A multi-grid extended finite element method for elastic crack growth simulation

The eXtended Finite Element Method (X-FEM) has been applied to a wide range of applications, in particular for crack growth simulations in structural mechanics. However, for real applications (engineering simulations,...), even if one does not need to mesh the crack, it is necessary to take into account the different spatial scales linked to the size of the domain, the geometry of the boundary, the size of the boundary with prescribed displacement or loading, the discretized "representation" of the crack,... In this respect, one proposes in this paper to couple the eXtended Finite Element Method with a multi-grid strategy. Details are given for numerical implementation with a hierarchical finite element strategy. Finally, some examples are given (mixed mode crack growth simulations) to validate the method.

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