The proposed plastic correction methodology, which currently operates under the assumption of proportional loading, could be extended to handle non-proportional loading conditions by incorporating a more sophisticated treatment of the loading history and its effects on the stress and strain states. One approach would be to modify the local proportionality rule to account for the changes in the loading path. This could involve developing a multi-axial Neuber-type rule that dynamically adjusts the scaling factors for the deviatoric stress and strain tensors based on the instantaneous loading conditions.
Additionally, the integration of a more comprehensive history-dependent model could be beneficial. This would require the implementation of a state variable approach that tracks the evolution of plastic strains and hardening parameters throughout the loading process. By utilizing a more complex constitutive model that captures the material's response to varying loading paths, the plastic correction algorithm could be adapted to predict the elasto-plastic behavior more accurately under non-proportional loading conditions.
Furthermore, machine learning techniques could be employed to learn the relationship between the loading history and the resulting stress-strain response. By training a neural network on a dataset generated from full elasto-plastic simulations under various non-proportional loading scenarios, the model could provide real-time corrections to the predictions made by the plastic corrector, thereby enhancing its accuracy and applicability.