Element-level elastoplastic integration for hybrid finite elements via physics-informed neural networks

Hybrid finite elements have proved highly accurate in plasticity problems, particularly when the assumed stress interpolation satisfies the equilibrium equations a priori. However, enforcing plastic admissibility in these formulations requires element-level constitutive updates, typically involving constrained local optimisation problems whose cost increases with the number of stress parameters and control points.This work proposes an unsupervised physics-informed neural network surrogate to accelerate the element-level return mapping in incremental elastoplastic analyses based on hybrid finite element discretisations. The network is trained by embedding the governing plasticity conditions directly during the learning process and is used to approximate the plastically corrected stress parameters from an elastic trial stress state. The strategy is tested on a plane-stress hybrid element with a five-parameter equilibrated stress field, including additional inputs that describe distorted element configurations.The results show excellent agreement with standard element-level return-mapping solutions in terms of equilibrium paths, limit loads, and stress-field reconstruction and generally reduce the number of global equilibrium iterations in the tested examples. Overall, the proposed approach achieves speed-up factors ranging from two to eight, suggesting an effective route for accelerating hybrid finite element elastoplastic analyses while retaining accuracy.