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Based on the shape sensitivity analysis ofmultiregion domains using the boundary element method, stress intensity factors of the cracks of arbitrary geometric shapes in anisotropic elastic solids are calculated. The results obtained agree very well with the existing analytical or numerical solutions. In contrast to the J-integral method, which would require the computation of stresses and strains at a series of internal points around the crack for evaluation of the path-independent integrals, the fracture mechanics parameters are evaluated here by direct differentiation of the structural response for a multiregion domain. Therefore, the present method is computationally more accurate and efficient. The length of the crack of arbitrary geometric shape is treated as the shape design variable. Then the shape variable is associated with the coordinates of a series of boundary nodes located on the crack surface. Thus, the relevant velocity terms are applied together in the sensitivity analysis with respect to that variable to determine the energy release rate, which is the total derivative of the strain energy with respect to crack length. Five example problems with anisotropic material properties are presented to validate the applications of this formulation. The results show that although the stress intensity factor is of fundamental importance in the prediction of brittle failure using linear elastic fracture mechanics, the direct evaluation of the strain energy release rate would easily characterize the crack instability of a loaded laminated composite for different fiber orientations. The results show that the strain energy release rate is highly influenced by the fiber orientation of the composite lamina. Therefore, a laminate can be tailored to crack-growth resistance.

Fracture Mechanics Analysis of Composite Structures Using the Boundary Element Shape Sensitivities