Random Fuse Model in the presence of self-healing

Self-regeneration is a fundamental property of biological materials, leading to enhanced mechanical strength and toughness if subjected to stress and fatigue. Numerous efforts have been devoted to emulate this property and various self-healing materials have been designed with the aim of a practical adoption in construction and mechanical engineering. To achieve this, it is important to understand how damage evolution and fracture propagation are modified by self-healing and to evaluate how mechanical behaviour is affected before failure. In this paper, we implement for the first time a self-healing procedure in the Random Fuse model, whose characteristic scaling properties have been widely studied in the literature on damage evolution modeling. We identify some characteristic signatures of self-healing, showing that it can delay the failure of a material undergoing loading, but it also lead to a hard-to-predict, more catastrophic breakdown.