Application of Enhanced Peridynamic Correspondence Formulation for Three-Dimensional Simulations at Large Strains

verfasst von: Philipp Hartmann, Christian Weißenfels, Peter Wriggers
Abstract: Within the theory of Peridynamics standard continuum mechanical material models can be applied using the so-called correspondence formulation. However, the correspondence formulation is susceptible to instabilities in the resulting displacement field, which makes the method inapplicable for simulations at large strains. Hence, the application of a suitable numerical approach to eliminate this drawback is required. Besides a general introduction into Peridynamics, different possibilities to prevent the appearing of the arising instabilities are presented in this chapter. One such approach comes without the necessity of additional stabilisation parameters and is based on the subdivision of the non-local interaction region of interest. Further, it is denoted as the enhanced peridynamic correspondence formulation. In the numerical examples it is demonstrated that for this formulation the instabilities in the displacement field disappear for three-dimensional examples at large strains. In addition, previously unknown limitations of the enhanced peridynamic correspondence formulation are shown within the numerical examples. These are slight, non-physical, deviations in the deformation field and in case of torsion dominated problems a non-physical representation of the stress field.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Typ: Beitrag in Buch/Sammelwerk
Seiten: 81-104
Anzahl der Seiten: 24
Publikationsdatum: 04.03.2020
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Maschinenbau, Theoretische Informatik und Mathematik
Elektronische Version(en): https://doi.org/10.1007/978-3-030-38156-1_5 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@inbook{a0abab0f62c348cc82806c2cf8233554,
title = "Application of Enhanced Peridynamic Correspondence Formulation for Three-Dimensional Simulations at Large Strains",
abstract = "Within the theory of Peridynamics standard continuum mechanical material models can be applied using the so-called correspondence formulation. However, the correspondence formulation is susceptible to instabilities in the resulting displacement field, which makes the method inapplicable for simulations at large strains. Hence, the application of a suitable numerical approach to eliminate this drawback is required. Besides a general introduction into Peridynamics, different possibilities to prevent the appearing of the arising instabilities are presented in this chapter. One such approach comes without the necessity of additional stabilisation parameters and is based on the subdivision of the non-local interaction region of interest. Further, it is denoted as the enhanced peridynamic correspondence formulation. In the numerical examples it is demonstrated that for this formulation the instabilities in the displacement field disappear for three-dimensional examples at large strains. In addition, previously unknown limitations of the enhanced peridynamic correspondence formulation are shown within the numerical examples. These are slight, non-physical, deviations in the deformation field and in case of torsion dominated problems a non-physical representation of the stress field.",
author = "Philipp Hartmann and Christian Wei{\ss}enfels and Peter Wriggers",
note = "Funding information: The author kindly acknowledges the DFG and ViVaCE (IRTG 1627) for financial support.",
year = "2020",
month = mar,
day = "4",
doi = "10.1007/978-3-030-38156-1_5",
language = "English",
isbn = "9783030381554",
series = "Lecture Notes in Applied and Computational Mechanics",
publisher = "Springer Nature",
pages = "81--104",
booktitle = "Lecture Notes in Applied and Computational Mechanics",
address = "United States",
}