Global Stress Generation and Spatiotemporal Super-Resolution Physics-Informed Operator under Dynamic Loading for Two-Phase Random Materials

Material stress analysis is a critical aspect of material design and performance optimization. Under dynamic loading, the global stress evolution in materials exhibits complex spatiotemporal characteristics, especially in two-phase random materials (TRMs). Such kind of material failure is often associated with stress concentration, and the phase boundaries are key locations where stress concentration occurs. In practical engineering applications, the spatiotemporal resolution of acquired microstructural data and its dynamic stress evolution is often limited. This poses challenges for deep learning methods in generating high-resolution spatiotemporal stress fields, particularly for accurately capturing stress concentration regions. In this study, we propose a framework for global stress generation and spatiotemporal super-resolution in TRMs under dynamic loading. First, we introduce a diffusion model-based approach, named as Spatiotemporal Stress Diffusion (STS-diffusion), for generating global spatiotemporal stress data. This framework incorporates Space-Time U-Net (STU-net), and we systematically investigate the impact of different attention positions on model accuracy. Next, we develop a physics-informed network for spatiotemporal super-resolution, termed as Spatiotemporal Super-Resolution Physics-Informed Operator (ST-SRPINN). The proposed ST-SRPINN is an unsupervised learning method. The influence of data-driven and physics-informed loss function weights on model accuracy is explored in detail. Benefiting from physics-based constraints, ST-SRPINN requires only low-resolution stress field data during training and can upscale the spatiotemporal resolution of stress fields to arbitrary magnifications.

Predicting Stress in Two-phase Random Materials and Super-Resolution Method for Stress Images by Embedding Physical Information

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.