关键词: 物理信息神经网络, 增量法, 非线性弹性本构, Duncan-Chang本构, 平面应变问题

Abstract: Nonlinear elastic constitutive models are one of the most commonly used constitutive models in geotechnical engineering, extensively applied in mechanical performance analysis and numerical simulations. For nonlinear elastic constitutive problems, numerical algorithms are generally employed to solve them due to the iterative process involved in each incremental step. Recently, physics-informed neural networks (PINN) have emerged as a prominent method for solving partial differential equations, offering a novel approach to geotechnical engineering challenges. Currently, predictions of nonlinear constitutive problems using physics informed neural networks often depend on stress-strain field data derived from numerical methods. Although this data-driven and physics-driven integration can improve the accuracy of predictions, it does not break away from the framework of numerical solutions and also reduces the ability of neural networks to solve problems independently. To address this, a physics-driven incremental step PINN architecture is developed specifically for nonlinear elastic constitutive problems. This architecture generates a set of sub-networks for training corresponding to each incremental step and utilizes transfer learning to accelerate the training efficiency of neural networks in each incremental step. The study evaluates the performance of the proposed incremental physics informed neural network architecture by testing the Duncan-Chang model, a representative nonlinear elastic constitutive model, in solving two-dimensional plane strain problems. The effectiveness and accuracy of the proposed network architecture are validated by comparing the neural network predictions with computational results obtained from finite element software.

Key words: physics informed neural networks, incremental method, nonlinear elastic constitutive model, Duncan-Chang constitutive model, plane strain problem