2. Benchmark solution

2.1. « Rectangular » crack

The aim of this test is to validate the definition of this crack by calculating the associated level sets. The test actually only looks at the value of \(\mathrm{lst}\) at points \(\mathrm{P4}\) and \(\mathrm{P5}\). A quick calculation gives \(\mathrm{lst}(\mathrm{P4})=\sqrt{({(\frac{1}{2}-(a-r))}^{2}+{(1-(b-r))}^{2})}-r\) and \(\mathit{lst}(\mathit{P5})\mathrm{=}\mathrm{0,2}\).

2.2. « Cylinder » crack

The aim of this test is to validate the definition of this crack by calculating the associated level sets. The test focuses on the values of \(\mathit{lsn}\) and \(\mathrm{lst}\) at points \(\mathrm{P4}\) and \(\mathrm{P5}\). A quick calculation gives:

\(\mathit{lsn}(\mathit{P4})\mathrm{=}\sqrt{2}\mathrm{-}r\) and \(\mathit{lst}(\mathit{P5})\mathrm{=}1\mathrm{-}r\),

\(\mathit{lst}(\mathit{P4})\mathrm{=}\mathrm{-}\mathrm{0,5}\) and \(\mathit{lst}(\mathit{P5})\mathrm{=}\mathrm{-}\mathrm{0,5}\).