THE PLANE PROBLEM FOR A CRACK BETWEEN 2 LINEARLY ELASTIC MEDIA

An exact solution of the plane problem of the non-linear theory of elasticity is constructed for a crack at the interface between two different media for an elastic potential corresponding to a linearly elastic prestressed material. A unified version [1] of the plane problem of the non-linear theory of elasticity is used. For comparison the solution of the corresponding problem for the linear theory with the same elastic potential is given. The asymptotic forms of the stresses in both cases are compared. It is shown that the asymptotic form of the components of the symmetric Blot tenser is of the same order as the asymptotic form of the stresses in the linear problem, but in this case the first has no oscillations while the squares of the coefficients of the principal terms of the asymptotic forms of these stresses are identical, apart from a factor, with the Rice-Cherepanov integral. The displacements in the non-linear problem do not oscillate only when a certain relation for the elasticity constants of the contacting media is satisfied.