深度卷积神经网络预测均匀化中的弹性张量及其界
Deep Convolutional Neural Networks Predict Elasticity Tensors and their Bounds in Homogenization
摘要：
在目前的工作中，3D卷积神经网络（CNN）被训练成将任意相分数的随机异质两相材料与其弹性宏观刚度联系起来，从而取代显式均匀化模拟。为了减少由于未知边界条件（BC）而导致的合成复合材料的真实刚度的不确定性，CNN在周期性BC的刚度之外通过运动学均匀BC预测上限，并且通过应力均匀BC预测下限。这项工作描述了均匀化-CNN的工作流程，从CNN设计的微观结构生成，卷积，非线性激活和池化的操作，以及训练和验证以及反向传播到测试中的性能测量。其中，CNN不仅证明了标准测试集的预测准确性，而且还证明了金刚石涂层的真实两相微观结构的样本的预测准确性。覆盖所有三种边界类型的CNN实际上与三种不同网络中的单独处理一样准确。该贡献的CNN通过刚度边界提供了单个快照样本的适当RVE大小的指标。此外，它们能够对合成微结构的集合进行有效弹性刚度的统计分析，而无需昂贵的模拟。
英文摘要：
In the present work, 3D convolutional neural networks (CNNs) are trained to link random heterogeneous, two-phase materials of arbitrary phase fractions to their elastic macroscale stiffness thus replacing explicit homogenization simulations. In order to reduce the uncertainty of the true stiffness of the synthetic composites due to unknown boundary conditions (BCs), the CNNs predict beyond the stiffness for periodic BC the upper bound through kinematically uniform BC, and the lower bound through stress uniform BC. This work describes the workflow of the homogenization-CNN, from microstructure generation over the CNN design, the operations of convolution, nonlinear activation and pooling as well as training and validation along with backpropagation up to performance measurements in tests. Therein the CNNs demonstrate the predictive accuracy not only for the standard test set but also for samples of the real, two-phase microstructure of a diamond-based coating. The CNN that covers all three boundary types is virtually as accurate as the separate treatment in three different nets. The CNNs of this contribution provide through stiffness bounds an indicator of the proper RVE size for individual snapshot samples. Moreover, they enable statistical analyses for the effective elastic stiffness on ensembles of synthetical microstructures without costly simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
