Microstructural insights into the enigmatic network of random fibers: van Wyk’s notions revisited

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Understanding the structure–property relationships of random materials is a long-standing problem of great interest as their applications span one of the most diverse fields of science and engineering. Polycrystals, polymer blends, foams, fluidized beds, cermets, rocks, fibrous materials, and composites are notable examples of these materials. In random fiber networks, the apparent disconnect between size effects, intricate porous characteristics, and the stochastic nature of constituents, leading to quasi-heterogeneous features, emphasizes the need to explore beyond their microstructure. Herein, we revisit the pioneering work of van Wyk on the architectural-based interfiber spacing model for random fiber networks established via the excluded area and excluded volume approaches. In van Wyk’s original work, the discrepancy between the excluded area and excluded volume frameworks has been ascertained and is now addressed by correlating with classical Bertrand’s paradox. Subsequently, the excluded area and excluded volume approaches of the interfiber spacing model have been modified to account for low-aspect-ratio fibers by including the side-side, end-end, and side-end interactions. van Wyk’s modified interfiber spacing model for low-aspect-ratio fibers has been compared with the other analytical model, developed for random fiber networks. A simple relationship between the maximum volume fraction and aspect ratio has also been deduced for cylindrical fibers. To demonstrate our analytical model’s versatility and wide-ranging applicability, the maximum volume fraction and aspect ratio relationship has been benchmarked with a plethora of analytical models, simulations, and experiments obtained from the literature that resulted in a reasonable agreement.