Cell-based smoothed finite element method for modelling interfacial cracks with non-matching grids

Abstract

Problems involving material interfaces are challenging, owing to the cumbersome requirements in meshing such as a fine matching mesh on both sides of the interface. Often one does not require very fine meshes on either side of the interface owing to different geometric and material properties. If the interface meshes are finer on either side, the degrees of freedom (DOFs) increases substantially. To address this difficulty, in this work the benefits of polygonal elements constructed based on the cell-based smoothed finite element method (SFEM) are explored and an alternate approach for modelling fracture along cohesive interfaces is introduced. The proposed approach greatly reduces the DOFs in the system by allowing for more nodes along the required interface region, whilst allowing for a coarse mesh elsewhere in an elegant way, without compromising the accuracy compared with the conventional finite element method. The proposed framework enables the interface to be represented independent of the meshes at the interface giving complete freedom on meshing. The robustness, accuracy and the convergence properties are demonstrated with a few numerical tests involving straight, curved and multiple interfaces.