The kinetic approach to fracture in transient networks

We introduce a model describing failure in transient networks. The two main ingredients are (i) the lifetime of a non connecting bond is far smaller than that of an active bond, (ii) the lifetime of an active bond is a decreasing function of the force carried by this bond. We show that these assumptions are sufficient to predict a failure threshold. Below this threshold the bonds distribution is driven by a diffusion equation. The bonds are redistributed homogeneously in the sample, leading to its self-adhesive feature. Beyond this threshold, the diffusion coefficient is negative, causing a catastrophic amplification of any heterogeneity. The final stage is the fracture. Finally, we give an interpretation of delayed fractures for these kinds of materials.