6. E modeling

In E modeling, we study a 3D structure whose geometry is based on that of the sslv134b test case. We test DEFI_FOND_FISS in the case of a crack with a curved bottom and both lips defined.

6.1. Characteristics of the mesh

The mesh and geometry used are those of the sslv134b test case. The mesh is presented by the

next figure:

It is composed of 5527 nodes, 784 HEXA20 and 432 PENTA15 solid elements. The background is a quarter circle in plane \(\mathrm{Oxy}\) composed of 17 knots.

6.2. Tested sizes and results

The crack is a quarter of a circle whose center is the origin of the coordinate system. Thus, the analytical values of the crack propagation direction vectors are the coordinates of the normalized bottom nodes.

At the bottom node number \(i\) with coordinates \(({\mathit{COORX}}_{i},{\mathit{COORY}}_{i},{\mathit{COORZ}}_{i})\):

The crack propagation direction vector is:

\({\mathit{VDIRX}}_{i}\mathrm{=}\frac{{\mathit{COORX}}_{i}}{\sqrt{({\mathit{COORX}}_{i}\mathrm{²}+{\mathit{COORY}}_{i}\mathrm{²}+{\mathit{COORZ}}_{i}\mathrm{²})}}\)

\({\mathit{VDIRY}}_{i}\mathrm{=}\frac{{\mathit{COORY}}_{i}}{\sqrt{({\mathit{COORX}}_{i}\mathrm{²}+{\mathit{COORY}}_{i}\mathrm{²}+{\mathit{COORZ}}_{i}\mathrm{²})}}\)

\({\mathit{VDIRZ}}_{i}\mathrm{=}\frac{{\mathit{COORZ}}_{i}}{\sqrt{({\mathit{COORX}}_{i}\mathrm{²}+{\mathit{COORY}}_{i}\mathrm{²}+{\mathit{COORZ}}_{i}\mathrm{²})}}\)

The vector normal to the crack plane for each of the fundus nodes is directed from the lower lip to the upper lip. It’s worth \((\mathrm{0,0}\mathrm{,1})\).

For all these values, 0.1% error between the analytical value and the calculated value is tolerated.