Periodic cracks in an infinite electrostrictive plane under the influence of a uniform remote electric field

We present a rigorous treatment of the problem of collinear periodic cracks in an infinite electrostrictive plane subjected to plane strain deformation in the presence of a uniform remote in-plane electric field. Using complex variable methods, exact electric and stress fields in the electrostrictive plane are obtained for both permeable and impermeable cracks. We show that the ratio of the mode-I stress intensity factors for periodic cracks to those for a single crack is determined by only the ratio of the period of the periodic crack-system to the crack length. Additionally, we find that the stress intensity factors for periodic cracks and the stress field in the proximity of periodic cracks can be treated essentially as those for a single crack when the period exceeds four times the crack length.