Benchmark solution
====


Method used for the reference solution
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For a circular crack of radius :math:`a` in an infinite medium, subjected to a uniform traction :math:`\sigma` following the normal to the plane of the lips, the local energy release rate :math:`G(s)` is independent of the curvilinear abscissa along the crack front :math:`s` and is expressed as follows [1]:

:math:`G(s)\mathrm{=}\frac{(1\mathrm{-}{\nu }^{2})}{\pi E}4{\sigma }^{2}a`

Stress intensity factor :math:`{K}_{I}(s)` is given by Irwin's formula:

:math:`G(s)\mathrm{=}\frac{(1\mathrm{-}{\nu }^{2})}{E}{K}_{I}^{2}`, which is :math:`{K}_{I}(s)\mathrm{=}\frac{2\sigma \sqrt{a}}{\sqrt{\pi }}`


Benchmark results
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With the numerical values of the statement, we find: :math:`{K}_{I}=\mathrm{1,5957}\mathit{MPa}\mathrm{.}\sqrt{m}` and :math:`G\mathrm{=}\mathrm{11,59}{\mathit{J.m}}^{\mathrm{-}2}`.


Bibliographical references
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*   H. Tada, P. Paris, G. Irwin, G. Irwin, The Stress Analysis of Cracks Handbook, 3rd edition, 2000