An XFEM‐strain gradient damage model for efficient modeling of materials with reinforcement particles

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A coupling of extended finite element method (XFEM) and strain gradient enhanced damage method is proposed to model damage initiation and growth in the materials with reinforcement particles. The proposed model inherits the advantages of both methods i.e., simple definition of reinforcement particles from XFEM and numerical stability during damage evolution from the strain gradient damage model. The capability of the proposed XFEM-strain gradient damage model has been demonstrated by simulating mode-I, mode-II, and the mix-mode failure mechanism in the SENB, SEN, and L-shaped specimen with reinforcement particles respectively. The numerical simulations are performed by considering hard and soft reinforcement particles in a matrix. Mesh-sensitivity and particle-sensitivity analysis are performed to quantify effect of various parameters like mesh size, particle size and volume fraction on behavior of SENB specimen. The proposed XFEM model is at least 10% efficient (at higher mesh densities) than the standard FEM model for solving the SENB specimen with reinforcement particles. In the particle sensitivity analysis, proposed XFEM model used only one mesh density (unlike FEM model that needs different conformal meshes) to simulate set of 400 realizations with random spatial distribution of reinforcement particles. The analysis shows that the computational demand for the creation of conformal mesh is alleviated with the use of XFEM for defining reinforcement particles. The mesh-sensitivity analysis shows that difference in the solution obtained using proposed XFEM model and standard FEM model is negligible (less than 1% at higher mesh densities). Therefore, the proposed XFEM-strain gradient damage model can substitute FEM-strain gradient damage model with above mentioned efficiencies.