Two-scale simulations of components classically rely upon finite element simulations on boundary- and interface-fitted meshes on both the macro and the micro scale. For complex microstructures fast and memory-efficient solvers posed on regular voxels grids, in particular the FFT-based homogenization method , provide a powerful alternative to FE simulations on unstructured meshes and can be used to replace the micro-solver [2, 3]. Since representative volume elements of the microstructure consist of up to 80003 voxels, even this micro-solver reaches its limits for nonlinear elastic computations.This talk focuses on the composite voxel technique , where sub-voxels are merged into bigger voxels to which an effective material law based on laminates is assigned. Due to the down-sampled grid, both the memory requirements and the computational effort are severely reduced. We discuss the extensions of linear elastic ideas [4, 5] to the physically non-linear setting and assess the accuracy of reconstructed solution fields by comparing them to direct full-resolution computations.References H. Moulinec and P. Suquet. A numerical method for computing the overall response of nonlinear composites with complex microstructure.Computer Methods in Applied Mechanics and Engineering, 157(1-2):69–94, 1998.  J. Spahn, H. Andra, M. Kabel, and R. Mueller.A multiscale approach for modeling pro- gressive damage of composite materials using fast Fourier transforms. Computer Methods in Applied Mechanics and Engineering, 268(0):871 – 883, 2014.  J. Kochmann, S. Wulfinghoff, S. Reese, J. R. Mianroodi, and B. Svendsen. Two-scale FEFFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior. Computer Methods in Applied Mechanics and Engi- neering, 305:89 – 110, 2016.  M. Kabel, D. Merkert, and M. Schneider. Use of composite voxels in FFT-based homog- enization. Computer Methods in Applied Mechanics and Engineering, 294(0):168–188,2015.  L. Gelebart and F. Ouaki. Filtering Material Properties to Improve FFT-based Methodsfor Numerical Homogenization. J. Comput. Phys., 294(C):90–95, 2015.