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Self-healing is the capability of a material to heal (repair) damages autogenously and autonomously. New theoretical investigation extended from the healing material which represents a strengthening material was recently proposed. It concerns the theory of super healing. The healing in this case continues beyond what is necessary to recover the original stiffness of the material, and the material becomes able to strengthen itself. In the present work, the definition of the super healing theory is extended and defined based on the elastic stiffness variation. It concerns the degradation, recovery, and strengthening of the elastic stiffness in the case of damage, healing, and super healing materials, respectively. Comparison of the healing and super healing efficiencies between the hypotheses of the elastic strain and elastic energy equivalence is carried out. The classical super healing definition is also extended to generalized nonlinear and quadratic super healing based on elastic stiffness strengthening, and comparison of the super healing behavior in each theory is performed. It is found that the hypothesis of the elastic energy equivalence overestimates both the generalized nonlinear and quadratic super healed elastic stiffness strengthening. In addition, the generalized nonlinear super healing theory gives a high strengthening of the super healed elastic stiffness compared to the quadratic super healing theory in both equivalence hypotheses. It is also demonstrated that both the generalized nonlinear and quadratic super healing theories can be applied in the case of plane stress.

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Over the last several years, self-healing materials have become more and more popular in terms of damage reparation. Moreover, a recent theoretical investigation of super healing materials that aims at repairing and strengthening itself was also developed. This research area is well known by the rich experimental studies compared to the numerical investigations. This paper provides a review of the literature of continuum damage-healing and super healing mechanics of brittle materials based on continuum damage and healing mechanics. This review includes various damage-healing models, methodologies, hypotheses and advances in continuum damage and healing mechanics. The anisotropic formulations of damage and healing mechanics are also highlighted. The objective of this paper is also to review the super healing theory based on continuum damage-healing mechanics and its role in material and structure strengthening. Finally, a conclusion of the reviewed damage-healing models is pointed out and future perspectives are given.

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