ANALYTIC SOLUTION OF MODE-I CRACK IN MATERIALS WITH NONLINEAR BEHAVIOR

The solution of Hutchinson and of Rice and Rosengren is the most impor tant achievement of nonlinear fracture mechanics. However, the angular distribution function of the solution was given in numerical form onl y. The function is governed by a very complicated nonlinear differenti al equation of the fourth order, and methods for finding the analytica l solution of the equation are currently not available in the literatu re. In this study, by using the constructing function method developed by us, the analytical solution is achieved. We also give proof for th e absolute uniform convergence and the uniqueness of the solution. The result is significant from the point of view of both practical applic ations and fundamental scientific interest.