The use of PINN in analyzing two-dimensional elastoplastic problems

Abstract By utilizing characteristics of neural networks, the Physics-Informed Neural Network (PINN) is truly an innovative method in dealing with differential equations. Despite being proposed and developed recently, it still brings an outstanding way to deal with traditional mechanics problems. Regarding PINN as a differential equation solver, the governing equation of a mechanics system can be directly handled using deep learning techniques. As a variation of PINN, the deep energy method (DEM) exhibits some superior properties compared to the traditional PINN, such as the requirement in the order of the derivative field for calculation is less, the implementation is easier, and the convergence rate is higher, etc. In order to examine the applicability of DEM in nonlinear systems, this study applies the DEM model to deal with elastoplastic problems, which possess material-kind nonlinearity. Through the study, problems with the assumption of a bilinear material model are handled and analyzed. The results are validated by the reference results obtained from previous studies. The findings show that DEM is extremely effective in solving nonlinear systems. Also, in comparison to other traditional approaches such as the Finite Element Method (FEM), meshless, etc., PINN is indeed a promising approach in the next stage of research in the computational mechanics field.