The numerical manifold method for crack modeling of two-dimensional functionally graded materials under thermal shocks

2019 ◽  
Vol 208 ◽  
pp. 90-106 ◽  
Author(s):  
H.H. Zhang ◽  
S.M. Liu ◽  
S.Y. Han ◽  
L.F. Fan
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Numerical Manifold Method ◽  
Two Dimensional ◽  
Graded Materials ◽  
Numerical Manifold ◽  
Thermal Shocks

Improved crack analysis of two-dimensional functionally graded materials by enriched natural element method

2020 ◽  
Vol 234 (10) ◽  
pp. 2012-2023
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

The numerical calculation of stress intensity factors of two-dimensional functionally graded materials is introduced by an enriched Petrov–Galerkin natural element method (enriched PG-NEM). The overall trial displacement field is basically approximated in terms of Laplace interpolation functions and it is enriched by the near-tip asymptotic displacement field. The overall strain and stress fields which were approximated by PG-NEM were smoothened and enhanced by the patch recovery. The modified interaction integral [Formula: see text] is used to evaluate the stress intensity factors of functionally graded materials with the spatially varying elastic modulus. The validity of present method is justified through the evaluation of crack-tip stress distributions and the stress intensity factors of four numerical examples. It has been found that the proposed method effectively and successfully captures the near-tip stress singularity with a remarkably improved accuracy, even with the remarkably coarse grid, when compared with an extremely fine grid and the analytical and numerical reference solutions.

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