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

TL;DR

The paper addresses deriving empirical constitutive models for age-hardenable aluminium alloy AA6082 and high-chromium martensitic steel X20CrMoV12-1 under plastic deformation. It applies symbolic regression via a multi-objective genetic programming pipeline with systematic cross-validation to generate closed-form stress–strain relationships from compression and tension data. Key findings include longer, more accurate expressions for AA6082 due to data availability, and more compact models with potential overfitting for the steel data, with expressions often incorporating logarithmic, hyperbolic, and square-root terms. The work demonstrates a data-driven route to transferable constitutive laws for metallic alloys while emphasizing data quality and uncertainty as critical factors, and suggests integrating domain knowledge and physics constraints to enhance extrapolation and generalization.

Abstract

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.