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Polyconvex neural network models of thermoelasticity

Fuhg, Jan N. ; Jadoon, Asghar ; Weeger, Oliver ; Seidl, D. Thomas ; Jones, Reese E. (2024)
Polyconvex neural network models of thermoelasticity.
In: Journal of the Mechanics and Physics of Solids, 192
doi: 10.1016/j.jmps.2024.105837
Artikel, Bibliographie

Kurzbeschreibung (Abstract)

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

Typ des Eintrags: Artikel
Erschienen: 2024
Autor(en): Fuhg, Jan N. ; Jadoon, Asghar ; Weeger, Oliver ; Seidl, D. Thomas ; Jones, Reese E.
Art des Eintrags: Bibliographie
Titel: Polyconvex neural network models of thermoelasticity
Sprache: Englisch
Publikationsjahr: 28 August 2024
Verlag: Elsevier
Titel der Zeitschrift, Zeitung oder Schriftenreihe: Journal of the Mechanics and Physics of Solids
Jahrgang/Volume einer Zeitschrift: 192
DOI: 10.1016/j.jmps.2024.105837
Kurzbeschreibung (Abstract):

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

ID-Nummer: Artikel-ID: 105837
Fachbereich(e)/-gebiet(e): 16 Fachbereich Maschinenbau
16 Fachbereich Maschinenbau > Fachgebiet Cyber-Physische Simulation (CPS)
Hinterlegungsdatum: 10 Sep 2024 05:48
Letzte Änderung: 10 Sep 2024 06:04
PPN: 521297443
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