Accounting for plasticity: An extension of inelastic constitutive artificial neural networks - Boes, Birte; Simon, Jaan Willem; Holthusen, Hagen (European Journal of Mechanics A-Solids, 2026)
In this work, we extend the framework of inelastic constitutive artificial neural networks (iCANNs) by incorporating plasticity. Thereby, we increase their applicability to capture more complex material behavior by solving the underlying inequality constraints associated with plasticity, aiming to automatically discover the formulation that matches the experimental data most accurately. Learning on stress–strain data, our approach enables the automatic discovery of the constitutive equations for elasto-plastic materials – including the identification of the material parameters and the underlying functional forms of the Helmholtz free energy, yield function and evolution equations for the inelastic deformations including linear and nonlinear kinematic hardening. These are captured using feed-forward neural networks. The proposed methodology ensures objectivity, material symmetry, and thermodynamic consistency, providing a robust and interpretable basis for automatic model discovery at finite strains. Investigation of our model's prediction showed that the extended iCANNs successfully predict both linear and nonlinear kinematic hardening behavior based on experimental and artificially generated datasets, showcasing promising capabilities of this framework. Nonetheless, challenges remain in fully capturing complex yield criteria – such as those exhibiting tension–compression asymmetry – and predicting complex nonlinear hardening.
CRIS-Team Scopus Importer:2025-12-26
Keywords: Automated model discovery; Constitutive artificial neural networks; Constitutive modeling; Kinematic hardening; Machine learning; Plasticity

A complement to neural networks for anisotropic inelasticity at finite strains - Holthusen, Hagen; Kuhl, Ellen (Computer Methods in Applied Mechanics and Engineering, 2026)
We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently incorporates anisotropy, and–unlike conventional convex formulations–satisfies the dissipation inequality without requiring convexity. Our neural network architecture employs invariant-based input representations in terms of mixed elastic, inelastic and structural tensors. It adapts Input Convex Neural Networks, and introduces Input Monotonic Neural Networks to broaden the admissible potential class. To circumvent the use of exponential-map time integration during training–which often leads to numerical instabilities–we employ recurrent Liquid Neural Networks as an auxiliary architecture. During inference, however, the exponential-map update is reinstated to ensure admissibility of the inelastic variables. The approach is evaluated at both material point and structural scales. We benchmark against recurrent models without physical constraints and validate predictions of deformation and reaction forces for unseen boundary value problems. In all cases, the method delivers accurate and stable performance beyond the training regime. The neural network and finite element implementations are available as open-source and are accessible to the public via Zenodo.org.
CRIS-Team Scopus Importer:2025-12-19
Keywords: Anisotropy; Automated model discovery; Finite element simulation; Finite strains; Inelasticity; Neural networks