PSI - Issue 42

Diego F. Mora et al. / Procedia Structural Integrity 42 (2022) 224–235 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 4. (a) Boundary conditions of the thermal analysis; (b) Boundary conditions of the mechanical analysis.

To complete the boundary conditions, the displacements U  and U z given in the local cylindrical coordinate system ( , , R Z  indicated in orange in Fig. 4(b)) are fixed at the edge on middle plane (orange symbols in Fig 4(b)) in order to avoid rigid body motion of the cylinder during loading. 2.4. XFEM in ABAQUS The XFEM implementation in ABAQUS/Standard is based on the phantom nodes method (Hansbo and Hansbo 2004); in this method, these phantom nodes are superposed to the standard ones, to reproduce the presence of the discontinuity. Phantom nodes are tied to their corresponding real nodes when the enriched element is intact. This situation holds until the element is not cut by a crack; as soon as the element is cracked, it is divided in two separate parts ( 0 +  and 0 −  ), each of them including both real and phantom nodes (see Fig. 5).

Fig. 5. (a) Real and phantom nodes

In particular, the separation procedure occurs when the equivalent strain energy release rate exceeds the critical strain energy release rate at the crack tip in an enriched element. Once this condition has been satisfied, every phantom node is no more restrained to its corresponding real one and thus, they can freely move apart. It is worthy to notice that ABAQUS/Standard distinguishes between two kinds of cracks, which could be present within a certain domain, i.e. stationary cracks and propagating cracks. In the first case, the crack is not allowed to propagate within the body and only a static analysis might be carried out (Fig. 6(a)).