An adaptive SBFEM based on a nonlocal macro/meso damage model for fracture simulation of quasibrittle materials

An adaptive scaled-boundary finite element method (SBFEM) is proposed to simulate the crack damage and propagation of quasibrittle materials on the basis of a nonlocal macro/meso damage model. The mesoscopic damage is defined by the deformation of the material bond between the two pairs in the model. First, the structure is discretized via an arbitrary polygon–quadtree mesh. During the damage propagation process, the damage value in each damaged element is determined by the model. Once the damage of an element reaches the damage threshold, the damaged element automatically undergoes mesh refinement until the refined mesh size meets the minimum mesh size requirement. This refinement strategy does not require manual intervention and is automatically implemented by computational software, greatly enhancing the computational efficiency of crack simulation. The transition elements between the refined area and the original elements are discretized using elements with a 2:1 size ratio, ensuring the high quality and efficiency of the automatically subdivided mesh. The nonlinear damage problem is solved iteratively via the arc-length method. The accuracy and efficiency of the proposed algorithm are verified through three numerical examples. The results also indicate that our method is not sensitive to mesh configurations, as commonly encountered in classic local damage mechanics. Moreover, increasing the mesh density results in smoother crack paths and higher computational accuracy.