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Title: A reproducing kernel enhanced approach for peridynamic solutions

Abstract

The most common discretization method for peridynamic models used in engineering problems is the node-based meshfree approach. This method discretizes peridynamic domains by a set of nodes, each associated with a nodal cell with a characteristic volume, leading to a particle-based description of continuum systems. The behavior of each particle is then considered representative of its cell. This limits the convergence rate to the first order. In this paper, we introduce a reproducing kernel (RK) approximation to the field variables in the peridynamic equations to increase the order of convergence of peridynamic numerical solutions. Furthermore, the numerical results demonstrate improved convergence rates in static peridynamic problems using the proposed method.

Authors:
 [1];  [2]; ORCiD logo [1];  [2]; ORCiD logo [3]
+ Show Author Affiliations
  1. Univ. of California San Diego, La Jolla, CA (United States)
  2. The Univ. of Texas at Austin, Austin, TX (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1465030
Alternate Identifier(s):
OSTI ID: 1548232
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 340; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Peridynamics; Reproducing kernel approximation; Meshfree method; Domain integration; Nonlocal

Citation Formats

Pasetto, Marco, Leng, Yu, Chen, Jiun -Shyan, Foster, John T., and Seleson, Pablo D. A reproducing kernel enhanced approach for peridynamic solutions. United States: N. p., 2018. Web. doi:10.1016/j.cma.2018.05.010.
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Pasetto, Marco, Leng, Yu, Chen, Jiun -Shyan, Foster, John T., & Seleson, Pablo D. A reproducing kernel enhanced approach for peridynamic solutions. United States. https://doi.org/10.1016/j.cma.2018.05.010
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Pasetto, Marco, Leng, Yu, Chen, Jiun -Shyan, Foster, John T., and Seleson, Pablo D. Tue . "A reproducing kernel enhanced approach for peridynamic solutions". United States. https://doi.org/10.1016/j.cma.2018.05.010. https://www.osti.gov/servlets/purl/1465030.
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@article{osti_1465030,
title = {A reproducing kernel enhanced approach for peridynamic solutions},
author = {Pasetto, Marco and Leng, Yu and Chen, Jiun -Shyan and Foster, John T. and Seleson, Pablo D.},
abstractNote = {The most common discretization method for peridynamic models used in engineering problems is the node-based meshfree approach. This method discretizes peridynamic domains by a set of nodes, each associated with a nodal cell with a characteristic volume, leading to a particle-based description of continuum systems. The behavior of each particle is then considered representative of its cell. This limits the convergence rate to the first order. In this paper, we introduce a reproducing kernel (RK) approximation to the field variables in the peridynamic equations to increase the order of convergence of peridynamic numerical solutions. Furthermore, the numerical results demonstrate improved convergence rates in static peridynamic problems using the proposed method.},
doi = {10.1016/j.cma.2018.05.010},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 340,
place = {United States},
year = {Tue May 22 00:00:00 EDT 2018},
month = {Tue May 22 00:00:00 EDT 2018}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.cma.2018.05.010
Copyright Statement
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Cited by: 28 works
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Figures / Tables:

Figure 1 Figure 1: Meshfree discretization with RK approximation kernel function.
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    Solutions of the linear and nonlinear differential equations within the generalized fractional derivatives
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