Accelerating Phase-Field Fracture Simulations with the I-FENN Framework
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The integrated finite element neural network (I-FENN) framework was recently developed as a computational paradigm for solving multi-physics problems by utilizing machine learning techniques within the finite element method (FEM). Within this framework, the coupled governing equations are split into two categories: the equilibrium equation is numerically integrated via FEM, whereas the remaining equations are solved using pre-trained neural networks (NNs). This approach offers high efficiency and robustness, as demonstrated in various multi-physics settings (e.g., non-local continuum damage mechanics and thermoelasticity problems). In this talk, we extend the I-FENN framework to efficiently simulate fracture mechanics problems using the phase-field method. First, we present the governing equations of the system, in which cracks are represented by a continuous field that ranges between two extreme values, denoting intact and fully damaged states, respectively. Second, we introduce a physics-informed neural network to infer the phase-field variable based on the elastic strain energy density, and we show how the NN can be integrated within conventional and staggered FEM-based solvers. Finally, we examine the accuracy and efficiency of I-FENN against several benchmark problems from the literature, including single- or multiple-crack domains under varying loading conditions.
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