XFEM SIMULATION OF 2-D FRACTURE MECHANICS PROBLEMS

Abstract

Standard Finite Element approximations are approximations with piecewise polynomial that are not well suited for the problems with strong and weak discontinuities. To accu-rately model these discontinuities, finite element mesh is required to be conformal with the line of discontinuity. Besides this, special elements are required to accurately model the crack tip asymptotic-fields. The extended finite element method (XFEM) is a finite element approximation that is able to handle arbitrary strong and weak discontinuities without conformal meshing. Hence, XFEM is more suitable for modelling problems with discontinuities moving or static. In this work, XFEM has been used to solve 2-D linear elastic fracture mechanics problems under mechanical and thermal loads. Various test cases of single and multiple cracks has been taken and analyzed. The domain with multiple cracks has been consid-ered and stress intensity factors have been evaluated at one of the crack tip. From the present analysis, it has been observed that there is a significant change in the values of stress intensity factors due to the presence of auxiliary (second) crack in both mechanical and thermal loading. The presence of second crack generates a finite value of mode-II stress intensity factor, even though the loading is purely in mode-I.