Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method

Abstract

ElsevierGonzález Albuixech, VF.; Giner Maravilla, E.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ.; Gravouil, A. (2013) AbstractThe computation of stress intensity factors (SIF) in curved and non-planar cracks using domain integrals introduces some difficulties related to the use of curvilinear gradients. Several approaches exist in the literature that consider curvilinear corrections within a finite element framework, but these depend on each particular crack configuration and they are not general. In this work, we introduce the curvilinear gradient correction within the extended finite element method framework (XFEM), based only on the level set information used for the crack description and the local coordinate system definition. Our formulation depends only on the level sets coordinates and, therefore, an explicit analytical description of the crack is not needed. It is shown that this curvilinear correction improves the results and enables the study of generic cracks. In addition, we have introduced a simple error indicator for improving the SIF computed via the interaction integral, thanks to the better behaviour of the J-integral as it does not need auxiliary extraction fields.

Computing stress intensity factors for curvilinear cracks

“…The main drawback of the curvilinear coordinates of [23] is the need to perform boundary integrals over both the real crack surfaces and a pair of fictitious crack surfaces. In [26], González-Albuixech et al proposed another curvilinear coordinate system that can eliminate the integration on the fictitious crack surfaces, and in this way facilitate the computation.…”

“…In [27,26], González-Albuixech et al studied the properties of the aforementioned methods in two-and three-dimensions, respectively, but not with all terms arising from the derivation of the interaction integral. Such omission of terms may have contributed to the observed slow convergence and occasional divergence.…”

A well‐conditioned and optimally convergent XFEM for 3D linear elastic fracture

“…Some directions of future work include the following: The improvement of the method in order to minimize the loss of accuracy observed for large enrichment radii. The use of improved SIF evaluation methods in order to better asses the accuracy of the predicted SIFs. The combination of the method with goal‐oriented a posteriori error estimators and local front mesh and FE mesh refinement in order to further improve the accuracy of the method. The application of the method to crack propagation problems through the use of different crack representation methods . …”

“…The use of improved SIF evaluation [58] methods in order to better asses the accuracy of the predicted SIFs. The combination of the method with goal-oriented a posteriori error estimators [42][43][44][45][46] and local front mesh and FE mesh refinement in order to further improve the accuracy of the method.…”

Minimum energy multiple crack propagation. Part III: XFEM computer implementation and applications

“…For the solution of the linear system we use Matlab's built-in direct solver (by calling the backslash operator "\"), which uses a Cholesky decomposition that is optimised for sparse symmetric positive definite matrices. The post-processing step involves mainly the computations of the stress intensity factors using the domain-form interaction integral approach [40,39,21], identification of the crack tips to grow and the management of crack coalescence. Our aim is to assess the computational speed-up of the efficient implementation compared to the basic implementation.…”