Evgeniya Kabliman

Evgeniya Kabliman, Gabriel Kronberger

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.

Gabriel Kronberger, Evgeniya Kabliman, Johannes Kronsteiner et al.

In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on processing conditions. Currently, these parameters must be optimized to fit measured data since their relations to processing conditions (e.g. deformation temperature, strain rate) are not fully understood. We present a new approach that identifies the functional dependency of calibration parameters from processing conditions based on genetic programming. We propose two (explicit and implicit) methods to identify these dependencies and generate short interpretable expressions. The approach is used to extend a physics-based constitutive model for deformation processes. This constitutive model operates with internal material variables such as a dislocation density and contains a number of parameters, among them three calibration parameters. The derived expressions extend the constitutive model and replace the calibration parameters. Thus, interpolation between various processing parameters is enabled. Our results show that the implicit method is computationally more expensive than the explicit approach but also produces significantly better results.