The very hard and the very soft: Modeling bio-inspired scaled skins using the discrete element method

Abstract Natural protective systems are attracting an increasing amount of attention for their ability to provide simultaneous flexibility and puncture resistance by combining hard and soft materials in mechanically efficient ways. In typical flexible natural armors, a continuous layer of soft material is either covered or embedded with segmented hard scales. The interaction between the hard scales and the softer surrounding materials give rise to unusual and attractive mechanisms which are not fully understood to this day. Here we propose and validate the discrete-element method (DEM) to capture the mechanics of stiff scales on soft substrates including scale-substrate elastic deformations, scale-scale interaction through the substrate, and direct scale-scale interaction by contact. We considered two configurations: (i) hard scales on soft substrates to capture scale tilting and penetration resistance, and (ii) hard scales on soft membranes to study flexural compliance. The computational efficiency of the DEM algorithm allowed for large parametric studies with many combinations of aspect ratio, slant angle, and gap size to identify the best designs in terms of resistance to unstable tilting, coverage, penetration resistance, and flexural compliance. DEM is a promising tool for the design and optimization of fish-skin-like protective structures, also providing new insights into the synergistic role of the hard scales and the soft substrate.