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The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known to prevent the locking of the F.E. approximation in the incompressible limit. However, the stability of these formulations is conditionned by the fullfilment of the inf-sup condition. Recently, finite elements method has evolved with the introduction of the partition of unity. The X-FEM uses it to remove the need to mesh (and remesh) physical surfaces. In this paper, a strategy is proposed for the treatment of holes within X-FEM in the incompressible setting. Numerical examples show that F.E. convergence rate is preserved and that the inf-sup condition is passed.
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