A meshfree unification: Reproducing kernel peridynamics

M. A. Bessa; J. T. Foster; T. Belytschko; Wing Kam Liu

doi:10.1007/s00466-013-0969-x

A meshfree unification: Reproducing kernel peridynamics

M. A. Bessa, J. T. Foster, T. Belytschko, Wing Kam Liu^*

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

150 Scopus citations

Abstract

This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM). It is concluded that the discretization of state-based peridynamics leads directly to an approximation of the derivatives that can be obtained from RKPM. However, state-based peridynamics obtains the same result at a significantly lower computational cost which motivates its use in large-scale computations. In light of the findings of this study, an update to the method is proposed such that the limitations regarding application of boundary conditions and the use of non-uniform grids are corrected by using the reproducing kernel approximation.

Original language	English (US)
Pages (from-to)	1251-1264
Number of pages	14
Journal	Computational Mechanics
Volume	53
Issue number	6
DOIs	https://doi.org/10.1007/s00466-013-0969-x
State	Published - Jun 2014

Funding

This work was funded in part by grants from the United States Air Force Office of Scientific Research grant number W911NF-11-1-0208 and National Energy Technology Laboratory grant number DE-FE0010808.

Keywords

Meshfree methods
Moving least squares
Reproducing kernel
State-based peridynamics
Strong form discretization
Weak form discretization

ASJC Scopus subject areas

Computational Mechanics
Ocean Engineering
Mechanical Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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Cite this

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title = "A meshfree unification: Reproducing kernel peridynamics",

abstract = "This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM). It is concluded that the discretization of state-based peridynamics leads directly to an approximation of the derivatives that can be obtained from RKPM. However, state-based peridynamics obtains the same result at a significantly lower computational cost which motivates its use in large-scale computations. In light of the findings of this study, an update to the method is proposed such that the limitations regarding application of boundary conditions and the use of non-uniform grids are corrected by using the reproducing kernel approximation.",

keywords = "Meshfree methods, Moving least squares, Reproducing kernel, State-based peridynamics, Strong form discretization, Weak form discretization",

author = "Bessa, {M. A.} and Foster, {J. T.} and T. Belytschko and Liu, {Wing Kam}",

note = "Funding Information: This work was funded in part by grants from the United States Air Force Office of Scientific Research grant number W911NF-11-1-0208 and National Energy Technology Laboratory grant number DE-FE0010808. ",

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AU - Bessa, M. A.

AU - Foster, J. T.

AU - Belytschko, T.

AU - Liu, Wing Kam

N1 - Funding Information: This work was funded in part by grants from the United States Air Force Office of Scientific Research grant number W911NF-11-1-0208 and National Energy Technology Laboratory grant number DE-FE0010808.

PY - 2014/6

Y1 - 2014/6

N2 - This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM). It is concluded that the discretization of state-based peridynamics leads directly to an approximation of the derivatives that can be obtained from RKPM. However, state-based peridynamics obtains the same result at a significantly lower computational cost which motivates its use in large-scale computations. In light of the findings of this study, an update to the method is proposed such that the limitations regarding application of boundary conditions and the use of non-uniform grids are corrected by using the reproducing kernel approximation.

AB - This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM). It is concluded that the discretization of state-based peridynamics leads directly to an approximation of the derivatives that can be obtained from RKPM. However, state-based peridynamics obtains the same result at a significantly lower computational cost which motivates its use in large-scale computations. In light of the findings of this study, an update to the method is proposed such that the limitations regarding application of boundary conditions and the use of non-uniform grids are corrected by using the reproducing kernel approximation.

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A meshfree unification: Reproducing kernel peridynamics

Abstract

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Keywords

ASJC Scopus subject areas

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