CRACKING SIMULATION OF QUASI-BRITTLE MATERIALS BY COMBINING SBFEM WITH NONLOCAL MACRO-MICRO DAMAGE MODEL

Concrete is a typical quasi-brittle material which is widely used in civil engineering and hydraulic engineering. Under the influence of various internal and external factors, cracking is the most commonly encountered failure mode of concrete structure. It is of great importance to accurately simulate the cracking process of structures for the safety evaluation of concrete structures. A new crack initiation and propagation simulation method for quasi-brittle materials is proposed by combing scaled boundary finite element method and nonlocal macro-micro damage model. The scaling centre of the scaled boundary finite element subdomain is taken as the material point. The microscopic damage is defined in terms of the stretch rate of bonds of material points, and then the macro-scale topologic damage is evaluated as the weighted averaging of micro-scale damage over bonds in the influence domain. Through the energetic degradation function, which connects the energy-based damage and the macro-scale topologic damage, the nonlocal macro-micro damage model is inserted into the framework of scaled boundary finite element method. The quadtree mesh discrete technique is used to achieve fast and high-quality multilevel mesh by taking full advantage of the hanging nodes allowed in the scaled boundary finite element mesh. Two typical examples including a mode I and a mixed-mode cracking simulation show that the proposed method can be used to simulate crack initiation and propagation of quasi-brittle materials and capture the correct crack propagation path and load-deformation curve. Compared with other existing methods, using the nonlocal macro-micro damage model in this paper can obtain more accurate local cracking damage zone, and the results are more reasonable with higher calculation accuracy and efficiency. The numerical examples also indicate that there is no mesh sensitivity problem when the mesh size of the damage process region is less than 1/5 of the radius of the influence domain.