LAUSR

Abstract Due to its ability to simulate complex microstructure evolution, the phase-field modeling has been extensively developed to investigate brittle fracture in recent years. However, low computational efficiency still imposes substantial difficulties in the development of phase-field models. In this work, we develop a novel adaptive phase-field approach based on the isogeometric meshfree collocation method (IMCM) to simulate the crack propagation in 2D and 3D polycrystalline materials. The concept of IMCM is based upon the correspondence between the isogeometric collocation and reproducing kernel meshfree method to facilitate a robust mesh adaptivity in isogeometric collocation. The strong form collocation formulation further enhances the computational efficiency of phase-field modeling by reducing the number of point evaluations. The present numerical framework is utilized for the adaptive phase-field modeling which introduces the anisotropy of fracture resistance for each grain in polycrystals. Furthermore, the discrete displacement and phase-field equations are generalized to enable the calculation of both second- and fourth-order gradients, which are required to solve the phase-field models using IMCM. The smoothness and higher-order continuity of IMCM enable the fourth-order phase-field equation to be solved directly without splitting it into two second-order differential equations. The fourth-order model can capture the crack surface accurately with fewer nodes than the second-order model. Several numerical examples of isotropic and anisotropic brittle fracture in polycrystalline materials are investigated to demonstrate the effectiveness and robustness of the proposed approach.