Trans-scale surface wrinkling model and scaling relationship analysis of stiff film-compliant substrate structures

The self-assembly of surface-order structures based on the surface wrinkling of stiff film-compliant substrate structures (SFCS) is potentially useful in the fabrication of functional devices, the manufacture of superhydrophobic or self-cleaning surfaces, and so on. Due to the influence of the intrinsic characteristic length (g), the surface wrinkling behavior of SFCS at the micro scale is different from that at the macro scale. In this work, based on the strain gradient theory, a trans-scale surface wrinkling model for SFCS is established. First, the effectiveness of this model is verified by previous experiments. Then, based on the model and dimensional analysis, the effect of gon the surface wrinkling behavior is investigated, and the scaling relationship of surface wrinkling of SFCS at different scales is analyzed. The results show that the influence of gcannot be neglected when the film thickness decreases to the one comparable to g. At the micro scale, gwill lead to the increase of the critical wrinkling wavelength and load. In addition, the scaling relationship of surface wrinkling at the micro scale will not follow the traditional one. Our study explains the underlying mechanism of the dissimilarity of surface wrinkling behaviors of SFCS at different scales and lays a theoretical foundation for the precise control of surface-order structures.