Multiple scale meshfree methods for damage fracture and localization

Wing Kam Liu; Su Hao; Ted Belytschko; Shao Fan Li; Chin Tang Chang

doi:10.1016/S0927-0256(99)00062-2

Multiple scale meshfree methods for damage fracture and localization

Wing Kam Liu^*, Su Hao, Ted Belytschko, Shao Fan Li, Chin Tang Chang

^*Corresponding author for this work

Mechanical Engineering

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

85 Scopus citations

Abstract

The Reproducing Kernel Particle Method (RKPM), which utilizes the fundamental notions of the convolution theorem, multiresolution analysis and meshfree properties, is reviewed. The multiple-scale RKPMs are then proposed as an alternative to commonly used numerical methods such as the finite element method. The elimination of a mesh, combined with the filtering properties of window functions, makes a particle method suitable for problems with large deformations, high gradients, and localization problems. This class of methods has been applied to shear band problems, and large deformation fracture and damage problems.

Original language	English (US)
Pages (from-to)	197-205
Number of pages	9
Journal	Computational Materials Science
Volume	16
Issue number	1-4
DOIs	https://doi.org/10.1016/S0927-0256(99)00062-2
State	Published - Dec 1999

Keywords

Damage
Finite element
Fracture
Large deformation
Localization
Meshfree methods
Methods
Multiple scale
Shear band

ASJC Scopus subject areas

Computer Science(all)
Chemistry(all)
Materials Science(all)
Mechanics of Materials
Physics and Astronomy(all)
Computational Mathematics

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10.1016/S0927-0256(99)00062-2

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title = "Multiple scale meshfree methods for damage fracture and localization",

abstract = "The Reproducing Kernel Particle Method (RKPM), which utilizes the fundamental notions of the convolution theorem, multiresolution analysis and meshfree properties, is reviewed. The multiple-scale RKPMs are then proposed as an alternative to commonly used numerical methods such as the finite element method. The elimination of a mesh, combined with the filtering properties of window functions, makes a particle method suitable for problems with large deformations, high gradients, and localization problems. This class of methods has been applied to shear band problems, and large deformation fracture and damage problems.",

keywords = "Damage, Finite element, Fracture, Large deformation, Localization, Meshfree methods, Methods, Multiple scale, Shear band",

author = "Liu, {Wing Kam} and Su Hao and Ted Belytschko and Li, {Shao Fan} and Chang, {Chin Tang}",

note = "Funding Information: The support of this research by Air Force Office of Scientific Research (AFOSR), Army Research Office (ARO), National Science Foundation (NSF) and Office of Naval Research (ONR) to Northwestern University is gratefully acknowledged. Sponsored in part by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army Research Laboratory. The content does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred.",

year = "1999",

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doi = "10.1016/S0927-0256(99)00062-2",

language = "English (US)",

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journal = "Computational Materials Science",

issn = "0927-0256",

publisher = "Elsevier",

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TY - JOUR

T1 - Multiple scale meshfree methods for damage fracture and localization

AU - Liu, Wing Kam

AU - Hao, Su

AU - Belytschko, Ted

AU - Li, Shao Fan

AU - Chang, Chin Tang

N1 - Funding Information: The support of this research by Air Force Office of Scientific Research (AFOSR), Army Research Office (ARO), National Science Foundation (NSF) and Office of Naval Research (ONR) to Northwestern University is gratefully acknowledged. Sponsored in part by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army Research Laboratory. The content does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred.

PY - 1999/12

Y1 - 1999/12

N2 - The Reproducing Kernel Particle Method (RKPM), which utilizes the fundamental notions of the convolution theorem, multiresolution analysis and meshfree properties, is reviewed. The multiple-scale RKPMs are then proposed as an alternative to commonly used numerical methods such as the finite element method. The elimination of a mesh, combined with the filtering properties of window functions, makes a particle method suitable for problems with large deformations, high gradients, and localization problems. This class of methods has been applied to shear band problems, and large deformation fracture and damage problems.

AB - The Reproducing Kernel Particle Method (RKPM), which utilizes the fundamental notions of the convolution theorem, multiresolution analysis and meshfree properties, is reviewed. The multiple-scale RKPMs are then proposed as an alternative to commonly used numerical methods such as the finite element method. The elimination of a mesh, combined with the filtering properties of window functions, makes a particle method suitable for problems with large deformations, high gradients, and localization problems. This class of methods has been applied to shear band problems, and large deformation fracture and damage problems.

KW - Damage

KW - Finite element

KW - Fracture

KW - Large deformation

KW - Localization

KW - Meshfree methods

KW - Methods

KW - Multiple scale

KW - Shear band

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JO - Computational Materials Science

JF - Computational Materials Science

IS - 1-4

ER -

Multiple scale meshfree methods for damage fracture and localization

Abstract

Keywords

ASJC Scopus subject areas

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