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A Penalty Method for Coupling of Finite-Element and Peridynamic Models

Pernatii, Anna and Gabbert, Ulrich and Naumenko, Konstantin and Hesse, Jan-Timo and Willberg, Christian (2023) A Penalty Method for Coupling of Finite-Element and Peridynamic Models. Proceedings in Applied Mathematics and Mechanics, 22 (1). Wiley. doi: 10.1002/pamm.202200151. ISSN 1617-7061.

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Official URL: https://onlinelibrary.wiley.com/doi/10.1002/pamm.202200151


A classical continuum mechanics model no longer fulfills its basic assumptions, when the deformations are not smooth or discontinuous. Peridynamics (PD) as an integral formulation could better overcome these issues. Therefore, it is better suited to solve fracture problems such as crack initiation, its growth and formation of crack patterns. In PD the magnitudes of internal forces at a material point depend on the collective interaction of all material points within a subdomain called horizon. To take advances from the formulation, typically it is implemented in a mesh-free form. In that case, it is easy to separate interactions between different material points. As consequence, a relatively high resolution is required to describe continuous deformation functions and, consequently computationally expensive. Therefore, the application of mesh-free PD in undamaged regions requires an unnecessary high effort for receiving sufficient accurate results. In contrast, the finite element method (FEM) as a classical continuum mechanics-based approach, is very efficient, if continuous stress distributions can be assumed. Consequently, a computational cost reduction can be achieved, if the PD is applied in the local damaged zone only and the remaining area is modeled and analyzed with the classical FEM. Realization of such an approach requires a sufficient accurate coupling of the PD and the FEM subdomains. A brief overview about different coupling approaches is given. Then the general approach of an Arlequin based method is presented. Here the coupling is achieved via an overlapping of PD and FEM areas. The coupling equations are developed and realized with help of the Penalty method. The Penalty method is considered as an alternative procedure to the Lagrange multiplier strategy without creating new unknowns, which essentially simplifies the coupled PD-FEM approach. The validity and limits of the proposed technique are demonstrated through analysis, where the choice of the Penalty number is discussed as well as artificial wave oscillations, caused by the coupling area

Item URL in elib:https://elib.dlr.de/194751/
Document Type:Article
Title:A Penalty Method for Coupling of Finite-Element and Peridynamic Models
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Pernatii, AnnaUNSPECIFIEDhttps://orcid.org/0000-0002-0004-0577UNSPECIFIED
Gabbert, UlrichInstitut für Mechanik, Universität MagdeburgUNSPECIFIEDUNSPECIFIED
Hesse, Jan-TimoUNSPECIFIEDhttps://orcid.org/0000-0002-3006-1520134149639
Willberg, ChristianUNSPECIFIEDhttps://orcid.org/0000-0003-2433-9183UNSPECIFIED
Date:24 March 2023
Journal or Publication Title:Proceedings in Applied Mathematics and Mechanics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:No
Keywords:Peridynamics, FEM, Numerics
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Efficient Vehicle
DLR - Research area:Aeronautics
DLR - Program:L EV - Efficient Vehicle
DLR - Research theme (Project):L - Virtual Aircraft and  Validation
Location: Braunschweig
Institutes and Institutions:Institut für Systemleichtbau > Structural Mechanics
Deposited By: Willberg, Dr.-Ing. Christian
Deposited On:02 May 2023 08:55
Last Modified:19 Oct 2023 14:58

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