Statistical analysis of brittle solid damage based on network model

A theoretical model of microcrack nucleation and growth is proposed based on the network model. The corresponding damage evolution law of the brittle solid under constant tensile stress is obtained by means of mesoscopic statistical analysis. Furthermore, a statistical strength distribution of damaged materials is deduced according to the weakest link concept. The results indicate that the strength distribution is related to the damage extent in the materials and nonlinearly dependent on the local stress concentration at the crack tip. A theoretical relation between the damage and the average strength of the damaged material is proposed.