Evaluation of stress intensity factors in functionally graded materials by natural element method

This paper is concerned with the numerical evaluation of the 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 inhomogeneous FGMs is reflected into the modified interaction integral M˜(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tilde M^{(1,2)}}$$\end{document}. The local NEM grid near the crack tip is refined, and the strain and stress fields that were directly approximated by PG-NEM were enhanced and smoothened by the patch recovery technique. Numerical examples with the exponentially varying elastic modulus are taken to illustrate the proposed method. The stress intensity factors are parametrically evaluated with respect to the exponent index in the elastic modulus and the crack length, and those were compared with the other reported results. It has been justified from the numerical results that the present method successfully and accurately evaluates the stress intensity factors of 2-D inhomogeneous functionally graded materials.