Three-dimensional percolation modeling of self-healing composites

We study the self-healing process of materials with embedded glue-carrying cells, in the regime of the onset of the initial fatigue. Three-dimensional numerical simulations within the percolation-model approach are reported. The main numerical challenge taken up in the present work has been to extend the calculation of the conductance to three-dimensional lattices. Our results confirm the general features of the process: The onset of material fatigue is delayed, by development of a plateaulike time dependence of the material quality. We demonstrate that, in this low-damage regime, the changes in the conductance and thus in similar transport and response properties of the material can be used as measures of the material quality degradation. A new feature found for three dimensions, where it is much more profound than in earlier-studied two-dimensional systems, is the competition between the healing cells. Even for low initial densities of the healing cells, they interfere with each other and reduce each other's effective healing efficiency.