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Steel and Composite Structures
  Volume 31, Number 1, April10 2019 , pages 43-51

Computation of mixed-mode stress intensity factors in functionally graded materials by natural element method
J.R. Cho

    This paper is concerned with the numerical calculation of mixed-mode stress intensity factors (SIFs) of 2-D isotropic functionally graded materials (FGMs) by the natural element method (more exactly, Petrov-Galerkin NEM). The spatial variation of elastic modulus in non-homogeneous FGMs is reflected into the modified interaction integral M(1,2). The local NEM grid near the crack tip is refined, and the directly approximated strain and stress fields by PG-NEM are enhanced and smoothened by the patch recovery technique. Two numerical examples with the exponentially varying elastic modulus are taken to illustrate the proposed method. The mixed-mode SIFs are parametrically computed with respect to the exponent index in the elastic modulus and external loading and the crack angle and compared with the other reported results. It has been justified from the numerical results that the present method successfully and accurately calculates the mixed-mode stress intensity factors of 2-D non-homogeneous functionally graded materials.
Key Words
    functionally graded materials (FGM); non-homogeneous material; mixed-mode stress intensity factor (SIF); modified interaction integral; near-tip grid refinement
Department of Naval Architecture and Ocean Engineering, Hongik University, Sejong 30016, Korea.

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