Parameter estimation in cyclic plastic loading

Abstract The increasing complexity of modern constitutive models of cyclic metal plasticity requires more efficient ways to achieve their optimal calibration. Traditional approaches, such as random search combined with Nelder–Mead optimization, are computationally expensive. In addition, they struggle with highly non-convex functions that have numerous local minima and complex behavior, making these methods highly sensitive to initial conditions. While numerical refinement is key, a better prediction for its initial point directly saves costs. In this work, we focus only on the uniaxial cyclic loading, as it is the dominant part of a general calibration process for such a model and can also utilize a closed-form solution, further speeding up the procedure. We propose a neural network framework with a loss function that combines the loss on both the predicted parameters and the generated stress responses. This network is then used to predict an initial point for Nelder–Mead optimization. Our method was also compared to the non-gradient Tensor Train Optimization method on both synthetic data and measured experiments.