Multiscale constitutive modeling of anisotropic plasticity: Coupling the visco-plastic self-consistent model with the recurrent neural network and its implementation in finite element analysis

The anisotropic and nonlinear strain-path-dependent nature of metal plasticity poses a major challenge for accurate constitutive modeling in finite element (FE) analysis. Traditional macroscale models are easily implemented but lack accuracy, while crystal plasticity (CP) models offer high fidelity at the cost of computational efficiency. To bridge this gap, we propose a deep neural network smart constitutive (DNNSC) framework that combines the visco-plastic self-consistent (VPSC) model with a gated recurrent unit (GRU) network. A VPSC model calibrated on pure aluminum generated 14,000 strain-paths for training GRU-based network. The optimized model has a prediction accuracy of up to 96 % on unknown strain-paths. Subsequently, the DNNSC model was implemented into the FE analysis through Fortran programming, and a benchmark simulation for thin sheet stamping was successfully performed. The simulation results demonstrated that the DNNSC model significantly improved prediction performance compared to conventional macroscale constitutive models. Especially, the ear height and plate thickness were accurately predicted with an accuracy of 91.85 % and 95.84 %, compared to only 68.85 % and 86.59 % achieved by the Yld model. Meanwhile, the simulation time was reduced to approximately one-tenth that of the fully coupled CP model, because the latter required calculating and homogenizing the mechanical responses of hundreds of grains at each integration point during the simulation. The DNNSC framework bridges the gap between CP models and FE simulations of plastic forming and breaks down the barrier between modeling and practical application. Furthermore, this framework can be extended to other materials by re-calibrating VPSC parameters and fine-tuning DNN parameters.