5. D modeling: non-meshed crack in real 3D#

In this modeling, we consider the structure in \(\mathrm{3D}\). The extended finite element method (\(\text{X-FEM}\)) is used.

This modeling involves two command files (hsnv132d.comm and hsnv132d.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.

hsnv132d.com 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.

hsnv132d.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.

5.1. Characteristics of the mesh#

The structure is modelled by a regular mesh composed of \(31\times 31\times 10\) HEXA8, respectively along the axes \(x\), \(y\) and \(z\). The crack is not meshed.

5.2. Tested sizes and results#

We test the value of the stress intensity factors \(G\) given by CALC_G_XFEM on point 5 at the bottom of the crack. These values are the same.

Identification

Reference type

Reference values

\(G\)

“NON_REGRESSION”

231.412800803

Notes:

  1. It should be noted that the bar is virtually free from thermal expansion.

  2. Note that G_ IRWIN is very different from G calculated by CALC_G_XFEM. It is a purely thermal problem. The fact that the singular solutions of a thermo-mechanical problem are used has resulted in bad K values. However, the G values are accurate. See the R docs for more information.

  3. Note that the G values obtained with options CALC_G and CALC_K_Gde CALC_G_XFEM are identical.