A continuum damage mechanics framework for modeling micro-damage healing

A novel continuum damage mechanics-based framework is proposed to model the micro-damage healing phenomenon in the materials that tend to self-heal. This framework extends the well-known Kachanov’s (1958) effective configuration and the concept of the effective stress space to self-healing materials by introducing the healing natural configuration in order to incorporate the micro-damage healing effects. Analytical relations are derived to relate strain tensors and tangent stiffness moduli in the nominal and healing configurations for each postulated transformation hypothesis (i.e. strain, elastic strain energy, and power equivalence hypotheses). The ability of the proposed model to explain micro-damage healing is demonstrated by presenting several examples. Also, a general thermodynamic framework for constitutive modeling of damage and micro-damage healing mechanisms is presented.