Particle method modeling of nonlocal multiresolution continua

Zili Dai; Miguel A. Bessa; Shaofan Li; Wing K Liu

doi:10.1007/978-3-319-06898-5_3

Particle method modeling of nonlocal multiresolution continua

Zili Dai, Miguel A. Bessa, Shaofan Li, Wing K Liu^*

^*Corresponding author for this work

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This work is concerned with the application of two different particle methods, the state-based peridynamics and the reproducing kernel particle method, to model the nonlocal multiresolution continuum. It is shown that both methods lead to the same results in uniform grids, and that they can offer an alternative to the finite element method based multiscale analysis. The equivalence between the two methods is explained in a comparison study, which shows that the statebased peridynamics may have better computational efficiency, but the RKPM synchronized derivative approach may have the possibility of faster convergence.

Original language	English (US)
Title of host publication	Meshfree Methods for Partial Differential Equations VII
Editors	Michael Griebel, Marc Alexander Schweitzer
Publisher	Springer Verlag
Pages	1-59
Number of pages	59
ISBN (Electronic)	9783319068978
DOIs	https://doi.org/10.1007/978-3-319-06898-5_3
State	Published - Jan 1 2015
Event	7th International Workshop on Meshfree Methods for Partial Differential Equations, 2013 - Bonn, Germany Duration: Sep 9 2013 → Sep 11 2013

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	100
ISSN (Print)	1439-7358

Other

Other	7th International Workshop on Meshfree Methods for Partial Differential Equations, 2013
Country/Territory	Germany
City	Bonn
Period	9/9/13 → 9/11/13

Keywords

Micromorphic continuum
Multiresolution continuum
Reproducing kernel particle method
State-based peridynamics

ASJC Scopus subject areas

Modeling and Simulation
Engineering(all)
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-319-06898-5_3

Cite this

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title = "Particle method modeling of nonlocal multiresolution continua",

abstract = "This work is concerned with the application of two different particle methods, the state-based peridynamics and the reproducing kernel particle method, to model the nonlocal multiresolution continuum. It is shown that both methods lead to the same results in uniform grids, and that they can offer an alternative to the finite element method based multiscale analysis. The equivalence between the two methods is explained in a comparison study, which shows that the statebased peridynamics may have better computational efficiency, but the RKPM synchronized derivative approach may have the possibility of faster convergence.",

keywords = "Micromorphic continuum, Multiresolution continuum, Reproducing kernel particle method, State-based peridynamics",

author = "Zili Dai and Bessa, {Miguel A.} and Shaofan Li and Liu, {Wing K}",

year = "2015",

month = jan,

day = "1",

doi = "10.1007/978-3-319-06898-5_3",

language = "English (US)",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Verlag",

pages = "1--59",

editor = "Michael Griebel and Schweitzer, {Marc Alexander}",

booktitle = "Meshfree Methods for Partial Differential Equations VII",

address = "Germany",

note = "7th International Workshop on Meshfree Methods for Partial Differential Equations, 2013 ; Conference date: 09-09-2013 Through 11-09-2013",

}

Dai, Z, Bessa, MA, Li, S & Liu, WK 2015, Particle method modeling of nonlocal multiresolution continua. in M Griebel & MA Schweitzer (eds), Meshfree Methods for Partial Differential Equations VII. Lecture Notes in Computational Science and Engineering, vol. 100, Springer Verlag, pp. 1-59, 7th International Workshop on Meshfree Methods for Partial Differential Equations, 2013, Bonn, Germany, 9/9/13. https://doi.org/10.1007/978-3-319-06898-5_3

Particle method modeling of nonlocal multiresolution continua. / Dai, Zili; Bessa, Miguel A.; Li, Shaofan; Liu, Wing K.

Meshfree Methods for Partial Differential Equations VII. ed. / Michael Griebel; Marc Alexander Schweitzer. Springer Verlag, 2015. p. 1-59 (Lecture Notes in Computational Science and Engineering; Vol. 100).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Particle method modeling of nonlocal multiresolution continua

AU - Dai, Zili

AU - Bessa, Miguel A.

AU - Li, Shaofan

AU - Liu, Wing K

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Y1 - 2015/1/1

N2 - This work is concerned with the application of two different particle methods, the state-based peridynamics and the reproducing kernel particle method, to model the nonlocal multiresolution continuum. It is shown that both methods lead to the same results in uniform grids, and that they can offer an alternative to the finite element method based multiscale analysis. The equivalence between the two methods is explained in a comparison study, which shows that the statebased peridynamics may have better computational efficiency, but the RKPM synchronized derivative approach may have the possibility of faster convergence.

AB - This work is concerned with the application of two different particle methods, the state-based peridynamics and the reproducing kernel particle method, to model the nonlocal multiresolution continuum. It is shown that both methods lead to the same results in uniform grids, and that they can offer an alternative to the finite element method based multiscale analysis. The equivalence between the two methods is explained in a comparison study, which shows that the statebased peridynamics may have better computational efficiency, but the RKPM synchronized derivative approach may have the possibility of faster convergence.

KW - Micromorphic continuum

KW - Multiresolution continuum

KW - Reproducing kernel particle method

KW - State-based peridynamics

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BT - Meshfree Methods for Partial Differential Equations VII

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ER -

Particle method modeling of nonlocal multiresolution continua

Abstract

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Keywords

ASJC Scopus subject areas

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