Physics-informed neural networks for friction-involved nonsmooth dynamics problems

Friction-induced vibration is very common in engineering areas, such as aerospace, high-speed railways, robotics, and human/artificial joints. Analysing the dynamic behaviour of systems containing a multiple-contact point frictional interface is an important topic. However, accurately simulating nonsmooth/discontinuous dynamic behaviour due to friction is challenging. This paper presents a new physics-informed neural network approach for solving nonsmooth dynamic problems involved in the friction-induced vibration or friction-involved vibration. Compared with schemes of the conventional time-stepping methodology, this novel computational framework integrates the theoretical formulations of nonsmooth multibody dynamics into the training process of the neural network. We found that this new framework can not only more accurately simulate nonsmooth dynamic behaviours, but also could be a promising method to improve the efficiency as it eliminates the need for extremely small time steps typically associated with the conventional time-stepping methodology for multibody systems. Specifically, four kinds of high-accuracy Physics-informed-neural network (PINN) strategies were proposed: (1) single PINN; (2) dual PINN; (3) advanced single PINN; and (4) advanced dual PINN. Two typical dynamics problems with nonsmooth contact were simulated, including a 1-dimensional contact problem with stick–slip and a 2-dimensional contact problem considering separation–reattachment and stick–slip. Both single and dual PINN methods showed their advantages in dealing with the 1-dimensional stick–slip problem, which outperformed conventional methods across friction models that are difficult to simulate with the conventional time-stepping method. In contrast, the advanced single and advanced dual PINN methods provided better accuracy in simulating the 2-dimensional problem, even in the cases where conventional methods failed to simulate.