Use of composite voxels in FFT-based homogenization

FFT-based homogenization methods operate on regular voxel grids. In general, such grids cannot resolve interfaces exactly. In this article we assign voxels containing an interface a stiffness different from the constituent materials in a systematic fashion. More precisely, we characterize the class of these so-called composite voxels leading to convergence of the discretizations. Considering the interface in the composite voxel as linear, we furnish the voxel with the corresponding laminate stiffness. These laminate voxels are shown to increase both the accuracy of the calculated effective properties and the local quality of the strain and stress fields dramatically.