Reduced-Order Modeling through Machine Learning Approaches for Brittle Fracture Applications
This work addresses computational cost challenges in fracture mechanics for materials like concrete, enabling faster simulations that could inform larger-scale models, though it is incremental as it compares existing ML methods with physics integration on a specific dataset.
The paper tackled the problem of modeling brittle fracture in concrete by developing and comparing five reduced-order modeling approaches, four of which use machine learning to approximate crack propagation under tensile loading with preexisting cracks, resulting in models that are orders of magnitude faster than a high-fidelity reference while maintaining physics through combined data-driven and physics-informed features.
In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms, each method incorporates different physics-based assumptions in order to reduce the computational complexity while maintaining the physics as much as possible. This work specifically focuses on using the ML approaches to model a 2D concrete sample under low strain rate pure tensile loading conditions with 20 preexisting cracks present. A high-fidelity finite element-discrete element model is used to both produce a training dataset of 150 simulations and an additional 35 simulations for validation. Results from the ML approaches are directly compared against the results from the high-fidelity model. Strengths and weaknesses of each approach are discussed and the most important conclusion is that a combination of physics-informed and data-driven features are necessary for emulating the physics of crack propagation, interaction and coalescence. All of the models presented here have runtimes that are orders of magnitude faster than the original high-fidelity model and pave the path for developing accurate reduced order models that could be used to inform larger length-scale models with important sub-scale physics that often cannot be accounted for due to computational cost.