Failure mechanism in stochastic network materials: the competition between fiber and crosslink failure

Materials whose main structural component is a network of fibers are known collectively as Network materials and are ubiquitous in engineering and biology. Their strength is critical in many biological applications and industrial processes. Failure in network materials without embedding matrix or with a fluidic matrix is controlled by the rupture of fibers and crosslinks. This work evaluates the competition between fiber and crosslink rupture mechanisms in defining the network strength. It is shown that a single parameter - the ratio of the crosslink to fiber strengths, ${\Gamma }^C$ - is sufficient to describe this physics. The mechanism dominance transition takes place in the approximate range $0.25<{\Gamma }^c\le 1$ , which is independent of other structural network parameters. The bias of ${\Gamma }^c$ to values somewhat smaller than 1 is due to the fact that in an elastic network in which failure is prevented, fibers carry larger forces than the crosslinks. Network strength is proportional to the strength of the critical component (fibers or crosslinks) and, for the type of networks considered here, is proportional to the square of the network density. This relation applies equally in the parametric regimes in which one mechanism dominates, and in the transition regime. The present data provides insight into the failure mechanism of network materials and the scaling laws relevant in material design.