Deep learning accelerating design of functionally graded materials for application in dynamic loading

Spallation is a fracture phenomenon induced by dynamic loading and significantly influenced by peak stress (${\sigma }_p$), strain rate ($\dot{\epsilon }$), and pulse duration ($\tau$) of loading stress history. Experimental studies of spallation often encounter coupling among these parameters due to limitations in loading techniques, leading to inconsistent findings. The study introduces a novel method to independently regulate these parameters using a graded density impactor (GDI). A deep learning-based inverse design model was developed to optimize the GDI structure. Results show that the unique architecture of the GDI generates segmented rarefaction waves, enabling precise control of their intensity and arrival time at the spall plane. This allows effective adjustment of ${\sigma }_p$, $\dot{\epsilon }$ and $\tau$ during spallation. The inverse design model was trained with a mixed loss function and achieved outstanding predictive accuracy with an R² value exceeding 0.99. Using the trained model, tailored GDI structures were designed to achieve specific expected ${\sigma }_p$, $\dot{\epsilon }$ and $\tau$. The designed GDI can cause spallation with ${\sigma }_p$, $\dot{\epsilon }$ and $\tau$ closely matching expected values. This machine learning-based approach offers a powerful tool for the precise design of spall experiments, advancing the study of material behavior under dynamic loading.