Application of symbolic regression for constitutive modeling of plastic deformation

Abstract

In numerical process simulations, in-depth knowledge about material behavior during processing in the form of trustworthy material models is crucial. Among the different constitutive models used in the literature one can distinguish a physics-based approach (white-box model), which considers the evolution of material internal state variables, such as mean dislocation density, and data-driven models (grey or even black-box). Typically, parameters in physics-based models such as physical constants or material parameters, are interpretable and have a physical meaning. However, even physics-based models often contain calibration coefficients that are fitted to experimental data. In the present work, we investigate the applicability of symbolic regression for (1) predicting calibration coefficients of a physics-based model and (2) for deriving a constitutive model directly from measurement data. Our goal is to find mathematical expressions, which can be integrated into numerical simulation models. For this purpose, we have chosen symbolic regression to derive the constitutive equations based on data from compression testing with varying process parameters. To validate the derived constitutive models, we have implemented them into a FE solver (herein, LS-DYNA®), and calculated the force-displacement curves. The comparison with experiments shows a reasonable agreement for both data-driven and physics-based (with fitted and learned calibration parameters) models.

Keywords

• Material constitutive equations
• Machine learning
• Symbolic regression
• Data-driven modelling
• Physics-based modelling
• Finite element analysis