A continuum damage-healing model of healing agents based self-healing materials

In this paper, a continuum damage-healing model is proposed to interpret the damage-healing phenomenon of healing agents based self-healing materials. The plasticity, damage and healing are respectively described by accumulated plastic strain, damage variable and healing variable. Based on the non-equilibrium thermodynamics and the phase field method, the energy dissipation and corresponding kinetic laws of plasticity, damage and healing are respectively obtained. The healing is motivated by the diffusion of healing agents released by capsules or solute atoms. The corresponding process is described by a diffusion equation with chemical reaction. Furthermore, the threshold and the criteria of damage and healing are established for self-healing materials. The theoretical model is then applied to simulate the healing of concentrated and dispersed damage including the cutting damage, the puncture damage, the homogeneous damage under uniaxial tensile stress and the inhomogeneous damage under pure bending. It is demonstrated that the mechanical loading, the accumulated damage and the diffusion of healing agents work together to govern the healing evolution of self-healing materials.