Statistical continuum damage healing mechanics (SCDHM)

Damage healing mechanics has been under tremendous development during the past decade in which many constitutive models for different classes of materials have been proposed in the literature. However, to bridge the gap between the physics of healing and the theoretical framework, the statistical nature of the damage healing mechanics must be considered. The statistical nature of the crack nucleation and propagation processes is well-known, and the healing mechanisms follow similar probabilistic processes. In general, the healing process consists of two steps: (I) sealing, in which the free crack surfaces are brought in contact with the help of external forces, and then, (ii) healing, which may include a variety of techniques including the flow of molten polymers or liquid healing agents into the crack free surface areas and solidifying. Both sealing and healing processes can be considered within statistical mechanics to include multiple uncertainties involved in the healing process. This work proposes a framework to integrate statistical mechanics into the continuum of damage healing mechanics. The proposed statistical damage healing mechanics may help designers and scientists to perform more realistic simulations for components under complex damage and healing cycles. The key outputs of the proposed statistical framework are (I) healing method choice, and (II) healing parameter optimization.