使用复合材料盒（ComBo）在有限应变下进行基于FFT的均匀化
FFT-based Homogenization at Finite Strains using Composite Boxels (ComBo)
摘要：
计算均匀化是并行多尺度模拟的黄金标准（例如，FE2）在规模桥接应用中。实验和合成材料的微观结构通常由3D图像数据表示。在包括数十亿个未知数的这种三维高分辨率体素数据上操作的模拟的计算复杂性引起对算法和数值上有效的求解器的需要。体素化的3D几何形状不能准确地捕获光滑的材料界面，以及复杂性降低的必要性，激发了一种称为复合体素的特殊局部粗粒化技术[Kabel，M.等人（2015）]。复合体素是利用层合板理论将多个精细尺度的体素凝聚成一个服从理论启发的本构模型的个体素。复合体素以适度的计算成本增强了局部域质量。我们的贡献包括对非等轴复合盒（ComBo）的推广，这是一个可以为具有首选方向的材料带来回报的功能。提出了一种新的基于图像的法线检测算法，该算法相对于传统的法线检测算法，提高了30%左右的检测精度。[Kabel，M.等人（2015）]。此外，使用ComBo有限应变模拟进行了详细研究。提出了一种有效的实现方法，并提出了一种防止物理不可接受状态的基本反投影算法，提高了鲁棒性。各种示例显示了ComBo的效率以及针对非线性力学问题提出的算法增强。通过检查和比较无数的快速傅里叶变换（FFT）为基础的求解器，包括新的双精细材料网格（DFMG）的详细描述的性能，强调了一般的可用性。所有采用的方案受益于组合离散化。
英文摘要：
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.
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