PSI - Issue 12

Venanzio Giannella et al. / Procedia Structural Integrity 12 (2018) 404–415 V. Giannella Structural Integrity Procedia 00 (2018) 000 – 000

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Figure 4. (a) DBEM submodel with the initial crack; (b) close-up of the crack insertion area; (c) internal view of the crack with highlight of tractions applied on the crack face elements and J-paths along the crack front (X representing the normalised abscissa along crack front).

3.2. FEM-DBEM LC approach

The FEM-DBEM LC approach is based on the application of the superposition principle to fracture mechanics problems and is here described (Fig. 5) with reference to a thermal-stress crack problem (see also Wilson, 1979):  starting from an original uncracked domain (A), a crack can be opened (B) and loaded with tractions corresponding to those calculated over the dashed line of the virtual crack in (A);  the new configuration (B), equivalent to the previous one (A), can be transformed by using the superposition principle, splitting the boundary conditions as provided in (C) and (D) (Eq. (2)). (C) represents the original problem to solve, whereas (D), after the tractions sign inversion turns into the equivalent problem (E) that will be effectively worked out; namely, SIFs for case (C) are equal (Eq. (2)) to those calculated for the simpler problem (E). In conclusion, using the boundary conditions retrieved from the considered thermal-stress problem (Fig. 5) a pure stress analysis for a crack problem can be solved, in which the crack faces undergo tractions equal in magnitude but opposite in sign to those calculated over the dashed line in Fig. 5 (position A). K a = K b = 0 = K c + K d (1) K c = − K d = K e (2)