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 the material fatigue is delayed, by developing a plateau-like time-dependence of the material quality. We demonstrate that in this low-damage regime, the changes in the conductance and thus, in similar transport/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. 
A. Dementsov, V. Privman