Abstract:

The extended finite element method (XFEM) is a new numerical method for modeling strong as well as weak discontinuities within a standard finite element framework. The computation mesh in XFEM is independent of the discontinuities, such that re-meshing for moving discontinuities can be overcome. An extended finite element method for modeling three-dimensional crack problems is described. In order to model the crack discontinuity, a Heaviside step function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation for the local enrichment by using the framework of partition of unity. The crack is described with two level set functions. The nonlinear contact conditions between the crack faces are resolved with the linear complementary method; the iterative procedure is avoided. Stress intensity factors of crack front are obtained with two-point displacement extrapolation method. Three examples for three-dimensional elastostatic problems are given; the results show that the method can obtain high accurate stress intensity factors and effectively treat the contact problem between crack surfaces, and the combination of the XFEM and linear complementary method has wonderful practical merits for solving discontinuous problems.

Key words: extended finite element method, three-dimensional cracks, contact conditions, linear complementary method, displacement extrapolation method, stress intensity factors