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发布时间：2019-11-07

论文类型：期刊论文

发表时间：2019-08-01

发表刊物：COMPUTATIONAL MECHANICS

收录刊物：SCIE

卷号：64

期号：2,SI

页面范围：281-305

ISSN号：0178-7675

关键字：Machine learning; Reduced order modeling; Materials database; Heterogeneous materials; Multiscale design optimization

摘要：Mechanical science and engineering can use machine learning. However, data sets have remained relatively scarce; fortunately, known governing equations can supplement these data. This paper summarizes and generalizes three reduced order methods: self-consistent clustering analysis, virtual clustering analysis, and FEM-clustering analysis. These approaches have two-stage structures: unsupervised learning facilitates model complexity reduction and mechanistic equations provide predictions. These predictions define databases appropriate for training neural networks. The feed forward neural network solves forward problems, e.g., replacing constitutive laws or homogenization routines. The convolutional neural network solves inverse problems or is a classifier, e.g., extracting boundary conditions or determining if damage occurs. We will explain how these networks are applied, then provide a practical exercise: topology optimization of a structure (a) with non-linear elastic material behavior and (b) under a microstructural damage constraint. This results in microstructure-sensitive designs with computational effort only slightly more than for a conventional linear elastic analysis.