In view of the non-local phenomena appearing in the rock and concrete-like materials, the non-local damage and fracture model of rock and concrete-like materials was established through non-local method of Gaussian weighting function. The result indicates that, the stress of one point in the material is correlated not only to its strain history, but also to the interaction of the points in its certain adjacent region of the material. Based on the established non-local model, the numerical simulation of notch containing three-point bending beam was carried out. The results show that the grid sensitivities have been avoided and the fracture direction of the material has not been influenced by the grid shape, and the model proposed can be used to better simulate the damage developing process of the rock and concrete-like materials.
