A FEM-PINN approach to modelling elastoplastic soil behaviour in boundary value problems

This study presents a physics-informed neural network (PINN) framework for modelling the elastoplastic behaviour of soils and its integration into the finite element method (FEM). The network jointly predicts stress, void ratio, and plastic strain, while the incremental strain decomposition is imposed as a physics-informed constraint in the loss function. This avoids explicit plastic yield functions or hardening rules and ensures compatibility with measurable laboratory quantities. The void ratio further defines a state-dependent elastic stiffness tensor, enabling a fully implicit FEM–PINN coupling in which element stiffness is updated at every Newton iteration. Compared with a multilayer perceptron (MLP) baseline, the PINN achieves superior accuracy, stability, and interpretability. The framework is validated on three unseen boundary value problems—biaxial compression, cavity expansion–contraction, and foundation loading—where it reproduces benchmark solutions with excellent agreement in stress, strain, and void ratio. It also captures stress concentration and unloading–reloading responses. Overall, the proposed FEM–PINN framework provides a robust and interpretable alternative to conventional soil constitutive models, combining the flexibility of data-driven learning with physics-based constraints to enable reliable analysis of complex geotechnical problems.