v7.22.132 HSNV132 - X-FEM crack in thermo-elasticity#
Summary
The purpose of this test is to validate the consideration of thermal loading for a cracking calculation by the X- FEM [bib1] method on an academic case \(\mathrm{2D}/\mathrm{3D}\).
This test involves a square plate with a straight through crack, embedded on the lower edge, and subjected to a horizontal temperature gradient. This loading has the effect of opening the crack. We compare the displacement for the end node at the top right, for FEM and X- FEM. This test includes a call to THER_LINEAIRE, then MECA_STATIQUE.
Four models are considered:
modeling \(A\): \(\text{FEM}\mathrm{2D}\) (taken as a reference),
modeling \(B\): \(\text{X-FEM}\mathrm{2D}\), crack in the middle of the elements,
modeling \(C\): \(\text{X-FEM}\mathrm{3D}\) (we block the movements following \(z\)), crack in the middle of the elements,
modeling \(D\): \(\text{X-FEM}\mathrm{3D}\), real modeling \(\mathrm{3d}\), without putting \(\mathit{DZ}=0\), to validate the calculation of \(G\) in \(\mathrm{3D}\).
modeling \(E\): \(\text{X-FEM}\mathrm{3D}\), real modeling \(\mathrm{3d}\), without putting \(\mathrm{DZ}=0\), to validate the calculation of \(G\) in \(\mathrm{3D}\). Similar to modeling \(D\) except that the top and bottom surfaces have been embedded to induce significant stresses.
There is a gap of less than \(\text{1\%}\) for travel, and a gap of \(\text{3,5\%}\) over \({K}_{I}\) and \(\text{1,4 \%}\) out of \({K}_{\mathit{II}}\).