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In this section an example featuring a strong discontinuity within the problem domain is considered. Contrary to publications that implement similar coupling methodologies (see e.g. [24, 54]), \( \varOmega^PD \) is localized near the crack tip only and the discontinuity that appears within \( \varOmega^FE \) is treated with the incorporation of the XFEM enrichment.

The simulated displacement fields for each of the cases considered are presented in Fig. 10. In the same figure, a black dotted line is used to indicate the coupling interface \( \partial \varOmega_1 \) in Case 3. For easier comparison the plots have been created using the same colour scales. Additionally, in Fig. 11, the plate is plotted in its deformed state for Case 3. The introduction of the shifted Heaviside enrichment at the elements cut by the crack, enables the FE method to facilitate discontinuous displacement fields and capture the displacement jump at the crack body. It is this property that allows the PD domain to be limited only in the area near the crack tip, without unmerging nodal displacements or specifically constructing the FE mesh to conform to the crack geometry. This will prove invaluable in the following paragraphs were crack propagation problems are considered. Notice also how using the definition from Eq. 14 the ghost particles that are positioned within an enriched element follow its deformation.

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