Quantitative solution on dosage of repair agent for healing of cracks in materials: short capsule model vs. two-dimensional crack pattern

Cracks are vitally detrimental to the load-bearing capacity of materials and further to the durability and service-life of various structures. Crack-repairing technology via embedded capsules with repair agent is becoming a promising approach to sustain the performance of structural materials. However, the appropriate dosage of capsulated repair agent for autonomic healing is not theoretically solved in the literature. In this study, taking cementitious materials as an example, the surface cracks in materials caused by various mechanisms are firstly simplified as linear cracks and zonal cracks in two-dimensional plane. Then, from the viewpoint of geometrical probability, the theoretical solutions on the exact dosage of capsules required are developed for different types of crack models via the knowledge of integral geometry and the concepts of probability distribution. Finally, reliability of these theoretical solutions is verified via computer modeling technology.