Abstract: Based on the finite element triangle mesh， the changing of manifold elements in crack propagation process was studied in depth， and the continuous and discontinuous unified processing of the numerical manifold method are interpreted from the perspective of geometric mesh. The first-order coverage function was used to derive the weight function expression of numerical manifold algorithm， so that the local displacement function can be established. Through the numerical manifold calculation program， the crack tip displacement was obtained， and the tip stress intensity factor was calculated and verified by the classical cracked plate model. The numerical result is in good agreement with the analytical solution， which proves the numerical manifold method is accuracy and can be used as a new numerical solution for solving the tip stress intensity factor in the crack propagation process.

Key words: crack propagation, geometric mesh, local displacement function, intensity factor, numerical manifold displacement method