# 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 language English 46-73 28 International Journal for Numerical Methods in Engineering 80 1 https://doi.org/10.1002/nme.2620 Published - 2009 Oct 1 Yes

### 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

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