Thermodynamic-based cohesive zone healing model for self-healing materials

• Thermodynamic framework for building cohesive zone healing models is presented.
• Continuum damage-healing mechanics is extended for cohesive zone models.
• Cohesive degradation and healing evolution laws have been proposed.
• Internal state variables that describe the bonding within the cohesive zone are proposed.
• Accelerated healing due to pressure tractions on the crack surfaces is considered.

This work presents a thermodynamic-based cohesive zone framework to model healing in materials that tend to self-heal. The nominal, healing and effective configurations of continuum damage-healing mechanics are extended to represent cohesive zone configurations. To incorporate healing in a cohesive zone model, the principle of virtual power is used to derive the local static/dynamic macroforce balance and the boundary traction as well as the damage and healing microforce balances. A thermodynamic framework for constitutive modeling of damage and healing mechanisms of cracks is used to derive the evolution equations for the damage and healing internal state variables. The effects of temperature, resting time, crack closure, history of healing and damage, and level of damage on the healing behavior of the cohesive zone are incorporated. The proposed model promises solid basis for understanding the self-healing phenomena in self-healing materials.