Normal contact of metainterfaces: The roles of finite size and microcontact interactions

The design of contact interfaces that meet quantitatively a specified friction law (friction force vs normal force) is challenging due to the multi-scale and multi-physics nature of contact interactions. Recently, a concept was proposed to address this question in the case of dry elastic microarchitected contact interfaces, so-called metainterfaces. These take their macroscopic friction properties from an array of discrete asperities whose geometrical descriptors are optimized through an inverse design phase. Such design is based on the experimentally-observed proportionality between friction force and real contact area under pure compression, reducing the friction problem to a simpler contact mechanics problem of designing the contact area. In this context, the design strategy assumes that asperities are placed on a linear elastic half-space and behave independently from each other. Both assumptions are likely to fail in experimental realizations of metainterfaces, potentially inducing discrepancies between the actual and target behaviours. Here, we use full 3D finite element modelling to critically assess the validity of those two assumptions in existing experimental metainterfaces, and their potential impact on the design quality. The results first confirm the validity of the strategy, in the conditions in which it was used in the literature. Then, by systematically varying the spatial arrangement of asperities, their interdistance and the size of their elastic base, we identify conditions under which the literature assumptions fail. Our findings provide critical insights into the robustness and practical limitations of the metainterface design strategy and guidelines for its future improvements.