Simulation of crack propagation in anisotropic structures using the boundary element shape sensitivities and optimisation techniques

Using the boundary element shape sensitivities of multi-region domains coupled with an optimisation algorithm and an automatic mesh generator, the crack kink angle and propagation path in anisotropic elastic solids are predicted. The maximum strain energy release rate criterion, best suited for the composite structures, has been employed. In contrast to the J-integral method, which would require the computation of stresses and strains at a series of internal points, here by direct differentiation of the structural response the strain energy release rates at the existing crack tip and new cracks for the period of crack growth are determined. The length of each kinked crack is treated as the shape design variable. The shape variable is then associated with the coordinates of a series of boundary nodes located on the new 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 derivative of the total strain energy with respect to the crack length extension. Wherever possible the results are compared with the existing experimental, analytical and/or numerical results reported in the literature, in which good agreement is observed. It is shown that the present method is computationally more accurate and efficient. Two example problems with different anisotropic material properties are presented to validate the applications of this formulation. The results show that material anisotropy has a profound influence on the crack propagation of composites.