Data-driven multiscale modelling of history-dependent plasticity using recurrent neural operators

Multiscale modelling in materials science, which connects and translates information across multiple length scales, has become increasingly prominent for its ability to link macroscopic behaviour with underlying microscale phenomena. This is crucial for structural integrity assessment of safety-critical components in industrial applications since a minor change to the microstructure can significantly affect the macroscopic results. Concurrent multiscale models, where mesoscale models are directly coupled to a macroscale model and run concurrently, could be a solution. However, they are prohibitively computationally expensive. In this work, we explore an alternative to this costly approach using a surrogate for mesoscale solutions based on a deep learning model. The deep learning model is a recurrent neural operator that learns the underlying history-dependent states of material via its differential form. It leverages large datasets to learn material deformation in homogenised macroscale from sampled mesoscale representative simulations. The model input is only strain, the output is stress, and the internal state variables learned during training control the evolution of the material. The performance of the surrogate model is evaluated using examples ranging from one-dimensional to full 3D cases of material elastoplastic cyclic deformation, incorporating combined isotropic and kinematic hardening. The results show the effects of model architecture on its predictive capability and the routes to use it for uncertainty quantification. Furthermore, the procedure of mesoscale crystal plasticity simulations to generate datasets for model training is explained. Finally, the model is applied to learn the homogenised mesoscale behaviour of an untextured material case.