Convergence studies in meshfree peridynamic simulations

Pablo Seleson; David J. Littlewood

doi:10.1016/j.camwa.2015.12.021

Convergence studies in meshfree peridynamic simulations

Pablo Seleson, David J. Littlewood

Multiscale Methods

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

125 Scopus citations

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. In this paper, we perform convergence studies of static peridynamic problems. We show 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. Numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions when using the proposed methods.

Original language	English
Pages (from-to)	2432-2448
Number of pages	17
Journal	Computers and Mathematics with Applications
Volume	71
Issue number	11
DOIs	https://doi.org/10.1016/j.camwa.2015.12.021
State	Published - Jun 1 2016

Funding

This study was supported in part by the Householder Fellowship which is jointly funded by: the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program , under award number ERKJE45 , and the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory (ORNL) , which is operated by UT-Battelle, LLC., for the US Department of Energy under Contract DE-AC05-00OR22725; and by the Laboratory Directed Research and Development program at Sandia National Laboratories , which is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. We acknowledge helpful discussions with Stephen Bond, Max Gunzburger, John Mitchell, Jakob Ostien, Michael L. Parks, Stewart Silling, and Dan Turner.

Funders	Funder number
US Department of Energy
Lockheed Martin Corporation
Office of Science
National Nuclear Security Administration	DE-AC04-94AL85000
Advanced Scientific Computing Research	ERKJE45
Oak Ridge National Laboratory	DE-AC05-00OR22725
Sandia National Laboratories
Laboratory Directed Research and Development

Keywords

Convergence
Influence functions
Meshfree method
Partial volumes
Peridynamics

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10.1016/j.camwa.2015.12.021

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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. In this paper, we perform convergence studies of static peridynamic problems. We show 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. Numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions when using the proposed methods.",

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AB - 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. In this paper, we perform convergence studies of static peridynamic problems. We show 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. Numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions when using the proposed methods.

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Convergence studies in meshfree peridynamic simulations

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