4. Modeling C: non-meshed crack in fake 3D#
In this modeling, we consider the structure in \(\mathrm{3d}\), but all the degrees of freedom following \(z\) (not only the displacements) are set to zero to reduce to the case \(\mathrm{2d}\). The extended finite element method (\(\text{X-FEM}\)) is used.
This modeling involves two command files (hsnv132c.comm and hsnv132c.com1). In each file, we model exactly the same problem, but with a different strategy (for validation purposes only). The quantities tested, as well as the non-regression values are identical from one file to another.
hsnv132c.comm file:
The elements X- FEM only intervene at the level of mechanical calculation to represent the discontinuity of the movement through the crack. For the thermal part, the temperature is calculated on a healthy thermal model, the temperature is in fact continuous across the lips of the crack.
hsnv132c.com1 file:
The elements X- FEM intervene at the level of thermal calculation and at the level of mechanical calculation. For the thermal part, a continuous temperature is imposed across the interface (via AFFE_CHAR_THER/ECHANGE_PAROI/TEMP_CONTINUE = “OUI”). The same problem as in the previous command file is therefore modelled, but with a different discretization.
4.1. Characteristics of the mesh#
The structure is modelled by a regular mesh composed of \(11\mathrm{\times }11\mathrm{\times }1\) HEXA8, respectively along the axes \(x\), \(y\) and \(z\). The crack is not meshed.
4.2. Boundary conditions and loads#
To get back to case \(\mathrm{2D}\), it is necessary to block all the following degrees of freedom \(z\).
Blocking movements following \(z\) is not enough, the enhanced degrees of freedom are of great importance. It is therefore necessary to impose \(\mathrm{DZ}=0\) on all the nodes, and also to impose \(\mathrm{H1Z}=0\) on the nodes enriched by Heaviside and \(\mathrm{E1Z}=\mathrm{E2Z}=\mathrm{E3Z}=\mathrm{E4Z}=0\) on all the nodes enriched by the asymptotic functions.
4.3. Tested sizes and results#
We test the values of the following displacement \(X\) and \(Y\) of the end point “PTEXTR” with coordinates \((\mathrm{1,1})\).
We do not test the value of the energy return rate \(G\) given by CALC_G_XFEM nor that of the stress intensity factor \({K}_{I}\) given by the \({K}_{I}\) of POST_K1_K2_K3 because the fact of constraining the following movements \(Z\) is not in accordance with the \(\mathrm{2D}\) from an energy point of view.
The reference values are those obtained by modeling A.
Identification |
Reference type |
Reference |
% tolerance |
DX (PTEXTR) |
AUTRE_ASTER |
|
2 |
DY (PTEXTR) |
AUTRE_ASTER |
3.826095 10-3 |
1 |