WEB Parameter optimization for a physics-based model of material plastic behavior using machine learning
In materials modeling the knowledge of correct model parameters is crucial. These parameters are usually found in the literature (ideally for the studied system, but more often for a simplified case), measured, or calculated using lower-scale methods (e.g. vacancy formation energy, etc.). The focus of present work is modeling the material plastic behavior during the hot deformation process where variance in processing conditions might have a big impact on product quality. The Finite Elements (FE) method is considered as the-state-of-the-art for numerical simulations of deformation processes. However, the used material models should usually be adapted for each specific material. In the present work, we concentrate on a model based on material internal state parameters (physics-based approach). This model describes the materials behavior in terms of the evolution of mean dislocation density (MD2M) as a superposition of dislocation production and dislocation decrease due to a spontaneous annihilation and a temperature-activated climb. The model contains several parameters including ten physical and material parameters such as Taylor factor, Burgers vector, Young’s modulus, diffusion activation energy etc., as well as three calibration coefficients, which are usually fitted to experimental data and can change depending on processing conditions. A difficulty is that these calibration parameters are interdependent, meaning that their values might strongly vary with respect to each other. In the present work, we study whether it is possible to learn models as a replacement for the parameter values using a machine learning method, in particular symbolic regression (SR). An advantage of SR is that the result is a rather simple closed-form mathematical expression, which is open for further inspection and can be easily integrated into FE solvers. The SR models are used in place of the calibration parameters in the physics-based model as analytical functions with respect to the processing conditions (temperature and strain rate). The resulting constitutive model is then implemented for the commercial FE solver LS-DYNA® and a number of compression tests are performed. The results are compared to previous work, where several SR (data-driven) models were derived to reproduce the stress-strain curves.