5. D modeling#

5.1. Characteristics of modeling D#

The simulation of the propagation of cracks by brittle fracture is carried out with modeling PLAN_JOINT and the law of behavior CZM_EXP_REG for cohesive meshes. The solid elements, in plane deformations D_ PLAN, are elastic.

5.2. Characteristics of the mesh#

A linear unstructured mesh of the perforated half-plate and of the potential crack is produced.

Volume elements (DCB): 804 TRIA3

Joint elements (crack path): 19 QUAD4

5.3. Tested sizes and results#

Non-regression tests are performed on the overall response: \({F}^{i}\) resulting from the force imposed on the upper face versus \(U\) displacement of the node \(P\) at the top of the hole.

Size tested

Aster_code

Tolerance ( \(\text{\%}\) )
_images/Object_62.svg

at moment 50

3.32215D-03

0.10
_images/Object_63.svg

at moment 50

4.21054D+07

0.10
_images/Object_64.svg

at the moment 100

2.52359D-03

0.10
_images/Object_65.svg

at the moment 100

5.3546D+06

0.10
_images/Object_66.svg

at the moment 150

7.09118D-03

0.10
_images/Object_67.svg

at the moment 150

6.75039D+06

0.10

We can see that the criminalization of cohesive law introduces a slight difference between the results. If we compare the results of modeling D to those of B in this way, we have the force-displacement curve of the figure.

_images/100000000000023E000001330BF9F91F452C7B80.png

Figure 5.3-a : comparison of joint elements with elements with internal discontinuity.