this boundary element, all the internal stresses and strains could be expressed
in terms of displacements and tractions on the boundaries excluding the hole,
crack and inclusion boundaries. These results could be applied to any kind of
linear anisotropic materials but was restricted to the 2-D problems which included
generalized plane stress, generalized plane strain and anti-plane problems.
Denda and Marante [21] developed a crack tip singular element (CTSE)
for the general anisotropic solids in 2-D with the built in V/ and 1/,r singular
stress behavior at its tip, which provided the SIF as an integral part of the main
solution, no post processing was required. It was an ideal fracture analysis tool
for 2-D multiple curvilinear cracks in general anisotropic solids, but as it was
based on plane strain assumption, it could not be incorporated into a generalized
3-D anisotropic model. The solution provided by Heppler and Hansen [22] for
combined mode (I and II) SIFs in case of planar, rectilinear, anisotropic structures
using a 12 node singular finite element was accurate, but was restricted to a 2-D
model. Likewise, Sosa and Eischen [12] calculated SIF for a plate containing a
through crack subjected to bending loads using the J integral. Two-D eight node
element was selected for this purpose where K = K111 = 0. Mews and Kuhn
[23] used the Green's function approach to calculate mixed mode SIF without any
crack discretization in an isotropic plate, which used an .,- iiii 1l tic displacement
field at the crack tip. They calculated SIFs for plate having multiple cracks, for
various inclinations, and found SIFs very close to that of Shih et al. [24]. Ishikava
[14] presented the idea of the strain energy release rate (virtual crack extension
method) to calculate SIF for mode I and II, and described SIF calculation based
on only one use of virtual crack extension.
Huang and Kardomateas [25] described the continuous dislocation technique
to calculate mixed-mode stress intensity factors in an anisotropic infinite strip.
This method was limited in its use to Mode I and II SIFs, and it was found to be