Hybrid Analytical and MLS-Based NMM for the Determination of Generalized Stress Intensity Factors

The numerical manifold method (NMM) is characterized by its two cover systems, the mathematical cover and the physical cover. In the standard NMM, the mathematical cover is required to cover the whole problem domain. In this study, however, around each crack tip we specify a small domain on which the displacement is taken as the truncated Williams’ displacement series. And accordingly all such small domains are not covered by the mathematical cover that only covers the rest of the problem domain. Meanwhile, the mathematical cover is constructed by designating all supports of the scattered nodes arising in the moving least squares interpolation as the mathematical patches. In this way, any physical patch contains no crack tip and can be approximated by polynomials. As a result, no blending element issue exists as in the extended finite element method and NMM. In addition to high precision, the proposed procedure is especially suitable for the situation where a crack tip is very close to other cracks, a case difficult to treat by the interaction integral procedure that is commonly used in the extraction of the stress intensity factors of mixed mode cracks.