Enriched finite elements and level sets for damage tolerance assessment of complex structures

Abstract

The extended finite element method (X-FEM) has recently emerged as an alternative to meshing/remeshing crack surfaces in computational fracture mechanics thanks to the concept of discontinuous and asymptotic partition of unity enrichment (PUM) of the standard finite element approximation spaces. Level set methods have been recently coupled with X-FEM to help track the crack geometry as it grows. However, little attention has been devoted to employing the X-FEM in real-world cases. This paper describes how X-FEM coupled with level set methods can be used to solve complex threedimensional industrial fracture mechanics problems through combination of an object-oriented (C++) research code and a commercial solid modeling/finite element package (EDS-PLM/I-DEAS Ò ). The paper briefly describes how object-oriented programming shows its advantages to efficiently implement the proposed methodology. Due to enrichment, the latter method allows for multiple crack growth scenarios to be analyzed with a minimal amount of remeshing. Additionally, the whole component contributes to the stiffness during the whole crack growth simulation. The use of level set methods permits the seamless merging of cracks with boundaries. To show the flexibility of the method, the latter is applied to damage tolerance analysis of a complex aircraft component.

Derivative recovery and a posteriori error estimate for extended finite elements

“…Figure 19 shows the strain εyy along line x = 0. We believe that using the enhanced strain and stress fields to compute the interaction integrals commonly used to obtain the stress intensity factors, the oscillations in the soobtained SIFs, reported in various papers [30,21,13,40,42] will be reduced. Not only is the enhanced strain field smoothed in the direction normal to the crack front, but also in the tangent direction, which should reduce the amount of oscillations in the SIFs.…”

“…Typically, XFEM and related methods add, locally, special functions to the FE approximation, in order to better approximate particular features of a problem. For problems with discontinuities in the primal dependent variable (cracks [29,28,13], fluid-structure interaction [26]), discontinuous functions are added. To handle discontinuities in the dual unknown (multi-materials [41], solidification [16], biofilms [35], multi-phase flow [15], Stokes flow [47]), functions with discontinuous derivatives enhance the standard basis.…”

Development of Efficient Finite Element Software of Crack Propagation Simulation using Adaptive Mesh Strategy

“…For case 2 the results of the present study for the crack path prediction is also compared qualitatively with the numerical results using enriched element free Galerkin method (EFGM) [9] and the extended finite element method results (X-FEM) [10] as shown in Fig. 9a and 9b respectively with a good agreement.…”

Mechanical Failure in Microstructural Heterogeneous Materials

“…This is possible through enrichment of the standard polynomial finite element space with special functions: discontinuous, to account for the displacement jump, and crack-tip fields to reduce the mesh density required for accurate fracture parameter computations. The method is now becoming quite mature, and has already been applied to industrial fracture mechanics problems [5]. Some elements are split by the crack and others contain the crack tips.…”