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A FEM-PD coupling based on an Arlequin approach to impose boundary conditions in Peridynamics

Pernatii, Anna and Gabbert, Ulrich and Willberg, Christian and Hesse, Jan-Timo (2023) A FEM-PD coupling based on an Arlequin approach to impose boundary conditions in Peridynamics. 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, 30. May - 2. June 2023, Dresden, Germany.

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Abstract

The peridynamic approach (PD) is a continuous theory that is well suited for solving damage problems. Because of the non-local formulation, PD can predict the response of a material and fracture patterns with high probability in high dynamic processes. In PD, some parameters differ from the continuum formulation and have some deviation in discretized PD systems, such as a horizon. A material constant becomes a parameter dependent on the meshsize. A sticking point, which has to be considered, is that an incomplete horizon at the boundaries results in an unphysical variation of the materials stiffness in these regions. Material points at the boundaries do not have an entire non-local neighborhood, meaning the points have fewer bonds and are softer than points within the domain. This leads to the so-called surface effect. The difficulties in applying the classical local initial and boundary conditions happen because of the non-local character of the PD. To overcome this problem, several correction techniques have been developed. Nevertheless, a standard method to describe them is not available yet. An alternative approach is the application of the earlier proposed FEM-PD coupling, which can be seen as a local-nonlocal coupling method. The damage-free zones are analyzed by the FEM as classical local theory, while the domain where the fracture is expected is modeled with the PD as a non-local theory. Consequently, the reduction of the computational effort as well as the imposing of the conventional local boundary conditions, is achieved. The coupling method is based on the Arlequin method - an energy-based procedure where the energy of a system is found as a weighted average of both systems. The mechanical ompatibility in the overlapping zone of both domains is reached by implementing constraints with the help of the penalty method. In the paper at hand, the focus is on imposing BCs. The proposed method is applied to both static and dynamic applications. The accuracy and convergence behavior is evaluated by analyzing test examples.

Item URL in elib:https://elib.dlr.de/195381/
Document Type:Conference or Workshop Item (Speech)
Title:A FEM-PD coupling based on an Arlequin approach to impose boundary conditions in Peridynamics
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Pernatii, AnnaUNSPECIFIEDhttps://orcid.org/0000-0002-0004-0577UNSPECIFIED
Gabbert, UlrichInstitut für Mechanik, Universität MagdeburgUNSPECIFIEDUNSPECIFIED
Willberg, ChristianUNSPECIFIEDhttps://orcid.org/0000-0003-2433-9183UNSPECIFIED
Hesse, Jan-TimoUNSPECIFIEDhttps://orcid.org/0000-0002-3006-1520136732782
Date:2023
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:Peridynamics, FEM, Numerics
Event Title:93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics
Event Location:Dresden, Germany
Event Type:international Conference
Event Dates:30. May - 2. June 2023
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:12 Jun 2023 09:56
Last Modified:12 Jun 2023 09:56

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