The mechanics of embedded fiber networks

Fiber networks underlie the mechanical behavior of a wide range of natural and engineered materials. Interestingly, these networks are often embedded within amorphous matrices rather than appearing in isolation. However, despite their frequent occurrence as embedded rather than isolated networks, few prior studies have focused on investigating the role of embedding on the emergent mechanical behavior of these systems. To address this, we adopt a mortar -type embedding approach within the finite element framework and perform simulations to systematically fill this knowledge gap. Within this study, we focus on soft tissues as an exemplary class of materials where embedded fiber networks are essential to mechanical function. Specifically, we investigate the role of embedding on the strain energy distribution within the networks across the bending, stretching, torsional, and shear fiber-level loading modes. Therein, we specifically focus on semi-flexible fiber networks. In addition to revealing the role of embedding on the networks themselves, we also investigate how the networks affect the mechanics of the matrix material. Together, we find that embedding fundamentally alters the mechanics of semi-flexible fiber networks and the surrounding matrices. Most importantly, we find that embedding semi-flexible fiber networks leads to strain-stiffening and negative Poynting effect of the resulting composite material. Furthermore, semi-flexible fiber networks induce stress heterogeneity in their host material and increase its resistance to compression. Overall, our work improves our fundamental understanding of an important class of materials. By making our implementation openly available, we also hope to help others learn more about embedded semi-flexible fiber networks in the context of materials other than soft tissues.