2. Benchmark solution

For a central crack of length \(\mathrm{2a}\) in a bar of thickness \(\mathrm{2b}\) and of infinite length stressed by a stress \({\sigma }_{\mathrm{\infty }}\) to infinity, the intensity factor of the analytical stresses can be expressed by the following equation:

\({K}_{\mathit{Ia}}\mathrm{\approx }\sqrt{\frac{\pi a}{\mathrm{cos}(\frac{\pi a}{\mathrm{2b}})}}\)

Given that in the case treated the crack is stressed in \(I\) mode, it is possible to introduce for a given characteristic length an equivalent to the stress intensity factor [1]:

\({K}_{\mathrm{IIc}}=\frac{5\pi }{6\Gamma \frac{3}{4}}\mathrm{.}\stackrel{ˉ}{{\sigma }_{\mathrm{Ip}}}\sqrt{\pi {l}_{c}}\)

with \(\stackrel{ˉ}{{\sigma }_{\mathrm{Ip}}}\) the maximum principal regulated stress at the crack point. In order to compare the numerical results to the analytical solution, the parameter \(\mathit{RKI}\mathrm{=}{K}_{{\mathit{Il}}_{c}}\mathrm{/}{K}_{\mathit{la}}\) is introduced.

The 2 equations above were introduced into the test case command file through table manipulations. The value of the stress regulated at the tip of the crack is extracted. The values of the analytical and numerical stress intensity factor are calculated in the command file. The ratio between the two values is then calculated (\(\mathit{RKI}\)). This report was tested using the TEST_TABLE command.