Stress and strain state of a square bar under complex loading

Background: Elastoplastic tension and torsion of a homogeneous square bar are examined for sequential and proportional loading paths. Methods: A displacement formulation is used: plastic shear strains contribute to the source in the warping Poisson equation and enter the Neumann boundary conditions. The Prandtl–Reuss model is compared with an average curvature model that accounts for deformation-path memory. A five-point finite-difference scheme and successive over-relaxation are employed. Results: Three elastic benchmark meshes exhibit second-order convergence; the torque error on the 181 × 181 mesh is 0.000941%. In the reported comparison at the same final kinematic state, the average curvature model predicts a torque 3.15–9.44% above the Prandtl–Reuss result. Conclusions: Local trajectories reveal sensitivity to the loading sequence. The conclusions are restricted to the adopted reduced cross-sectional description and the elastic verification of the algorithm.