Stable 3D XFEM/vector-level sets for non-planar 3D crack propagation and comparison of enrichment schemes

in International Journal for Numerical Methods in Engineering (2017)

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting ... [more ▼]

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near-tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, i.e., the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach significantly simplifies implementation and reduces the computational cost associated with numerical integration. The two dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for non-planar crack propagation problems. [less ▲]

Well Conditioned and Optimally Convergent Extended Finite Elements and Vector Level Sets for Three-Dimensional Crack Propagation

Scientific Conference (2016, June)

A three-dimensional (3D) version of the vector level set method [1] is combined to a well conditioned and optimally convergent XFEM variant in order to deal with non-planar three dimensional crack ... [more ▼]

A three-dimensional (3D) version of the vector level set method [1] is combined to a well conditioned and optimally convergent XFEM variant in order to deal with non-planar three dimensional crack propagation problems. The proposed computational fracture method achieves optimal convergence rates by using tip enriched elements in a fixed volume around the crack front (geometrical enrichment) while keeping conditioning of the resulting system matrices in acceptable levels. Conditioning is controlled by using a three dimensional extension of the degree of freedom gathering technique [2]. Moreover, blending errors are minimized and conditioning is further improved by employing weight function blending and enrichment function shifting [3,4]. As far as crack representation is concerned, crack surfaces are represented by linear quadrilateral elements and the corresponding crack fronts by ordered series of linear segments. Level set values are obtained by projecting points at the crack surface and front respectively. Different criteria are employed in order to assess the quality of the crack representation. References [1] Ventura G., Budyn E. and Belytschko T. Vector level sets for description of propagating cracks in finite elements. Int. J. Numer. Meth. Engng. 58:1571-1592 (2003). [2] Laborde P., Pommier J., Renard Y. and Salaün M. High-order extended finite element method for cracked domains. Int. J. Numer. Meth. Engng. 64:354-381 (2005). [3] Fries T.P. A corrected XFEM approximation without problems in blending elements. Int. J. Numer. Meth. Engng. 75:503-532 (2008). [4] Ventura G., Gracie R. and Belytschko T. Fast integration and weight function blending in the extended finite element method. Int. J. Numer. Meth. Engng. 77:1-29 (2009). [less ▲]

Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture

in Computer Methods in Applied Mechanics and Engineering (2016), 306

An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area ... [more ▼]

An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area around the crack front, while also improving the conditioning of the resulting system matrices. This is achieved by fusing a novel form of enrichment with existing blending techniques. Further, the adoption of higher order terms of theWilliams expansion is also considered and the effects in the accuracy and conditioning of the method are studied. Moreover, some problems regarding the evaluation of stress intensity factors (SIFs) and element partitioning are dealt with. The accuracy and convergence properties of the method as well as the conditioning of the resulting stiffness matrices are investigated through the use of appropriate benchmark problems. It is shown that the proposed approach provides increased accuracy while requiring, for all cases considered, a reduced number of iterations for the solution of the resulting systems of equations. The positive impact of geometrical enrichment is further demonstrated in the accuracy of the computed SIFs where, for the examined cases, an improvement of up to 40% is achieved. [less ▲]