  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.
