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

• Published in: Computer methods in applied mechanics and engineering Vol. 264; pp. 129 - 144
• Main Authors: González-Albuixech, Vicente F., Giner, Eugenio, Tarancón, José E., Fuenmayor, F. Javier, Gravouil, Anthony
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2013; Elsevier
• Subjects: Computation; Cracks; Curved; Curved and non-planar cracks; Engineering Sciences; Finite element method; Formulations; Integrals; Interaction integral; J-integral; Level sets; Mathematical analysis; Mathematical models; Mechanics; Physics; SIF; Solid mechanics; XFEM; SIF; J-integral; Level sets; Curved and non-planar cracks; Interaction integral; XFEM
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2013.05.016

The computation of stress intensity factors (SIFS) 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 set 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 behavior of the J-integral as it does not need auxiliary extraction fields.