Comparison of one-dimensional and two-dimensional functionally graded materials for the backing shell of the cemented acetabular cup

2005 ◽  
Vol 74B (2) ◽  
pp. 732-739 ◽  
Author(s):  
H. S. Hedia
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Acetabular Cup ◽  
Graded Materials ◽  
One Dimensional

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

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.

Sign in / Sign up

Export Citation Format

Share Document