PSI - Issue 2_B

Jaime Planas et al. / Procedia Structural Integrity 2 (2016) 3676–3683 J. Planas et al. / Structural Integrity Procedia 00 (2016) 000–000

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Fig. 9. Evolution of crack pattern in the shrinking slab when the nominal shrinkage strain σ S is increased from f t to 4 f t in 30 steps (a), 6 steps (b), and 3 steps (c).

from the 13 prominent cracks in step 15, only 7 survive as main cracks in the last step and 5 more are still visible as secondary cracks in retreat. Overall, similar results are obtained when the calculation is carried out in six steps —Figure 9(b)— or in three steps —Figure 9(c)—. However, the details of the crack patterns clearly di ff er. This has a negative reading: the procedure is not robust enough to reproduce exactly the same pattern for any step size. However, there is also a positive reading: the crack pattern is not predetermined by the mesh layout. Of course, the localization is triggered by the small inhomogeneities induced by the mesh itself (which is a spurious, purely numerical inhomogeneity, not a material one). But there seems to be a su ffi ciently rich set of locally stable configurations for the calculations to be meaningful at large.

5. Conclusions

From the foregoing results the following conclusions can be drawn:

• The strictly local method devised in Sancho et al. (2007a) to describe crack growth in quasibrittle materials consistently captures the transition from distributed or smeared cracking to localized cracking. • As long as global behavior is concerned the method is basically insensitive to mesh and to step size. • The method seems to be robust since it comes to a solution for any step size. • The details of the localization do depend on the mesh and on the step size. Besides, since the exact position of localized cracks may not be accessible, theidentification of the invariant statis tical parameters of the crack distribution would be very helpful in deciding the final adequacy of the method.