A Physics-Informed Neural Network Integration Framework for Efficient Dynamic Fracture Simulation in an Explicit Algorithm

The conventional dynamic fracture simulation by using the explicit algorithm often involves a large number of iteration computation due to the extremely small time interval. Thus, the most time-consuming process is the integration of constitutive relation. To improve the efficiency of the dynamic fracture simulation, a physics-informed neural network integration (PINNI) model is developed to calculate the integration of constitutive relation. PINNI employs a shallow multilayer perceptron with integrable activations to approximate constitutive integrand. To train PINNI, a large number of strains in a reasonable range are generated at first, and then the corresponding stresses are calculated by the mechanical constitutive relation. With the generated strains as input data and the calculated stresses as output data, the PINNI can be trained to reach a very high precision, whose relative error is about <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>7.8</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></semantics></math></inline-formula>%. Next, the mechanical integration of constitutive relation is replaced by the well-trained PINNI to perform the dynamic fracture simulation. It is found that the simulation results by the mechanical and PINNI approach are almost the same. This suggests that it is feasible to use PINNI to replace the rigorous mechanical integration of constitutive relation. The computational efficiency is significantly enhanced, especially for the complicated constitutive relation. It provides a new AI-combined approach to dynamic fracture simulation.