DEEP LEARNING-BASED CONSTITUTIVE MODELING OF MAGNESIUM ALLOY AND ITS VERIFICATION

For the problem of plane stress in sheet metal forming, a new idea based on deep learning has been proposed for the integrated elastic-plastic constitutive model, aiming to accurately and efficiently describe the mechanical behavior of metallic materials under complex loading conditions. Using AZ31B magnesium alloy as the research object, a deep learning model was constructed using the PyTorch framework to address different in-plane stress states in metal sheet forming. For the in-plane principal stress state, the deep learning model employs convolutional neural networks (CNN) and recurrent neural networks (RNN) modules. The proposed model successfully characterized the material's mechanical response and predicted the subsequent stress-strain relationship during the loading process. To deal with more complex in-plane general stress states (i.e., those involving both in-plane normal stress and shear stress), a Sobolev training method was introduced to construct a deep learning model. By explicitly constraining the stress-strain derivative in the loss function, this approach effectively ensures the continuity and smoothness of the constitutive model's tangent stiffness matrix. Subsequently, by writing a user-defined material subroutine (UMAT) for ABAQUS software, and the pre-trained network model was successfully embedded as part of the UMAT subroutine within ABAQUS. Uniaxial tensile tests were conducted on specimens with circular holes, and finite element simulations were performed using constitutive models based on the von Mises and Hill48(SD) yield criteria, as well as a deep learning-based constitutive model. The results show that the simulation results from all three finite element models agree well with the experimental force-displacement curves. Among the three models, the finite element simulation based on the deep learning constitutive model performed best in terms of both prediction accuracy and computational efficiency. These results verify the accuracy and efficiency of the proposed deep learning model and providing a new and effective method for modeling the mechanical properties of metallic materials.