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

TL;DR

This paper introduces a physics-informed deep learning framework for generating high-resolution spatiotemporal stress fields in two-phase random materials under dynamic loading, addressing data limitations and capturing stress concentrations.

Contribution

It proposes a diffusion model-based stress generation method and a physics-informed super-resolution operator that require only low-resolution data, improving stress field analysis in complex materials.

Findings

The STS-diffusion effectively generates global stress data.

ST-SRPINN achieves high-resolution stress field upscaling with physics constraints.

Model accuracy depends on attention placement and loss function weights.

Abstract

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.