10. Summaries of results

When closing a crack, taking into account the contact between the lips significantly affects the stress intensity factor \({K}_{I}\), compared to the XFEM non-contact method.

In this test case, we find a difference of the order of \(8\text{\%}\) on the value of \({K}_{I}\) calculated by Aster, going from modeling A (without contact between the lips) to modeling B (with contact). This difference is in line with theoretical predictions.

In fact, the theory states that the difference is equal to:

\(\frac{{K}_{I}^{\text{avec contact}}-{K}_{I}^{\text{sans contact}}}{{K}_{I}^{\text{avec contact}}}=\frac{({(2/3)}^{\frac{3}{2}}-1/2)}{{(2/3)}^{\frac{3}{2}}}\approx \mathrm{8,14413}\text{\%}\)

The results obtained show that the value of \({K}_{I}\) with contact taken into account is correctly evaluated and higher than that obtained without taking contact into account. This result highlights the importance of taking into account the effects related to contact in numerical simulations of cracking, as this example illustrates a case where the solution with interpenetration (without contact) is not a step conservative in terms of stress intensity factors. This may prove to be not without consequences for the study of propagation, based on propagation criteria written according to stress intensity factors.