Finite element analysis of the anti-plane problem of a doubly periodic parallelogram array of cracks

A finite element scheme is developed to analyze an elastic solid weakened by a doubly periodic parallelogramic array of cracks under antiplane shear. With periodic boundary condition of the unit cell and a singular element at the crack tips, the computational efficiency and accuracy are greatly improved. A comparison with the available exact solution in the case of a rectangular array of cracks shows that the relative errors for the stress intensity factor get less than 0.2%. It differs from the available researches confined to the case of a symmetric array of cracks, the present method can be applied to the case of non-symmetric general parallelogramic array of cracks. The numerical results reveal that the interaction of row-directional cracks shows an amplifying effect on the stress intensity factors, but the interaction of stack- directional cracks shows a shielding effect. In the case of a parallelogramic array of cracks, the two opposite effects result in nonmonotonic relations between the stress intensity factors and the staggered parameters.