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Title: Convergence studies in meshfree peridynamic simulations

Abstract

Meshfree methods are commonly applied to discretize peridynamic models, particularly in numerical simulations of engineering problems. Such methods discretize peridynamic bodies using a set of nodes with characteristic volume, leading to particle-based descriptions of systems. For this study, we performed convergence studies of static peridynamic problems. We demonstrate that commonly used meshfree methods in peridynamics suffer from accuracy and convergence issues, due to a rough approximation of the contribution of nodes near the boundary of the neighborhood of a given node to numerical integrations. We propose two methods to improve meshfree peridynamic simulations. The first method uses accurate computations of volumes of intersections between neighbor cells and the neighborhood of a given node, referred to as partial volumes. The second method employs smooth influence functions with a finite support within peridynamic kernels. Lastly, numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions when using the proposed methods.

Authors:
;
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1631366
Alternate Identifier(s):
OSTI ID: 1259537; OSTI ID: 1311292; OSTI ID: 1351648
Report Number(s):
SAND-2015-8836J
Journal ID: ISSN 0898-1221; S0898122115005891; PII: S0898122115005891
Grant/Contract Number:  
ERKJE45; AC05-00OR22725; AC04-94AL85000
Resource Type:
Published Article
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford) Journal Volume: 71 Journal Issue: 11; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United Kingdom
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; peridynamics; meshfree method; convergence; partial volumes; influence functions

Citation Formats

Seleson, Pablo, and Littlewood, David J. Convergence studies in meshfree peridynamic simulations. United Kingdom: N. p., 2016. Web. https://doi.org/10.1016/j.camwa.2015.12.021.
Seleson, Pablo, & Littlewood, David J. Convergence studies in meshfree peridynamic simulations. United Kingdom. https://doi.org/10.1016/j.camwa.2015.12.021
Seleson, Pablo, and Littlewood, David J. Wed . "Convergence studies in meshfree peridynamic simulations". United Kingdom. https://doi.org/10.1016/j.camwa.2015.12.021.
@article{osti_1631366,
title = {Convergence studies in meshfree peridynamic simulations},
author = {Seleson, Pablo and Littlewood, David J.},
abstractNote = {Meshfree methods are commonly applied to discretize peridynamic models, particularly in numerical simulations of engineering problems. Such methods discretize peridynamic bodies using a set of nodes with characteristic volume, leading to particle-based descriptions of systems. For this study, we performed convergence studies of static peridynamic problems. We demonstrate that commonly used meshfree methods in peridynamics suffer from accuracy and convergence issues, due to a rough approximation of the contribution of nodes near the boundary of the neighborhood of a given node to numerical integrations. We propose two methods to improve meshfree peridynamic simulations. The first method uses accurate computations of volumes of intersections between neighbor cells and the neighborhood of a given node, referred to as partial volumes. The second method employs smooth influence functions with a finite support within peridynamic kernels. Lastly, numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions when using the proposed methods.},
doi = {10.1016/j.camwa.2015.12.021},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 11,
volume = 71,
place = {United Kingdom},
year = {2016},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.camwa.2015.12.021

Citation Metrics:
Cited by: 7 works
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