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Meshless EFG Simulation of Linear Elastic Fracture Propagation Under Various Loadings

  • Research Article - Mechanical Engineering
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Abstract

We used computational mechanics consisting of various numerical methods to analyze different problems under various boundary conditions. The main advantage of the element free Galerkin (EFG) method is that the model meshing stage is not required and the nodal points are distributed throughout the model domain instead of being meshed. Nodal points are distributed within the model domain to capture a stress singularity around the crack tip. In this paper, various 2D problems in the field of linear elastic fracture mechanics were analyzed to validate the accuracy of the EFG code that was developed in a Matlab environment. To simulate the fracturing process based on the maximum hoop stress criterion, stress intensity factors and the angle of crack propagation were calculated under different loading conditions and the crack trajectory was determined. The obtained results of the developed EFG-code were compared with available experimental data and other numerical (boundary element method and finite element method) methods.

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Abbreviations

(σ θ max):

Maximum hoop stress

(G max):

Maximum energy release rate

(S θ max):

Strain energy density factor

K I , K II :

Stress intensity factors for mode-I and mode-II

θ C , θ 0 :

Angle of crack propagation

β :

Angle of crack inclination

a :

Half crack length

w I :

Weight function of node I

d I :

Support size of node I

x I :

Coordinate vector of node I

n i , n j :

Number of nodes are i, j directions

r :

Normalized radius

Ω:

Domain of problem geometry

Γ:

Global boundary

Γ u :

Displacement boundary condition

Γ t :

Traction boundary condition

u :

Displacement vector

\({\bar{\bf u}}\) :

Prescribed boundary displacement

b :

Vector of body forces

\({\bar{t}}\) :

Prescribed boundary tractions

λ:

Lagrangian multiplier

\({\Phi}^{\mathbf T}\) :

Shape functions matrix

B :

Strain–displacement relationship matrix

N :

Lagrange interpolation matrix

D :

Stress–strain relationship matrix

f :

Force vector

K :

Stiffness matrix

G :

Transition matrix

E :

Young’s modulus

ν :

Poisson’s ratio

σ T ∞ :

Stress applied in infinite

L :

Model length

D :

Model width

t :

Model thickness

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Authors and Affiliations

  1. Department of Rock Mechanics, Faculty of Mining and Metallurgical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., PO Box 15875-4413, Tehran, Iran

    Hossein Salari-Rad, Morteza Rahimi-Dizadji & Mahmood Delforouzi

  2. Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., PO Box 15875-4413, Tehran, Iran

    Shiva Rahimi-Pour

Authors
  1. Hossein Salari-Rad
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  2. Morteza Rahimi-Dizadji
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  3. Shiva Rahimi-Pour
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  4. Mahmood Delforouzi
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Correspondence to Hossein Salari-Rad.

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Salari-Rad, H., Rahimi-Dizadji, M., Rahimi-Pour, S. et al. Meshless EFG Simulation of Linear Elastic Fracture Propagation Under Various Loadings. Arab J Sci Eng 36, 1381–1392 (2011). https://doi.org/10.1007/s13369-011-0125-x

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