FUsion-based ConstitutivE model (FuCe): Towards model-data augmentation in constitutive modelling

Constitutive modelling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying stress conditions due to their fixed forms and limited parameters. While recent advances in deep learning have addressed some limitations of classical models, purely data-driven methods tend to require large datasets, lack interpretability, and struggle to generalize beyond their training data. To tackle these issues, we introduce "Fusion-based Constitutive model (FuCe): Towards model-data augmentation in constitutive modelling". This approach combines established phenomenological models with an ICNN architecture, designed to train on the limited and noisy force-displacement data typically available in practical applications. The hybrid model inherently adheres to necessary constitutive conditions. During inference, Monte Carlo dropout is employed to generate Bayesian predictions, providing mean values and confidence intervals that quantify uncertainty. We demonstrate the model's effectiveness by learning two isotropic constitutive models and one anisotropic model with a single fibre direction, across six different stress states. The framework's applicability is also showcased in finite element simulations across three geometries of varying complexities. Our results highlight the framework's superior extrapolation capabilities, even when trained on limited and noisy data, delivering accurate and physically meaningful predictions across all numerical examples.