Arbitrary 3D crack propagation with Improved XFEM: Accurate and efficient crack geometries

Abstract

Extended finite element method (XFEM) achieves unprecedented success in crack growth simulations, in particular in 2D. However, challenges still remain for a 3D crack growth simulation. Among other issues like increased computational expense, one challenge is robust and efficient geometry representation of the non-planar surface and the usually curved front of the 3D crack, two unique features distinguished from its 2D counterpart. With a special emphasis on accurate geometries of the 3D crack, we propose in this paper a B-spline ruled surface (BRS), a smooth, explicit, meshfree crack representation algorithm, which offers good geometrical accuracy, good numerical efficiency, and no mesh-resolution dependence. The technique accurately represents the geometry of an evolving 3D crack in a lightweight manner and leads to highly efficient point-surface projections for level set values. The technique is applied to modeling arbitrary 3D crack propagation in context of the Improved XFEM (IXFEM) that has been developed to eliminate the daunting issues of linear dependence and ill-conditioning of the standard XFEM (Tian and Wen (2015); Wen and Tian (2016)). Numerical tests show that IXFEM with the technique of crack description provides accurate solutions for the benchmarks of 3D crack propagation; the effectiveness of the proposed algorithm is demonstrated.