Equilibrium of a prestressed elastic body weakened by a plane elliptical crack
The problem of normal pressure loading of the edges of a plane elliptical crack is considered. The crack subjected to the load is in the open state. The medium in which it is located is first subjected to homogeneous biaxial tension or compression along the plane of the crack. A model of incompressible neo-Hooke material is considered. The problem is reduced to solving a singular integral equation of the first kind. In the case when the intensity of the initial loading is identical in both directions, the problem has an exact solution. If the coefficients of preliminary tension differ slightly, construction of the solution of the problem is possible by an asymptotic method. It is shown that as in the case of equal coefficients, the initial stress does not alter the order of the singularity of the stress field near the crack edge and only affects the normal stress intensity factor.
singular integral equation of the first kind
scientific article; zbMATH DE number 3978575