  Computational homogenization is the gold standard for concurrent multi-scale
simulations (e.g., FE2) in scale-bridging applications. Experimental and
synthetic material microstructures are often represented by 3D image data. The
computational complexity of simulations operating on such three-dimensional
high-resolution voxel data comprising billions of unknowns induces the need for
algorithmically and numerically efficient solvers. The inability of voxelized
3D geometries to capture smooth material interfaces accurately, along with the
necessity for complexity reduction, motivates a special local coarse-graining
technique called composite voxels [Kabel,M. et al. (2015)]. Composite voxels
condense multiple fine-scale voxels into a single voxel obeying a
theory-inspired constitutive model by employing laminate theory. Composite
voxels enhance local field quality at a modest computational cost. Our
contribution comprises the generalization towards composite boxels (ComBo) that
are nonequiaxed, a feature that can pay off for materials with a preferred
direction. A novel image-based normal detection algorithm is devised which
improves the accuracy by around 30\% against the orientation cf. [Kabel,M. et
al. (2015) ]. Further, the use of ComBo for finite strain simulations is
studied in detail. An efficient implementation is proposed, and an essential
back-projection algorithm preventing physically inadmissible states is
developed, which improves robustness. Various examples show the efficiency of
ComBo and the proposed algorithmic enhancements for nonlinear mechanical
problems. The general usability is emphasized by examining and comparing the
performance of myriad Fast Fourier Transform (FFT) based solvers including a
detailed description of the new Doubly-Fine Material Grid (DFMG). All of the
employed schemes benefit from the ComBo discretization.
