论文标题
使用复合盒（组合）在有限菌株处基于FFT的均质化（组合）
FFT-based Homogenization at Finite Strains using Composite Boxels (ComBo)
论文作者
论文摘要
计算均质化是在规模桥接应用中并发多尺度模拟（例如FE2）的金标准。实验和合成材料微观结构通常由3D图像数据表示。在此类三维高分辨率体素数据上运行的模拟的计算复杂性，包括数十亿个未知数，引起了对算法和数值有效的求解器的需求。体素化的3D几何形状无法准确捕获光滑的材料界面，以及降低复杂性的必要性，激发了一种特殊的局部粗粒技术，称为复合体素[Kabel，m。等。 （2015）]。复合体素将多个细尺度体素凝结成单个体素，通过采用层压板理论来遵守理论启发的本构模型。复合体素以适度的计算成本增强本地田地质量。我们的贡献包括对非quiax的复合盒（组合）的概括，该功能可以为凭借优选方向的材料获得回报。设计了一种基于图像的新型正常检测算法，该算法将准确性提高了30 \％，相对于方向CF。 [卡贝尔，米。等。 （2015）]。此外，详细研究了使用组合对有限应变模拟的使用。提出了有效的实施，并开发了一种基本的反射算法，以防止身体不可接受的状态，从而提高鲁棒性。各种示例表明，对于非线性机械问题，组合的效率和提议的算法增强功能。通过检查和比较基于众多快速傅立叶变换（FFT）的求解器的性能，包括对新的双偶发材料网格（DFMG）的详细描述，可以强调一般的可用性。所有就业计划都受益于组合离散化。
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.
