1. Reference problem#
1.1. Geometry#
Figure 1.1-a
Point coordinates |
\(X\) |
|
\(A\) |
-1.0 |
-1.0 |
\(B\) |
1.0 |
-1.0 |
\(C\) |
1.0 |
1.0 |
\(D\) |
-1.0 |
1.0 |
The geometry of the structure is a square with side length \(\mathrm{1m}\).
The test is carried out on a single finite isoparametric element of quadratic form, a group of elements named \(\text{ROCHE}\). The different sides of this square, useful for this modeling, are groups of cells, \(\text{DA}\) and \(\text{BC}\) . The group of elements \(\text{ROCHE}\) , also contains the cell groups \(\text{SROCHE}\) and \(\text{MROCHE}\); which correspond respectively to the vertex and middle nodes of this same group; which correspond respectively to the vertex and middle nodes of this same group.
1.2. Material properties#
In the context of second gradient media, it is necessary to define material properties for the parts associated with the first and second gradients of the displacement field. The properties of the material are elastic for these two parts:
Young’s module: \(\text{E}=1000\text{Pa}\);
Poisson’s ratio: \(\nu =0\);
Second gradient stiffness module: \({a}_{1}=10{\text{Pa.m}}^{2}\).
Penalty setting: \(r=1E8\)
1.3. Boundary conditions and loads#
\(\mathrm{Dy}=0\) everywhere (Modeling is reduced in the case \(\mathrm{1D}\))
\(\mathrm{Dx}=0\) on the \(\text{BC}\) segment
\(\mathrm{Dx}=\mathrm{0.1m}\) on the \(\text{AD}\) segment