Data-driven physics-constrained recurrent neural networks for multiscale damage modeling of metallic alloys with process-induced porosity

Computational modeling of heterogeneous materials is increasingly relying on multiscale simulations which typically leverage the homogenization theory for scale coupling. Such simulations are prohibitively expensive and memory-intensive especially when modeling damage and fracture in large 3D components such as cast metallic alloys. To address these challenges, we develop a physics-constrained deep learning model that surrogates the microscale simulations. We build this model within a mechanistic data-driven framework such that it accurately predicts the effective microstructural responses under irreversible elasto-plastic hardening and softening deformations. To achieve high accuracy while reducing the reliance on labeled data, we design the architecture of our deep learning model based on damage mechanics and introduce a new loss component that increases the thermodynamical consistency of the model. We use mechanistic reduced-order models to generate the training data of the deep learning model and demonstrate that, in addition to achieving high accuracy on unseen deformation paths that include severe softening, our model can be embedded in 3D multiscale simulations with fracture. With this embedding, we also demonstrate that state-of-the-art techniques such as teacher forcing result in deep learning models that cause divergence in multiscale simulations. Our numerical experiments indicate that our model is more accurate than pure data-driven models and is much more efficient than mechanistic reduced-order models.