_images/Cadre1.gif

Figure 1.1-1: geometry and elliptical crack background

v3.04.110 SSLV110 - Elliptical crack in an infinite medium#

Summary:

It is a static test for a three-dimensional problem. This test makes it possible to calculate the local energy release rate on the crack bottom by the theta method (command CALC_G in FEM and CALC_G_XFEM in X-FEM).

The radius of the integration rings is variable along the crack, and the local energy restoration rate is calculated using two different methods (LEGENDRE and LINEAIRE/LAGRANGE). Integration crowns are defined in two ways: by the data of a variable radius (R_ INF_FO and R_ SUP_FO) and the data of the number of layers (NB_COUCHE_INF and NB_COUCHE_SUP).

The interest of the test is the validation of the theta method in \(\mathrm{3D}\) and the following points:

  • comparison of the results with an analytical solution,

  • stability of the results with respect to integration rings,

  • comparison between two different methods for calculating local \(G\),

  • 2 cases of equivalent loads (distributed pressure and volume loading).

  • Calculate \(\mathrm{K1}\) from \(G\) and Irwin’s formula

This test contains 3 different models (A, F, G).

The F modeling tests the calculation of \(\mathrm{K1}\) for a non-meshed crack (method X- FEM). It also allows you to compare the errors made when calculating \(\mathit{K1}\) with the POST_K1_K2_K3 operator or the CALC_G_XFEM operator.

The G modeling validates the calculation of the intensity factor of equivalent stresses in the presence of cohesive zones (see documentation [R7.02.18]), by the CALC_G_XFEM operator.