Microstructures are attracting academic and industrial interests with the rapid development of additive manufacturing. The numerical homogenization method has been well studied for analyzing mechanical behaviors of microstructures; however, it is too time-consuming to be applied to online computing or applications requiring high-frequency calling, e.g., topology optimization. Data-driven homogenization methods emerge as a more efficient choice but limit the microstructures into a cubic shape, which are infeasible to the periodic microstructures with a more general shape, e.g., parallelepiped. This paper introduces a fine-designed 3D convolutional neural network (CNN) for fast homogenization of parallel-shaped microstructures, named PH-Net. Superior to existing data-driven methods, PH-Net predicts the local displacements of microstructures under specified macroscope strains instead of direct homogeneous material, motivating us to present a label-free loss function based on minimal potential energy. For dataset construction, we introduce a shape-material transformation and voxel-material tensor to encode microstructure type,base material and boundary shape together as the input of PH-Net, such that it is CNN-friendly and enhances PH-Net on generalization in terms of microstructure type, base material, and boundary shape. PH-Net predicts homogenized properties with hundreds of acceleration compared to the numerical homogenization method and even supports online computing. Moreover, it does not require a labeled dataset and thus is much faster than current deep learning methods in training processing. Benefiting from predicting local displacement, PH-Net provides both homogeneous material properties and microscopic mechanical properties, e.g., strain and stress distribution, yield strength, etc. We design a group of physical experiments and verify the prediction accuracy of PH-Net.
Unraveling impacts of polycrystalline microstructures on ionic conductivity of ceramic electrolytes by computational homogenization and machine learning
Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials
提出了一种两层统计等效的周期性单胞模型，用于预测平纹编织多层碳-碳纺织复合材料的宏观响应。在描述这些材料系统的最典型的几何缺陷时，在（Zeman和Šejnoha，International Journal of Solids and Structures，41（2004），pp. 6549- 6571）进行了实质性修改，现在允许纺织织物的各个层在所有三个方向上嵌套和相互移位。然而，本配方的最有价值的资产被认为是通过在晶胞的两层之间引入的扁球形空隙的系统反映可忽略的中尺度孔隙率的影响的可能性。数值预测的有效热导率和弹性刚度和它们的比较与现有的实验室数据和使用Mori-Tanaka平均方案得出的结果支持本方法的可信度，大约一样多的可靠性，发现从纳米压痕测试直接进行分析的复合材料样品的局部机械性能。
Consistent machine learning for topology optimization with microstructure-dependent neural network material models
Delft University of Technology（代尔夫特理工大学）；Princeton University（普林斯顿大学）；Princeton Materials Institute (PMI), Princeton University（普林斯顿材料研究所（PMI），普林斯顿大学）；Brown University（布朗大学）
A new Surrogate Microstructure Generator for Porous Materials with Applications to the Buffer Layer of TRISO Nuclear Fuel Particles
Laboratoire de Mécanique des Solides, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris（固体力学实验室，巴黎综合理工学院，法国国家科学研究中心，巴黎理工学院）；Safran Tech（赛峰技术）；Department of Mathematics,Technical University of Munich（慕尼黑工业大学数学系）
Predicting cement microstructure and mechanical properties in hydrating cement paste with a Phase-Field model
Duke University（杜克大学）；UCLouvain（天主教鲁汶大学）；ENPC, Institut Polytechnique de Paris, Univ Gustave Eiffel（法国国立路桥学校，巴黎理工学院，古斯塔夫·埃菲尔大学）；University of Montpellier（蒙彼利埃大学）
Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions
Machine learning materials physics: Deep neural networks trained on elastic free energy data from martensitic microstructures predict homogenized stress fields with high accuracy
