A stable X‐FEM in cohesive transition from closed to open crack

Ignoring crack tip effects, the stability of the X‐FEM discretizations is trivial for open cracks but remains a challenge if we constrain the crack to be closed (i.e., the bi‐material problem). Here, we develop a formulation for general cohesive interactions between crack faces within the X‐FEM framework. The stability of the new formulation is demonstrated for any cohesive crack stiffness (including the closed crack) and illustrated for a nonlinear cohesive softening law. A benchmark of the new model is carried out with simpler approaches for a closed crack (i.e., Lagrange multipliers) and for a cohesive crack (i.e., penalty approach). Due to the analogies between stable cohesive X‐FEM and Nitsche's methods, the new method simplifies the implementation and is attractive in dynamic explicit codes. Copyright © 2014 John Wiley & Sons, Ltd.