Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)

Recent progress in AI-enabled constitutive modeling has concentrated on moving from a purely data-driven paradigm to the enforcement of physical constraints and mechanistic principles, a concept referred to as physics augmentation. Classical phenomenological approaches rely on selecting a pre-defined model and calibrating its parameters, while machine learning methods often focus on discovery of the model itself. Sparse regression approaches lie in between, where large libraries of pre-defined models are probed during calibration. Sparsification in the aforementioned paradigm, but also in the context of neural network architecture, has been shown to enable interpretability, uncertainty quantification, but also heterogeneous software integration due to the low-dimensional nature of the resulting models. Most works in AI-enabled constitutive modeling have also focused on data from a single source, but in reality, materials modeling workflows can contain data from many different sources (multi-modal data), and also from testing other materials within the same materials class (multi-fidelity data). In this work, we introduce physics augmented finite element model updating (paFEMU), as a transfer learning approach that combines AI-enabled constitutive modeling, sparsification for interpretable model discovery, and finite element-based adjoint optimization utilizing multi-modal data. This is achieved by combining simple mechanical testing data, potentially from a distinct material, with digital image correlation-type full-field data acquisition to ultimately enable rapid constitutive modeling discovery. The simplicity of the sparse representation enables easy integration of neural constitutive models in existing finite element workflows, and also enables low-dimensional updating during transfer learning.