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

Abstract

Featured Application: This work presents PINNI, a novel approach that is different from the traditional integral approximation methods. It employs the integrand fitting via a shallow neural network. This enables the creation of compact models, which deliver superior precision in sequential simulations, effectively addressing the limitations of neural networks in explicit algorithms and providing efficient, accurate integrand approximation for complex constitutive relations. Furthermore, PINNI is integrated into simulation code, where it replaces the mechanical integration. The application shows that this integration makes the fracture simulation results almost identical to those by conventional methods, but the computation efficiency has been significantly enhanced. 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 (Formula presented.) %. 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.