3. Modeling A#

3.1. Characteristics of modeling#

It is a nonlinear elasticity calculation under the hypothesis of small displacements, in plane deformations. The crack is opened in pure I mode. Only half of the structure is represented by symmetry.

3.2. Characteristics of the mesh#

The mesh at the input of the test case into a linear mesh with the following characteristics:

-Number of knots: 8936

-Number of elements:

-Triangles: 6494

-quadrangles: 5408

The radius of the radiating domain at the bottom of the crack is \(25\mathit{mm}\). The size of the elements connected to the bottom of the crack is \({10}^{-3}\mathit{mm}\)

At the execution of the test case, a new quadratic mesh with elements of BARSOUM at the bottom of the crack is created by executing the commands CREA_MAILLAGE (keyword LINE_QUAD) then MODI_MAILLAGE (keyword MODI_MAILLE, option NOEUD_QUART).

_images/10000201000001700000026D166DD6E2353657AC.png

3.3. Tested sizes and results#

The results obtained for three different integration rings are compared:

The reference values of G from method 3 POST_K1_K2_K3 selected as well as the associated details are provided in the table below.

Calculation instant

Surface effort taxed (MPa)

Reference: \(G(N/m)\) From POST_K1_K2_K3 (method 3)

Tolerance (%)

1

\(\mathrm{0,7}\ast \text{SY}=105\)

1.13702E+05

0.3

2

\(\text{SY}=150\)

2.85869E+05

0.3

3

\(3\ast \text{SY}=450\)

3.42359E+06

0.2