3. Modeling B: non-meshed crack in dimension 2

In this modeling, we consider the structure in \(\mathrm{2D}\). The extended finite element method (X- FEM) is used.

This modeling involves two command files (hsnv132b.comm and hsnv132b.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.

hsnv132b.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.

hsnv132b.com1 file:

The elements X- FEM are involved in thermal calculation and in 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.

3.1. 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.

3.2. 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 also test the value of the stress intensity factor \({K}_{I}\) given by CALC_G_XFEM, option CALC_K_G as well as that given by the \({K}_{I}\) of POST_K1_K2_K3.

Finally, we test the \(G\) given by CALC_G_XFEM, option CALC_G.

The reference values are those obtained by modeling A.

Identification	Reference Type	Reference	% Tolerance
DX (PTEXTR)	AUTRE_ASTER	8.740426 10-4	2.0
DY (PTEXTR)	AUTRE_ASTER	3.826096 10-3	1.0
K1 (CALC_G_XFEM/CALC_K_G)	AUTRE_ASTER	9.0328413 106	2.0
K1 (POST_K1_K2_K3)	AUTRE_ASTER	9.0328413 106	4.0
G (CALC_G_XFEM/CALC_G)	AUTRE_ASTER	492.82	2,0