X-ray tomography techniques give researchers the full access to material inner structures. With such ample information, employing numerical simulation on real material images becomes more and more common. Material behavior, especially, of heterogeneous materials, e.g. polycrystalline, composite, can be observed at the microscopic scale with the computed tomography (CT) techniques. In this work, an efficient strategy is proposed to carry out simulations on large 3D CT images. A proposed matrix free type finite element based MultiGrid method is applied to improve convergence speed and to reduce memory space requirements. Homogeniza-tion techniques are used to obtain specific operators to enhance the convergence of the MultiGrid method when large material property variations are present. Hybrid parallel computing is implemented for memory space and computing time reasons. Free edge effects in a laminate composite with more than 16 billion degrees of freedom and crack opening in a cast iron are studied using the proposed strategy.

中文翻译：

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一种有效的基于有限元的多重网格方法，用于使用 CT 图像模拟异质材料的机械行为

X 射线断层扫描技术使研究人员能够完全了解材料的内部结构。有了如此丰富的信息，对真实材料图像进行数值模拟变得越来越普遍。可以使用计算机断层扫描 (CT) 技术在微观尺度上观察材料行为，尤其是异质材料（例如多晶、复合材料）的行为。在这项工作中，提出了一种有效的策略来对大型 3D CT 图像进行模拟。提出的基于矩阵自由型有限元的MultiGrid 方法被应用于提高收敛速度并减少存储空间需求。当存在较大的材料属性变化时，均质化技术用于获得特定算子以增强 MultiGrid 方法的收敛性。出于内存空间和计算时间的原因，实现了混合并行计算。使用所提出的策略研究了具有超过 160 亿自由度的层压复合材料中的自由边缘效应和铸铁中的裂纹开口。