The self-healing materials have become more and more popular due to their active capacity of repairing the (micro-) damages, such as the (micro-) cracks, the (micro-) voids and the other defects. In this paper, the thermodynamic based damage-healing framework is presented for the hydration induced self-healing composite with a compatible healing variable. The new variable is incorporated to consider the time-dependent properties of the hydration products, with which a new damage healing law is proposed. The hydration kinetics are employed to describe the healing process. The properties of the hydration products are arrived with the multiscale and multilevel homogenization scheme. The presented damage-healing model is applied to an isotropic cementitious composite under the tensile loading histories. The presented framework is compared with the classic continuum damage-healing theory and the experimental data. The results show that the presented damage-healing model is capable of describing the hydration induced self-healing of the cementitious composite. It can describe the behavior of the partially and fully healed concrete material. The effects of the healing time and the compatible healing variables on the damage-healing results are investigated based on our proposed framework.
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