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Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks

Sahin, Tarik and von Danwitz, Max and Popp, Alexander (2024) Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks. Advanced Modeling and Simulation in Engineering Sciences, 11. Springer Nature. doi: 10.1186/s40323-024-00265-3. ISSN 2213-7467.

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Official URL: https://amses-journal.springeropen.com/articles/10.1186/s40323-024-00265-3

Abstract

This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush-Kuhn-Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer-Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.

Item URL in elib:https://elib.dlr.de/203753/
Document Type:Article
Title:Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Sahin, TarikUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
von Danwitz, MaxUNSPECIFIEDhttps://orcid.org/0000-0002-2814-0027158928719
Popp, AlexanderUNSPECIFIEDhttps://orcid.org/0000-0002-8820-466X158928722
Date:3 May 2024
Journal or Publication Title:Advanced Modeling and Simulation in Engineering Sciences
Refereed publication:Yes
Open Access:Yes
Gold Open Access:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:11
DOI:10.1186/s40323-024-00265-3
Editors:
EditorsEmailEditor's ORCID iDORCID Put Code
Ladevèze, PierreUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Publisher:Springer Nature
Series Name:Advances in Machine Learning and Computational Mechanics
ISSN:2213-7467
Status:Published
Keywords:Physics-informed neural networks, Mixed-variable formulation, Contact mechanics, Enforcing inequalities, Fischer-Burmeister NCP-function
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:no assignment
DLR - Program:no assignment
DLR - Research theme (Project):no assignment
Location: Rhein-Sieg-Kreis
Institutes and Institutions:Institute for the Protection of Terrestrial Infrastructures > Simulation Methods for Digital Twins
Institute for the Protection of Terrestrial Infrastructures
Deposited By: von Danwitz, Max
Deposited On:17 Apr 2024 16:22
Last Modified:03 May 2024 15:22

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