Numerical analysis of growing crack problems using particle discretization scheme

M. L L Wijerathne, Kenji Oguni, Muneo Hori

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

This paper presents the particle discretization scheme (PDS) to analyze brittle failure of solids. The scheme uses characteristic functions of Voronoi and Delaunay tessellations to discretize a function and its derivatives, respectively. A discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks, without making any extra computation to accommodate new displacement discontinuities. When the scheme is implemented to a finite element method (FEM), the resulting stiffness matrix coincides with the one that is obtained by using linear elements. The accuracy of computing a stress intensity factor at a crack tip is examined. It is shown that the accuracy is better than that of a FEM with linear elements when the rotational degree of freedom is included in discretizing displacement functions. Three three-dimensional growing crack problems are solved by means of the PDS and the results are presented.

Original languageEnglish
Pages (from-to)46-73
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Volume80
Issue number1
DOIs
Publication statusPublished - 2009 Oct 1
Externally publishedYes

Fingerprint

Discretization Scheme
Numerical analysis
Numerical Analysis
Crack
Cracks
Discontinuity
Finite Element Method
Displacement Discontinuity
Tessellation
Delaunay
Voronoi
Crack Tip
Stress Intensity Factor
Stiffness Matrix
Characteristic Function
Finite element method
Stiffness matrix
Degree of freedom
Stress intensity factors
Crack tips

Keywords

  • Brittle failure in 3D
  • Discrete physics
  • Particle discretization scheme
  • Rotational degree of freedom
  • Stress intensity factor

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

Numerical analysis of growing crack problems using particle discretization scheme. / Wijerathne, M. L L; Oguni, Kenji; Hori, Muneo.

In: International Journal for Numerical Methods in Engineering, Vol. 80, No. 1, 01.10.2009, p. 46-73.

Research output: Contribution to journalArticle

@article{91426fd21aa04f8a97c06b61e288a7b4,
title = "Numerical analysis of growing crack problems using particle discretization scheme",
abstract = "This paper presents the particle discretization scheme (PDS) to analyze brittle failure of solids. The scheme uses characteristic functions of Voronoi and Delaunay tessellations to discretize a function and its derivatives, respectively. A discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks, without making any extra computation to accommodate new displacement discontinuities. When the scheme is implemented to a finite element method (FEM), the resulting stiffness matrix coincides with the one that is obtained by using linear elements. The accuracy of computing a stress intensity factor at a crack tip is examined. It is shown that the accuracy is better than that of a FEM with linear elements when the rotational degree of freedom is included in discretizing displacement functions. Three three-dimensional growing crack problems are solved by means of the PDS and the results are presented.",
keywords = "Brittle failure in 3D, Discrete physics, Particle discretization scheme, Rotational degree of freedom, Stress intensity factor",
author = "Wijerathne, {M. L L} and Kenji Oguni and Muneo Hori",
year = "2009",
month = "10",
day = "1",
doi = "10.1002/nme.2620",
language = "English",
volume = "80",
pages = "46--73",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "1",

}

TY - JOUR

T1 - Numerical analysis of growing crack problems using particle discretization scheme

AU - Wijerathne, M. L L

AU - Oguni, Kenji

AU - Hori, Muneo

PY - 2009/10/1

Y1 - 2009/10/1

N2 - This paper presents the particle discretization scheme (PDS) to analyze brittle failure of solids. The scheme uses characteristic functions of Voronoi and Delaunay tessellations to discretize a function and its derivatives, respectively. A discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks, without making any extra computation to accommodate new displacement discontinuities. When the scheme is implemented to a finite element method (FEM), the resulting stiffness matrix coincides with the one that is obtained by using linear elements. The accuracy of computing a stress intensity factor at a crack tip is examined. It is shown that the accuracy is better than that of a FEM with linear elements when the rotational degree of freedom is included in discretizing displacement functions. Three three-dimensional growing crack problems are solved by means of the PDS and the results are presented.

AB - This paper presents the particle discretization scheme (PDS) to analyze brittle failure of solids. The scheme uses characteristic functions of Voronoi and Delaunay tessellations to discretize a function and its derivatives, respectively. A discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks, without making any extra computation to accommodate new displacement discontinuities. When the scheme is implemented to a finite element method (FEM), the resulting stiffness matrix coincides with the one that is obtained by using linear elements. The accuracy of computing a stress intensity factor at a crack tip is examined. It is shown that the accuracy is better than that of a FEM with linear elements when the rotational degree of freedom is included in discretizing displacement functions. Three three-dimensional growing crack problems are solved by means of the PDS and the results are presented.

KW - Brittle failure in 3D

KW - Discrete physics

KW - Particle discretization scheme

KW - Rotational degree of freedom

KW - Stress intensity factor

UR - http://www.scopus.com/inward/record.url?scp=70349245106&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349245106&partnerID=8YFLogxK

U2 - 10.1002/nme.2620

DO - 10.1002/nme.2620

M3 - Article

AN - SCOPUS:70349245106

VL - 80

SP - 46

EP - 73

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 1

ER -