Size effect and fractal geometry of micro--cracks for disordered materials
无序材料微裂缝分形几何与尺寸效应的微观机理

Two-dimensional displacement discontinuity boundary element method was applied to simulate the mechanical behavior of brittle disordered materials, assuming that the specimens contain identical micro-crack density but with different degrees of disorder of micro-crack size distributions. The micro-mechanism for the size effect of the brittle or quasi-brittle disordered materials is explained by a new point of view of fractal geometry. The numerical simulation results are in good agreement with the Bazant size effect law. The size effect, which is more significant as the degrees of disorder of micro-crack size distribution increases, is related to not only the micro-defects density, but also the degrees of disorder of micro-crack size distribution. In addition, an empirical expression relating the fractal dimension of fracture surface with initial fractal dimension was obtained, which can be used to explain the micro-mechanism of size effect and the micro-crack evolution processes more deeply.