The XFEM is a powerful method to handle strong discontinuities in a finite element environment, especially in the study of the final stages of material failure, modelling the propagation of cracks, suppressing the need of remeshing. Nevertheless, for some materials undergoing large strain processes without noticeable volume changes, the discretization technique employed must not only describe the material behaviour but also correctly address the incompressibility constraints. In order to develop a robust formulation for this type of problems, an approach based on the analyses of the underlying sub-space of incompressible deformations embedded in the XFEM approximation is used, in the context of both infinitesimal and finite strains. This study motivated the extension of the conventional formulations of B-bar and F-bar to include the XFEM enrichment functions, whose performance is evaluated through some numerical examples and compared with competing methods such as the enhanced strain formulation.
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