ABSTRACT
To make the numerical scheme comparable to FEM, eq. 2 is converted into the equation not of the tractions on the elements, but of the nodal forces, as follow :
^domain 1 = ^domain 2'
t fj^domain 1 + >domain 2 = °*
2.3 LEFM model for crack propagation in an arbitrary direction
The stress intensity factors Kj and K-J-J at the crack tip are determined from the displacements on the crack-tip element by using Smith's one point formulae (1982). The direction of crack propagation is determined from the criterion of the maximum circumferential stress,
Kj*sin φ + K I I*(3cos φ - 1) = 0, ( 4 )
and the crack is nucleated when the following equation holds,
* 3 ΐ η φ ] > 1, (5) •k *
where Kj = Kj/K l c and K J J = K J J / K I c . From the crack axis, the angle φ is taken as corresponding to the bigger maximum tensile stress. Crack propagation is modeled by creating new boundaries along the direction determined from eq. 4 ahead of the crack tip. At the crack tip, bound aries of the two domains are initially stitched. A con straint at the crack tip is released right after eq. 5 holds. Thus, automatic remeshing at the crack boundary is accommodated with the increment of crack growth.
