Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

Airy stress function.


Benchmark results
----------------------


.. csv-table::

    ":math:`{K}_{I}\mathrm{=}{\sigma }_{0}\sqrt{({\pi }_{0})}{\mathrm{cos}}^{2}\beta`"
    ":math:`{K}_{\mathit{II}}\mathrm{=}{\sigma }_{0}\sqrt{({\pi }_{0})}\mathrm{sin}\beta \mathrm{cos}\beta`"
    ":math:`{G}_{\mathit{ref}}\mathrm{=}\frac{1}{E}({K}_{I}^{2}+{K}_{\mathit{II}}^{2})` (in plane constraints)"



Uncertainty about the solution
----------------------------

Exact analytical solution (Irwin) in an unlimited environment.


Bibliographical references
----------------------------


1. Y. MURAKAMI Stress Intensity Factors Handbook, box 4.2, page 188. The Society of Materials Science, Japan, Pergamon Press, 1987.