The problem on an annular crack at the interface between an elastic layer and an elastic half-space (Q2761305)

The authors consider an elastic body consisting of a layer of thickness \(h\) with the shift modulus \(G_1\) and the Poisson ratio \(\nu_1\) joined with a half-space with characteristics \(G_2\) and \(\nu_2\). It is assumed that to the layer boundary \(\,z = h\,\) a normal load is applied with the intensity \(q(r)\), distributed on the circle of radius \(c\). Outside this circle the body surface is assumed unloaded. The authors study an axisymmetric problem on circular crack. In order to determine the real crack dimensions it is proposed to use the integral fracture criterion (see [{ N.~F.~Morozov}, ``Mathematical questions in the theory of cracks'', Nauka, Moscow (1984; Zbl 0566.73079)]).