Non-planar 3D crack growth by the extended finite element and level sets - Part II: Level set update

We present a level set method for treating the growth of non-planar three-dimensional cracks. The crack is de5ned by two almost-orthogonal level sets (signed distance functions). One of them describes the crack as a two-dimensional surface in a three-dimensional space, and the second is used to describe the one-dimensional crack front, which is the intersection of the two level sets. A Hamilton–Jacobi equation is used to update the level sets. A velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface. The technique is coupled with the extended 5nite element method which approximates the displacement 5eld with a discontinuous partition of unity. This displacement 5eld is constructed directly in terms of the level sets, so the discretization by 5nite elements requires no explicit representation of the crack surface. Numerical experiments show the robustness of the method, both in accuracy and in treating cracks with signi5cant changes in topology