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Models involving interfaces with discontinuities or even singularities of some fieldsacross them are very frequent in real life problems modelling. The use of the eXtendedFinite Element Method (XFEM) instead of the traditional FEM has two advantages: themesh of the domain can be independent of the interface position, and it allows toenrich an area with specific shape functions fitted to singularities of the expectedsolution. Nevertheless, a critical point of its implementation is the different kind (andnumber) of degrees of freedom on each node. In this paper we present a detaileddescription of XFEM implementation, with special emphasis on the terms that involveintegration over interfaces. The methodology is presented in a general context, and asan example, we will apply it to a problem of solids mechanics. In particular, we willcontextualize the procedure on a Rayleigh waves propagation problem in a crackedstructure considering a Signorini contact condition on the crack sides. |
