A high coordination of cross-links in fiber bundles prevents local strain concentrations

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We investigate the influence of the coordination of cross-links on the plastic (i.e., permanent) deformation in cross-linked fiber bundles. Yield strain and strength as well as the resilience are studied as a function of cross-linker and grafting density. It is found that classical twofold coordinated cross-links lead to a pronounced strain concentration in the system, while cross-links with higher coordination allow for a more homogeneous load transfer through the system. This results in inferior mechanical properties related to plastic behavior in the first system compared to the latter. Particularly, in twofold coordinated systems, the resilience shows a non-monotonic behavior with respect to cross-linker density. This means that inserting always more and stronger cross-links do not necessarily improve the mechanical performance of a material. These findings may help to interpret experimental findings on the fracture energy in hydro-gels cross-linked with zinc ions.