Thermodynamically Consistent Machine Learning for Fracture Prediction in Heterogeneous Materials

Abstract

Understanding fracture behavior is critical for assessing the structural integrity and longevity. Highly time-consuming physics-based fracture simulations motivate the development of machine-learning-based fracture evolution prediction with surrogate models. However, most existing machine-learning models for fracture prediction operate as black boxes and require large training datasets to generalize reliably. In this work, Thermodynamically Consistent Latent Dynamics Identification (tLaSDI) for parametric systems is introduced to predict fracture patterns and evolution in heterogeneous materials. The model learns the thermodynamic state variable in a lower-dimensional latent space using parametric GENERIC Formalism-Informed Neural Networks (pGFINNs) that enforce key thermodynamic principles, such as total energy conservation and entropy generation. This model embeds physics into the neural network architecture using a hard-constraint method that inherently complies with the underlying thermodynamic principles. The proposed tLaSDI-pGFINNs is further enhanced by a Geometry-Conditioned Autoencoder in learning the geometry configuration for effective geometry-guided learning. The energy and entropy evolution histories demonstrate that the model preserves the thermodynamic constraints on unseen testing samples. The results further show that tLaSDI-pGFINNs can more accurately capture both fracture patterns and the subsequent fracture evolution than the purely data-driven Autoencoder Long Short-Term Memory (AE-LSTM) model.