Identification of Empirical Constitutive Models for Age-Hardenable Aluminium Alloy and High-Chromium Martensitic Steel Using Symbolic Regression

Process-structure-property relationships are fundamental in materials science and engineering and are key to the development of new and improved materials. Symbolic regression serves as a powerful tool for uncovering mathematical models that describe these relationships. It can automatically generate equations to predict material behaviour under specific manufacturing conditions and optimize performance characteristics such as strength and elasticity. The present work illustrates how symbolic regression can derive constitutive models that describe the behaviour of various metallic alloys during plastic deformation. Constitutive modelling is a mathematical framework for understanding the relationship between stress and strain in materials under different loading conditions. In this study, two materials (age-hardenable aluminium alloy and high-chromium martensitic steel) and two different testing methods (compression and tension) are considered to obtain the required stress-strain data. The results highlight the benefits of using symbolic regression while also discussing potential challenges.

Predicting Calibration Parameter Values for Constitutive Models using Genetic Programming

In material science, models are derived to describe emergent properties (e.g. elasticity, strength, conductivity, ...) and their relations to the material and processing conditions. Constitutive models are models that describe the behaviour of materials for instance deformation processes through applied forces. We describe a general method for the extension of constitutive white-box models using genetic programming (GP). The method is demonstrated for a constitutive model which is used in computational mechanics to describe the material response to various thermo-mechanical loading conditions. This model operates with internal material variables such a dislocation density and contains a number of parameters. Among them there are three calibration parameters, which are usually fit to measured data since the relations to the processing conditions (e.g. deformation temperature, strain rate) are not fully understood. Our proposed GP-based method identifies these relations and generates short expressions which can be plugged into the constitutive model instead of the calibration parameters. This would enable interpolation as well as extrapolation which is crucial for constitutive modelling. Our results show that evolving extensions for the constitutive model implicitly with GP leads to better predictive accuracy than explicitly learning independent formulas for predicting calibration parameters with symbolic regression.