Physics-Informed Neural Networks for Nonlinear Analysis of Reinforced Concrete Beams

Reinforced concrete (RC) beams are a common structural component in buildings and bridges and play a pivotal role in design and verification processes. Current structural computations often rely on linear elastic analyses which potentially yield overly conservative representations of the load-deformation behaviour of RC. Despite the superior accuracy offered by nonlinear analyses, they are limited in engineering practise due to computational inefficiency and intricate dependencies on uncertain material parameters. The scarcity of nonlinear calculations hinders exploration of diverse design, verification, and uncertainty quantification scenarios, necessitating a computational tool for improved assessment. This paper proposes physics-informed neural networks (PINNs) as an innovative differentiable computational approach for analysis and design of RC beams. We investigate the training and predictive quality of PINNs for a single-span simply supported beam structure, where we start with a linear elastic material model and from this deduce a PINN for the commonly used multi-linear (uncracked-cracked-plastic) material law idealisation of RC beams. To achieve this PINN representation, we propose a novel mixed-approach reformulation of PINNs. A hyperparameter tuning study reveals medium-sized networks of 8 layers with tanh or SiLU activation to be most suitable. By comparing the PINN predictions to analytical as well as Finite-Element solutions we demonstrate its accuracy in forecasting displacements and rotations, however no increase in computational time can be identified. The outlook highlights the enhancement of physics-informed deep operator networks to allow fast and accurate analysis and design of parametric beam structures.