Accelerating the solving of mechanical equilibrium caused by lattice misfit through deep learning method

Precipitation is a common phenomenon that occurs during heat treatments. There is internal stress around the precipitate owing to the lattice misfit between the precipitate and matrix. This internal stress has a significant influence not only on the precipitation kinetics but also on the material properties. The misfit stress can be obtained by numerically solving the mechanical equilibrium equations. However, this process is complex and time-consuming. We developed a new approach based on deep learning to accelerate the solution process. The training data were first generated by a phase-field model coupled with elastic mechanical equilibrium equations, which were solved using the finite difference method. The obtained precipitate morphologies and corresponding stress distributions were input data for training the physics-informed (PI) UNet model. The well-trained PI-UNet model can then be applied to predicting stress distributions with the precipitate morphology as the input. Prediction accuracy and efficiency are discussed in this study. The results showed that the PI-UNet model was an appropriate approach for quickly predicting the misfit stress between the precipitate and matrix.