An element free Galerkin formulation for stable crack growth in an elastic solid

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/s0045-7825(97)00133-3 ◽

1998 ◽

Vol 154 (3-4) ◽

pp. 331-343 ◽

Author(s):

Yu Xu ◽

Sunil Saigal

Keyword(s):

Crack Growth ◽

Elastic Solid ◽

Stable Crack Growth ◽

Element Free Galerkin ◽

Galerkin Formulation ◽

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A coupled finite element and element-free Galerkin approach for the simulation of stable crack growth in ductile materials

Theoretical and Applied Fracture Mechanics ◽

10.1016/j.tafmec.2014.02.006 ◽

2014 ◽

Vol 70 ◽

pp. 49-58 ◽

Author(s):

Sachin Kumar ◽

I.V. Singh ◽

B.K. Mishra

Keyword(s):

Finite Element ◽

Crack Growth ◽

Stable Crack Growth ◽

Galerkin Approach ◽

Ductile Materials ◽

Element Free Galerkin ◽

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Stress Analysis of a Continuous Casting Process, on the Basis of the Element-Free Galerkin Formulation

steel research international ◽

10.1002/srin.201600019 ◽

2016 ◽

Vol 88 (2) ◽

pp. 1600019 ◽

Author(s):

Juan C. Álvarez Hostos ◽

Eli S. Puchi Cabrera ◽

Alfonso D. Bencomo

Keyword(s):

Continuous Casting ◽

Stress Analysis ◽

Casting Process ◽

Continuous Casting Process ◽

Element Free Galerkin ◽

Galerkin Formulation ◽

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Modeling of Nonlinear Crack Growth in Steel and Aluminum Alloys by the Element Free Galerkin Method

Materials Today Proceedings ◽

10.1016/j.matpr.2018.06.227 ◽

2018 ◽

Vol 5 (9) ◽

pp. 18805-18814 ◽

Author(s):

Showkat Ahmad Kanth ◽

G.A. Harmain ◽

Azher Jameel

Keyword(s):

Aluminum Alloys ◽

Galerkin Method ◽

Crack Growth ◽

Element Free Galerkin Method ◽

Element Free Galerkin ◽

Nonlinear Crack ◽

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A slices based Element Free Galerkin formulation

Computational Mechanics ◽

10.1007/s004660050471 ◽

2000 ◽

Vol 25 (2-3) ◽

pp. 220-229 ◽

Author(s):

S. Saigal ◽

W. Barry

Keyword(s):

Element Free Galerkin ◽

Galerkin Formulation ◽

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Element-free Galerkin formulation for solving transient heat transfer problems of direct chill casting processes

Canadian Metallurgical Quarterly ◽

10.1080/00084433.2017.1288882 ◽

2017 ◽

Vol 56 (2) ◽

pp. 156-167 ◽

Author(s):

J. C. Álvarez Hostos ◽

A. D. Bencomo ◽

E. S. Puchi Cabrera

Keyword(s):

Heat Transfer ◽

Direct Chill ◽

Direct Chill Casting ◽

Transient Heat Transfer ◽

Chill Casting ◽

Element Free Galerkin ◽

Galerkin Formulation ◽

Element Free ◽

Transfer Problems

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Fatigue crack growth simulations of homogeneous and bi-material interfacial cracks using element free Galerkin method

Applied Mathematical Modelling ◽

10.1016/j.apm.2013.11.030 ◽

2014 ◽

Vol 38 (13) ◽

pp. 3093-3123 ◽

Author(s):

Himanshu Pathak ◽

Akhilendra Singh ◽

Indra Vir Singh

Keyword(s):

Fatigue Crack ◽

Fatigue Crack Growth ◽

Galerkin Method ◽

Crack Growth ◽

Element Free Galerkin Method ◽

Element Free Galerkin ◽

Interfacial Cracks ◽

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Fracture and crack growth by element free Galerkin methods

Modelling and Simulation in Materials Science and Engineering ◽

10.1088/0965-0393/2/3a/007 ◽

1994 ◽

Vol 2 (3A) ◽

pp. 519-534 ◽

Author(s):

T Belytschko ◽

L Gu ◽

Y Y Lu

Keyword(s):

Crack Growth ◽

Galerkin Methods ◽

Element Free Galerkin ◽

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An improved element free Galerkin formulation

International Journal for Numerical Methods in Engineering ◽

10.1002/(sici)1097-0207(19970830)40:16<2953::aid-nme201>3.0.co;2-s ◽

1997 ◽

Vol 40 (16) ◽

pp. 2953-2974 ◽

Author(s):

Igor Kaljević ◽

Sunil Saigal

Keyword(s):

Element Free Galerkin ◽

Galerkin Formulation ◽

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Element free galerkin study of steady quasi-static crack growth in plane strain tension in elastic-plastic materials

Computational Mechanics ◽

10.1007/s004660050358 ◽

1998 ◽

Vol 22 (3) ◽

pp. 255-265 ◽

Author(s):

Y. Xu ◽

S. Saigal

Keyword(s):

Crack Growth ◽

Plane Strain ◽

Elastic Plastic ◽

Plane Strain Tension ◽

Element Free Galerkin ◽

Static Crack ◽

Plastic Materials ◽

Elastic Plastic Materials ◽

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Fatigue Crack Growth Simulations in Ductile Materials by Coupled FE-EFG Approach

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.829.73 ◽

2016 ◽

Vol 829 ◽

pp. 73-77

Author(s):

Sachin Kumar ◽

Indra Vir Singh ◽

B.K. Mishra

Keyword(s):

Fatigue Crack ◽

Fatigue Crack Growth ◽

Crack Growth ◽

Shape Functions ◽

Problem Domain ◽

Material Interface ◽

Ductile Materials ◽

Element Free Galerkin ◽

Element Free ◽

In this paper, a coupled finite element (FE) and element free Galerkin (EFG) approach is presented for the simulation of fatigue crack growth problems. The problem domain is subdivided into two regions i.e. EFG region and FE region. A ramp function is used in the transition region to obtain the resultant shape functions. This approach effectively handles the crack growth problems without remeshing, and is found computationally more efficient than other meshfree methods. The effectiveness of this approach is demonstrated by simulating material interface fatigue crack growth problems. These simulations show that the results obtained by coupled approach are in good agreement with the XFEM results.

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