Prediction of evolving plasticity in rails under steady state rolling contact based on Reduced-Order Modeling

Predicting railhead damage due to multiple wheel passes in railway operations can be computationally demanding, especially when accounting for the rail’s inelastic material response. In this paper, we use a steady-state assumption within a convective coordinate system and employ Reduced-Order Modeling (ROM) through the Proper Generalized Decomposition (PGD) method to increase the computational efficiency. Our approach solves a nonlinear reduced-order problem for the displacements in a 3D railhead with elastic–plastic material properties considering various contact scenarios. The ROM framework includes domain decomposition and a parametric loading framework using PGD. It accounts for the elastic–plastic rail material through three key features: (1) treatment of the moving load under the assumption of steady state, by using a convective coordinate system along the railhead to convert the problem into a stationary contact load problem, (2) implementation of PGD to solve the 3D displacement field efficiently, and (3) use of fixed-point iterations to treat the coupling for solving plastic strains and displacements. In this iterative process, plastic strains are solved from displacements, and displacements are solved based on a loading scenario and updated plastic strains. The accuracy and computational efficiency are assessed by comparing our strategy with 3D finite element simulations for moving contact loads. The results show convergence with only a few fixed-point iterations for each over rolling, which results in a solution that is 63 times faster. This efficiency is crucial for assessing the accumulated plastic deformation from multiple wheel passes.