A simple and robust computational homogenization approach for heterogeneous particulate composites

In this article, a computationally efficient multi-split MsXFEM is proposed to evaluate the elastic properties of heterogeneous materials. The multi-split MsXFEM is the combination of multi-split XFEM with multiscale finite element methods (MsFEM). The multi-split XFEM is capable to model multiple discontinuities in a single element which leads to reduction in the number of mesh elements, whereas MsFEM helps in reducing the computational time. Strain energy based homogenization has been implemented on an RVE (having volume fraction of heterogeneities up to 50%) for evaluating the elastic properties. From macro-element size analysis, we estimate that the RVE edge length must be 5 times the edge length of the macro-element. The directional analysis has been performed to verify the isotropic behavior of the material, whereas contrast analysis has been done to check the numerical accuracy of the proposed scheme. A level set correction (LSC) based on higher order shape functions has been proposed to reduce mapping errors of level set values. It is also observed that multi-split MsXFEM is about 16 times computationally more efficient than MsXFEM for 50% volume of heterogeneities.