A physics-informed neural network approach to modelling elastoplastic soils and the implicit finite-element coupling

This study presents a physics-informed neural network (PINN) that captures the elasto-plastic behaviour of soils under complex strain and stress paths. The PINN uses the void ratio and plastic strain as the outputs of the neural networks and then includes them in a general elasto-plastic stress-strain relationship as an additional loss function. The PINN provides a more stable prediction and a superior performance than deep neural networks in forecasting the stress, strain, plastic strain, and void ratio. The PINN was then incorporated into a FEM framework as a replacement for the constitutive model to solve boundary value problems (BVPs). Three cases, biaxial test, layered-soil compression, and cavity expansion, showed that the FEM-PINN framework results in excellent agreements of deviatoric stress, plastic shear strain, and void ratio compared to state-of-the-art numerical methods as a benchmark. The approach captures the stress-history memory of soils as well as the volumetric and shear response of soil, including contractive and dilative behaviour. The stress concentration and strain localization characteristics were also reproduced by the FEM-PINN framework in the BVPs. Critically this approach also achieves outstanding performance in plasticity without the need to define plastic yield functions or hardening rules. Added to the comparable accuracy, the PINN is significantly better from a computational effort point of view.