The accuracy requirements of numerical manifold method (NMM) can be reached by changing the density of mathematical covers and the order of cover functions. In this study

NMM coupled with nonuniform rational B-splines (NURBS) and T-splines in the context of isogeometric analysis is proposed. Computational formula for a 9-node NMM based on quadratic B-splines is derived. For the case of crack propagation problems where singular fields around crack tips exist

local refinement technique by the application of T-spline discretizations is incorporated into NMM

which facilitates a truly local refinement without extending the entire row of control points. A local refinement strategy for the 4-node mathematical cover mesh based on T-splines and Lagrange interpolation polynomial is proposed. The results from numerical examples show that the 9-node NMM based on NURBS has higher accuracies. The local mesh refinement using T-splines reduces the number of degrees of freedom while maintaining calculation accuracy at the same time

and T-splines refinement method is a natural truly local refinement algorithm.