Imperfection-insensitive flexible random network materials with horseshoe microstructures

Flexible network materials with periodic constructions of bioinspired wavy microstructures are of focusing interest in recent years, because they combine outstanding mechanical performances of low elastic modulus, high stretchability, biomimetic stress-strain responses, and strain-limiting behavior. In practical applications (e.g., bio-integrated devices and tissue engineering), small holes are often strategically designed in flexible network materials to accommodate functional chips and other individual electronic components. The design of imperfection insensitive flexible network materials is therefore of pivotal importance. While random structural constructions are believed to play crucial roles in the excellent mechanical properties of many biological materials, the effect of randomness on mechanical performances of flexible network materials has not yet been explored. In this work, a class of two-dimensional (2D) flexible random network materials consisting of horseshoe microstructures is introduced. Their node distance distributions, which can be characterized by a parameter related to randomness, follow well the Weibull probability density function. Combined numerical and experimental studies were performed to elucidate the effect of randomness on nonlinear mechanical responses of flexible network materials. Simple analytical equations are obtained for their key mechanical properties (e.g., strength, stretchability, and initial modulus). Flexible random network materials (with randomness ≥ 0.4) were found to exhibit approximately isotropic J-shaped stress-strain responses, even in the high-strain regime. Finally, we study the reduction of stretchability and strength in random network materials induced by different types of imperfections (e.g., a missing filament, a missing node, or many missing filaments). In comparison to periodic network materials, random network materials (e.g., with randomness ≥ 0.6) show much smaller reductions of stretchability/strength when the imperfection appears, and are therefore more imperfection-insensitive. Such an imperfection-insensitive behavior can be mainly attributed to a relieved stress concentration around the imperfection of random network materials.