A new insight into analysis of linear elastic fracture mechanics with spherical Hankel boundary elements

•Increasing robustness and efficiency in interpolation with the first and second kinds of Bessel function fields‘ participation by utilizing spherical Hankel shape functions.•The infinite piecewise continuity and utilization of complex space with no influence on the imaginary part of the partition of unity property in Hankel shape functions.•Stress intensity factors desired answers at different lengths of the quarter-point element using Hankel shape functions in linear elastic fracture mechanics problems.•Satisfying polynomial, oscillatory Bessel function fields for proposed basis, unlike classical ones. In this research, the solution of linear elastic fracture mechanics problems when using spherical Hankel shape functions in the boundary element method is investigated. These shape functions benefit from the advantages of Bessel function fields of the first and second kind in addition to the polynomial ones, which makes them a robust and efficient tool for interpolation. Among the most important features of Hankel shape functions, the infinite piecewise continuity and the utilization of complex space with no influence on the imaginary part of the partition of unity property can be pointed out. The calculation of the stress intensity factors (SIFs) is carried out in five numerical examples so that the accuracy of the present study can be illustrated. Comparisons are made between the results of using spherical Hankel shape functions, the experimental ones, and those obtained by classical BEM with Lagrange shape functions. According to the results of these comparisons, the proposed spherical Hankel shape functions present more accurate and reliable results in comparison with the classic Lagrange ones.