A new multiscale XFEM for the elastic properties evaluation of heterogeneous materials

In the present work, extended finite element method (XFEM) in conjunction with multiscale finite element method (MsFEM) is employed to model heterogeneous materials i.e. matrix having particles and/or voids. This approach, named as multiscale extended finite element method (MsXFEM), is used to determine the effective elastic properties of heterogeneous materials. The elastic properties are calculated by analyzing a representative volume element (RVE) under periodic boundary conditions. Three cases of particles and voids in the matrix i.e. matrix with hard particles, matrix with voids, and matrix with voids and hard particles both, are considered for analysis. The particles and voids are randomly distributed in the matrix. A strain energy based homogenization is carried out numerically for reinforcement volume fractions up to 50%. RVEs containing large number of discontinuities are analyzed by the proposed MsXFEM. The evaluated effective properties of the heterogeneous material are compared with the results available in the literature. These simulations show that the use of MsXFEM leads to a significant reduction in the CPU time as compared with the standard XFEM.