Abstract:

The significant scale difference between microstructure and macro structure， and the coupling of complex micro-geometric configuration and substrate properties which make the analysis of macro-equivalent performance of microstructure is very difficult. Therefore， a prediction model of microstructure homogenization elastic tensor was proposed based on three-dimensional convolutional neural network. A parametric modeling of microstructure was completed by level set method， and the equivalent elastic tensor of microstructure was calculated by numerical homogenization. A data representation method coupling geometric configuration and substrate properties was proposed to match the mixed inputs and equivalent elastic tensor labels， and the matched data samples were used as the dataset for neural network training. Finally， model performance was analyzed from partial errors of the predicted results and the calculation efficiency. The proposed model may significantly improve the performance analysis efficiency of the microstructure within the allowable error range.

Key words: neural network, microstructure, numerical homogenization, level-set method

摘要：

微结构与宏观结构的显著尺度差异，以及复杂的微观几何构型与基材属性的耦合导致微结构的宏观等效性能分析十分困难。提出了一种基于三维卷积神经网络的微结构均质化弹性张量预测模型。采用水平集方法完成微结构的参数化建模，通过数值均质化计算微结构的等效弹性张量。提出几何构型与基材属性耦合的数据表达方法，实现混合输入与等效弹性张量标签的匹配，并将匹配的数据样本作为神经网络训练的数据集。最后，从预测结果的分项误差、计算效率两个方面进行了模型性能分析，所提模型在允许的误差范围内能显著提高微结构的性能分析效率。

关键词: 神经网络, 微结构, 数值均质化, 水平集方法