A consistent iterative scheme for 2D and 3D cohesive crack analysis in XFEM

• A two-dimensional subspace is constructed to perform calculations related to cohesive tractions.
• A simple and effective way to transform quantities from subspace to global three-dimensional space is presented.
• In the presented approach, cohesion laws connected with crack opening, crack sliding and their mixture can be applied easily.
• Special attention is given to consistent linearization of the transformation.

This paper presents a consistent algorithm for cohesive crack modeling with the extended finite element method (XFEM). A new formulation for the transformation from global to local quantities for the cohesive law is presented. This formulation works as a generic shell around any cohesive law so that the cohesive law needs only to be implemented in two dimensions while it can be used in both two and three dimensional analysis. Particular attention is paid to consistent linearization of the contribution from the cohesive tractions. The proposed formulation is tested on three relevant examples of three-dimensional analysis.