3. Modeling A

3.1. Characteristics of modeling

The idea is to perform a numerical simulation corresponding to the problem presented in the previous part and to compare the results obtained. The discontinuous elements make it possible to represent the crack along \({\Gamma }_{0}\). The latter have PLAN_ELDI modeling and CZM_EXP behavior. The other elements of the mesh are QUAD4 elastics in D_ PLAN modeling.

The values of the parameters of the Airy function for the construction of the analytical solution are taken arbitrarily:

\(\alpha =0{\text{MPa.mm}}^{-1},\beta =1/4\pi {\text{MPa.mm}}^{-1},\gamma =1/2\text{MPa}\text{et}\eta =0\text{MPa}\)

3.2. Characteristics of the mesh

The plate is meshed structured in quadrangles with 20 meshes in the width and 50 in the height. Elements are arranged at discontinuity along side \({\Gamma }_{0}\) with the normal directed following \(-X\). This is achieved using the CREA_FISS keyword from CREA_MAILLAGE (see documentation [U4.23.02]).

3.3. Tested sizes and results

Size tested	Type	Reference	Tolerance ( \(\text{\%}\) )
Threshold variable: \(\mathrm{VI1}\) On the element \(\mathrm{MJ15}\)	“ANALYTIQUE”	0.49315	0.10
Threshold variable: \(\mathrm{VI1}\) On element \(\mathrm{MJ45}\)	“ANALYTIQUE”	1.075	0.10
Normal stress: \(\mathrm{VI6}\) On element \(\mathrm{MJ30}\)	“ANALYTIQUE”	0.4489	0.10