Peridynamic Petrov–Galerkin method

A generalization of the peridynamic theory of correspondence materials

authored by: T. Bode, C. Weißenfels, P. Wriggers
Abstract: The Peridynamic Petrov–Galerkin (PPG) method is a meshfree approach based on the peridynamic integro-differential form of the momentum equation. The spurious oscillations in the common peridynamic correspondence formulation are investigated. They occur due to an inadmissible linearized mapping of the family deformation field. This leads to a generalized correspondence formulation, which contains the common formulation as a special case. It is based on the weak form of the peridynamic momentum equation. Test and trial function requirements are examined which ensure an exact imposition of Dirichlet and Neumann boundary conditions and Weighted Least Square (WLS) shape functions as well as Local Maximum Entropy (LME) approximants are utilized to examine the PPG Method. A consistent linearization is provided, which can also be used to speed up common implicit peridynamic correspondence codes. It is used in an implicit quasistatic framework to investigate the impact of different shape function combinations. Test cases show that low-energy modes can be prevented by the PPG Method and highlight the fast convergence and stability.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 358
ISSN: 0045-7825
Publication date: 24.09.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2019.112636 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{493b7bd52209418b8683e24fa5c6f16e,
title = "Peridynamic Petrov–Galerkin method: A generalization of the peridynamic theory of correspondence materials",
abstract = "The Peridynamic Petrov–Galerkin (PPG) method is a meshfree approach based on the peridynamic integro-differential form of the momentum equation. The spurious oscillations in the common peridynamic correspondence formulation are investigated. They occur due to an inadmissible linearized mapping of the family deformation field. This leads to a generalized correspondence formulation, which contains the common formulation as a special case. It is based on the weak form of the peridynamic momentum equation. Test and trial function requirements are examined which ensure an exact imposition of Dirichlet and Neumann boundary conditions and Weighted Least Square (WLS) shape functions as well as Local Maximum Entropy (LME) approximants are utilized to examine the PPG Method. A consistent linearization is provided, which can also be used to speed up common implicit peridynamic correspondence codes. It is used in an implicit quasistatic framework to investigate the impact of different shape function combinations. Test cases show that low-energy modes can be prevented by the PPG Method and highlight the fast convergence and stability.",
keywords = "Consistent linearization, Meshfree method, Peridynamic correspondence formulation, Peridynamic reduction, Petrov–Galerkin method, Smoothed particle hydrodynamics",
author = "T. Bode and C. Wei{\ss}enfels and P. Wriggers",
year = "2019",
month = sep,
day = "24",
doi = "10.1016/j.cma.2019.112636",
language = "English",
volume = "358",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}