2. Benchmark solution#

2.1. Calculation method used for the reference solution#

(1) The reference solution for a lens-shaped crack with radius \(R\) in an infinite medium, subjected to a uniform pressure \(\sigma\) quite far from the crack, shows that the stress intensity factors are constant along the crack background and equal: ——————————————————— —-

\({K}_{I}\mathrm{=}\mathrm{0,877}(\frac{2}{\pi })\sigma \sqrt{\pi a}\)

\({K}_{\mathit{II}}\mathrm{=}\mathrm{0,235}(\frac{2}{\pi })\sigma \sqrt{\pi a}\)

\({K}_{\mathit{III}}\mathrm{=}0\)

with \(a\mathrm{=}R\mathrm{sin}\alpha\).

2.2. Benchmark results#

For the load under consideration \(\sigma \mathrm{=}1\mathit{MPa}\) and the following geometric characteristics:

\(L\mathrm{=}10m\), \(R\mathrm{=}2m\), \(a=\sqrt{2}\), we find:

\({K}_{I}\mathrm{=}\mathrm{1,177}\mathit{MPa}\mathrm{.}\sqrt{m}\)

\({K}_{\mathit{II}}\mathrm{=}\mathrm{0,3153}\mathit{MPa}\mathrm{.}\sqrt{m}\)

\({K}_{\mathit{III}}\mathrm{=}0\)

2.3. Bibliographical references#

  1. J.P. Pereira, C. A. Duarte, D. Duarte, D. Guoy, and X. Jiao: HP-Generalized FEM and Crack Surface Representation for Non-Planar 3-D Cracks, Int. Mr Numer. Engng, 77:601-633, 2009.