International Journal of Solids and Structures Vol. 40, No. 15, pp.3967-4001, 2003
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Newmark
Laboratory, 205 North Mathews Avenue, IL
61801, U.S.A.
Abstract
The interaction integral is an accurate and robust scheme for evaluating mixed-mode stress intensity factors. This
paper extends the concept to orthotropic functionally graded materials and addresses fracture mechanics problems with
arbitrarily oriented straight and/or curved cracks. The gradation of orthotropic material properties are smooth functions
of spatial coordinates, which are integrated into the element sti.ness matrix using the so-called ‘‘generalized
isoparametric formulation’’. The types of orthotropic material gradation considered include exponential, radial, and
hyperbolic-tangent functions. Stress intensity factors for mode I and mixed-mode two-dimensional problems are
evaluated by means of the interaction integral and the .nite element method. Extensive computational experiments
have been performed to validate the proposed formulation. The accuracy of numerical results is discussed by comparison
with available analytical, semi-analytical, or numerical solutions.
Keywords: Functionally graded material (FGM), Fracture mechanics, Stress
intensity factor (SIF), Interaction integral, Finite element method (FEM), Generalized
isoparametric formulation (GIF)