Non-linear surface crack analysis by three dimensional boundary element with mixed boundary conditions

Abstract

In this paper, an effective three dimensional boundary element method with mixed boundary conditions is prescribed for nonlinear surface crack analyses. The line spring model originally proposed by Rice and Levy is used to form the non-linear mixed boundary conditions of the 3D crack problem in a continuum manner, which is then combined with the three dimensional boundary element method to compute the fracture parameter J integral of non-linear surface crack. A predictor–corrector method is presented for the nonlinear compliance matrix of the mixed boundary so that a more accurate result can be reached. Two numerical examples are discussed to show the effectiveness of the method. Especially, the surface crack problem is addressed in which the non-linear region only happens at the mixed boundary condition area, and most of the remaining area is still elastic.