A complement to neural networks for anisotropic inelasticity at finite strains

Holthusen H, Kuhl E (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Computer Methods in Applied Mechanics and Engineering Elsevier

Book Volume: 450

Article Number: 118612

DOI: 10.1016/j.cma.2025.118612

Abstract

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.

Authors with CRIS profile

Hagen Holthusen Lehrstuhl für Technische Mechanik (LTM) Ellen Kuhl

Involved external institutions

Stanford University US United States (USA) (US)

How to cite

APA:

Holthusen, H., & Kuhl, E. (2026). A complement to neural networks for anisotropic inelasticity at finite strains. Computer Methods in Applied Mechanics and Engineering, 450. https://doi.org/10.1016/j.cma.2025.118612

MLA:

Holthusen, Hagen, and Ellen Kuhl. "A complement to neural networks for anisotropic inelasticity at finite strains." Computer Methods in Applied Mechanics and Engineering 450 (2026).

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