.. _V3.02.103:

**v3.02.103** SSLP103 - Calculation of the stress intensity coefficients KI and KII for a cracked circular plate in linear elasticity
================================================================================================================================================

**Summary**

This is a test of fracture mechanics in static linear elasticity for a two-dimensional problem. We consider a cracked circular plate (with a crack inclined by 30 degrees with respect to the x-axis) for which we calculate:


* the stress intensity coefficients :math:`{K}_{I}` and :math:`{K}_{\mathrm{II}}`,


* the :math:`G` energy return rate based on the IRWIN formula.

The advantage of the test is to know the analytical solution that gives the stress intensity coefficients and to have an inclined crack.

Two models are:


* Modeling A: FEM for elements C_ PLAN, D_ PLAN


* B modeling: FEM for elements D_ PLAN_INCO_UPG

This test includes modeling that successively treats plane deformations and plane stresses (elements of continuous media).

The numerical results do not deviate more than :math:`\text{1 \%}` to :math:`\text{2 \%}` from the reference values.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A___FEM_pour__l_ments_D_PLAN_et_C_PLAN
    Mod_lisation_B___FEM_pour__l_ments_D_PLAN_INCO_UPG
    Synth_ses_des_r_sultats