ICF13A

13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- summarized below. At z = L/2 (side surface) ) (0 ( , /2) 0 x W x L zz     (16) ) (0 ( , /2) 0 x W x L zx     (17) ) (0 ( , / 2) 0 x W D x L z    (18) At x = 0 (top surface) (0, ) ( /2) () (0 / 2) xx z P z z L      (19) (0, ) 0 (0 / 2) xz z z L     (20) (0, ) 0 (0 / 2) xD z z L    (21) At x = W (bottom surface) /2), ( , /2) 0 /2, /2 ( , ) 0 (0       u W S z S S z L W z x xx (22) ( , ) 0 (0 / 2) xz W z z L     (23) ( , ) 0 (0 / 2) xD W z z L    (24) In Eq. (19), ( ) is the Dirac-delta function. Next, we consider the Case 2 (see Figure 2(b)). The boundary conditions at x = 0 are ) (0, ) 0 ( ) (0, ) 0 (0 z W a z W z W a u z xx x          (25) ) (0, ) 0 (0 z W z xz     (26) ) (0, ) ( (0, ) ) (0, ) ( (0, ) ) (0 (0, ) 0 , D z D z W a z W E z E z W a z W z W a z c x x c z z x              (27) The partial derivative of the electric potential with respect to x is all zero on the symmetry planes inside the crack and ahead of the crack, so the boundary conditions of Eqs. (27) reduce to ,x(x, 0) = 0 (0 x W   ). A mechanical load is produced by the application of the prescribed force P, at x = 0, z = 0 along the z-direction. For an electrical load, the electric potential 0 is applied at the surface 0 x <L0/2, z = W, and the surface 0x < L0/2, z = 0 is grounded, so the conditions are

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