Journal of Applied Mechanics The Crack Problem for Bonded Non- homogeneous Materials Under Antiplane

C. Atkinson.2 The author states as his main objective the in-vestigation of the singular nature of the crack-tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative. He studies particularly the case of a mode three crack terminating at an interface of a bimaterial, the shear modulus of each component varying exponentially with position from the interface but the moduli continuous at the interface. A conclusion similar to his was reached earlier by Atkinson (1977) where a finite crack in a medium (1) of a constant modulus meets an interface, the modulus of the inter-face (included in medium (2)) being continuous at the interface by varying with position from the interface as (i) /z2 = (a 2 x 2 + /3,)2 a,> 0, /3,> 0; / t 1 = / 3 1 2 or as (//) /x2 = (a2x2 + (32)~2, a2>0, / i, = /3 2 ~ 2, x 2> 0. Medium (1) lies in x2 £ 0, Medium (2) in x2 S: 0. In each of these examples there is a discontinuous derivative of the modulus at x2 = 0 but con-tinuity in the modulus itself. The usual r~Vl stress singularity is obtained for r small enough. The object of Atkinson (1977) was to study the properties of diffuse interfaces, in particular the effect of their thickness on the local stress field