On the combination of Moving Mesh technique and M-integral method for predicting crack propagation mechanisms in Functionally Graded Materials

This work presents an efficient FE modeling approach for predicting crack propagation mechanisms in Functionally Graded Materials (FGMs). The proposed strategy combines the Moving Mesh (MM) technique and the Interaction Integral method (M-integral). The MM is used to reproduce the geometry evolution induced by the crack advance. Specifically, the mesh nodes around the crack tip are moved in such a way to follow crack path evolutions, thus reducing the need for continuous remeshing events that affect negatively the computational efficiency of standard FE modeling strategies. In particular, the proposed scheme employs a moving mesh strategy consistent with the Arbitrary Lagrangian-Eulerian (ALE) formulation, which is suitable for handling the motion of mesh nodes with great flexibility. In addition, the use of proper regularization procedures ensures the consistency of the mesh motion, reducing elevated elements distortions. The motion of the mesh nodes requires a proper definition of crack onset conditions and propagation direction. Hence, a correct evaluation of fracture variables at the crack front (i.e., Stress Intensity Factors and T-stress) is necessary. For this purpose, the proposed method adopts the M-integral approach, which is a widely used method due to its simplicity and accuracy. Since the crack front moves during the crack advance, the M-integral is implemented by using the ALE formulation, thus extracting fracture variables on distorting elements. The validity of the proposed strategy has been validated through comparisons with experimental and numerical data reported in the literature.