fiber-filled soft substrate. In particular, the effects of the cross-section dimension, spacing, and positions of fibers on the wrinkling patterns in the film/substrate bilayer system are investigated. We show that diverse wrinkling patterns, including sinusoidal wrinkling, period-doubling, period-tripling and mountain ridge modes, may occur at a small or moderate overall compression strain due to the inhomogeneous deformation in the substrate and they can be well controlled by tuning geometrical and physical parameters of the system. To illustrate the potential use of the wrinkling patterns revealed in this study, we investigate the elastic wave propagation in such a wrinkled bilayer using the Bloch wave theory. Our computational results show that diverse stress patterns generated in the soft composites give rise to a rich variety of band structures. Desired bandgaps of elastic waves can be achieved and tuned by simply designing the geometric parameters and controlling the external stimuli imposed on the soft metamaterials.