Inelastic Constitutive Kolmogorov–Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models

Ji C, Abdolazizi KP, Holthusen H, Cyron CJ, Linka K (2026)

Publication Type: Journal article

Publication year: 2026

Journal

International Journal of Engineering Science Elsevier

Book Volume: 228

Article Number: 104630

DOI: 10.1016/j.ijengsci.2026.104630

Abstract

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has led to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov–Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding free energy and dissipation potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.

Authors with CRIS profile

Hagen Holthusen Lehrstuhl für Technische Mechanik (LTM)

Involved external institutions

Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen DE Germany (DE) Technische Universität Hamburg-Harburg (TUHH) DE Germany (DE)

How to cite

APA:

Ji, C., Abdolazizi, K.P., Holthusen, H., Cyron, C.J., & Linka, K. (2026). Inelastic Constitutive Kolmogorov–Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models. International Journal of Engineering Science, 228. https://doi.org/10.1016/j.ijengsci.2026.104630

MLA:

Ji, Chenyi, et al. "Inelastic Constitutive Kolmogorov–Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models." International Journal of Engineering Science 228 (2026).

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