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Polyconvex anisotropic hyperelasticity with neural networks

Klein, Dominik K. ; Fernández, Mauricio ; Martin, Robert J. ; Neff, Patrizio ; Weeger, Oliver (2022)
Polyconvex anisotropic hyperelasticity with neural networks.
In: Journal of the Mechanics and Physics of Solids, 2021, 159
doi: 10.26083/tuprints-00020163
Article, Secondary publication, Postprint

Copyright Information: CC BY-NC-ND 4.0 International - Creative Commons, Attribution NonCommercial, NoDerivs.

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Item Type: Article
Type of entry: Secondary publication
Title: Polyconvex anisotropic hyperelasticity with neural networks
Language: English
Date: 3 August 2022
Place of Publication: Darmstadt
Year of primary publication: 2021
Publisher: Elsevier
Journal or Publication Title: Journal of the Mechanics and Physics of Solids
Volume of the journal: 159
Collation: 32 Seiten
DOI: 10.26083/tuprints-00020163
Corresponding Links:
Origin: Secondary publication service

In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. In addition, the models are calibrated with transversely isotropic data, generated with an analytical polyconvex potential. For this case, both models show excellent results, demonstrating the straightforward applicability of the polyconvex neural network constitutive models to other symmetry groups.

Uncontrolled Keywords: constitutive modeling, nonlinear elasticity, anisotropic hyperelasticity, polyconvexity, ellipticity, material stability, soft materials, metamaterials, invariants, structural tensors, parameter identification, data-driven modeling, machine learning, input convex neural networks
Status: Postprint
URN: urn:nbn:de:tuda-tuprints-201634
Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 03 Aug 2022 12:18
Last Modified: 30 Nov 2023 00:04
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/20163
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