用物理约束提升材料应力图分辨率,精准捕捉界面应力集中。
Predicting Stress in Two-phase Random Materials and Super-Resolution Method for Stress Images by Embedding Physical Information
- 结合相界面信息设计新网络,降低边界预测误差。
- 无需配对数据,可任意倍数超分辨应力图像。
- 适合材料失效分析与多尺度应力研究者使用。
应力分析在材料设计中至关重要。对于具有复杂微观结构的两相随机材料(TRMs),材料失效常伴随应力集中,而相界面是应力集中的关键区域。因此,相边界处的应力预测误差尤为关键。实际工程中,获取的材料微观结构图像像素有限,限制了深度学习生成的应力图像分辨率,难以观测应力集中区。现有图像超分辨率(ISR)技术均为数据驱动的监督学习,但应力图像具有天然物理约束,为新方法提供思路。本研究构建了针对TRMs的应力预测框架:首先采用提出的多组成U-net(MC U-net)预测低分辨率微观结构下的应力;通过融合相界面信息,有效降低边界处的预测误差。其次提出基于混合物理信息神经网络(MPINN)的应力超分辨率方法(SRPINN),引入物理约束,无需配对应力图像即可训练,可将应力图像分辨率提升至任意倍数,实现相界面应力集中区的多尺度分析。最后通过迁移学习对不同相体积分数和加载状态的TRMs进行应力分析,结果表明该框架具备良好准确性和泛化能力。
原文摘要 · Abstract (English)
Stress analysis is an important part of material design. For materials with complex microstructures, such as two-phase random materials (TRMs), material failure is often accompanied by stress concentration. Phase interfaces in two-phase materials are critical for stress concentration. Therefore, the prediction error of stress at phase boundaries is crucial. In practical engineering, the pixels of the obtained material microstructure images are limited, which limits the resolution of stress images generated by deep learning methods, making it difficult to observe stress concentration regions. Existing Image Super-Resolution (ISR) technologies are all based on data-driven supervised learning. However, stress images have natural physical constraints, which provide new ideas for new ISR technologies. In this study, we constructed a stress prediction framework for TRMs. First, the framework uses a proposed Multiple Compositions U-net (MC U-net) to predict stress in low-resolution material microstructures. By considering the phase interface information of the microstructure, the MC U-net effectively reduces the problem of excessive prediction errors at phase boundaries. Secondly, a Mixed Physics-Informed Neural Network (MPINN) based method for stress ISR (SRPINN) was proposed. By introducing the constraints of physical information, the new method does not require paired stress images for training and can increase the resolution of stress images to any multiple. This enables a multiscale analysis of the stress concentration regions at phase boundaries. Finally, we performed stress analysis on TRMs with different phase volume fractions and loading states through transfer learning. The results show the proposed stress prediction framework has satisfactory accuracy and generalization ability.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。