3. Modeling A: non-meshed crack in dimension 2#

Since the crack is not meshed, the exchange condition between the lips of the crack is applied using the keyword FISSURE of the keyword factor ECHANGE_PAROI of the operator AFFE_CHAR_THER [U4.44.02].

3.1. Characteristics of modeling#

We use the PLAN model of the THERMIQUE phenomenon. The extended finite element method (X- FEM) is used.

3.2. Characteristics of the mesh#

The structure is modelled by a regular mesh composed of \(101\mathrm{\times }101\) QUAD4, respectively along the axes \(x\), \(y\). The crack is not meshed.

3.3. Tested sizes and results#

The quantities below are first tested in the case where the load making it possible to impose the continuity of the temperature field (keyword TEMP_CONTINUE) results from the operator AFFE_CHAR_THER, they are then tested when the operator AFFE_CHAR_THER_F results.

The temperature is tested at points \({P}^{\text{+}}\), \({P}^{\text{-}}\) and \(Q\) (see Figure). To do this, the temperature field is tested after using operators POST_MAIL_XFEM and POST_CHAM_XFEM.

The two components of the temperature gradient stored in field TEMP_ELGA are then tested in the result produced by the operator THER_LINEAIRE. These components are tested:

  • at a Gauss point of a « Heaviside » element

  • at a Gauss point of a « crack-tip » element

  • at a Gauss point of a « Heaviside/Crack-Tip » element

Identification

Reference type

Reference value

Tolerance

Points \({P}^{\text{+}}\), \({P}^{\text{-}}\), and \(Q\) - \(\mathit{TEMP}\)

“ANALYTIQUE”

15

0.1%

In 3 Gauss points \(\mathit{DTX}\)

“ANALYTIQUE”

0

1.E-9

In 3 Gauss points \(\mathit{DTY}\)

“ANALYTIQUE”

10

0.1%