1. Reference problem#
1.1. Geometry#
We consider a rectangular bar oriented along the \(\mathrm{Oy}\) axis.
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The coordinates of the points are given in the following table:
Point |
\(\mathrm{N4}\) |
|
\(\mathrm{N27}\) |
|
|
||
Abscissa (\(m\)) |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
|
Ordered (\(m\)) |
5 |
5 |
2.5 |
2.5 |
2.5 |
-5 |
-5 |
The problem is modelled on the time interval \([0;\mathrm{10s}]\).
1.2. Material properties#
One gives here the parameters of the bar
Liquid water |
\(\rho\): density (\({\mathrm{kg.m}}^{-3}\)) \(1/{K}_{\mathrm{lq}}\): inverse of compressibility (\({\mathrm{Pa}}^{-1}\)) |
1000 0.5E-9 |
Material coefficients |
\(r\): homogenized density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) \(E\): Young’s modulus (\(\mathit{Pa}\)) \(\nu\): Poisson’s ratio (–) \(b\): Biot coefficient (—) \({K}_{i}\): intrinsic permeability (\({m}^{2}\)) |
2800 5.8E9 0. 1 1.E-8 |
Additional material coefficients for DRUCK_PRAGER |
\(\alpha\): pressure dependence coefficient (–) \({P}_{\mathit{ultm}}\): ultimate cumulative plastic deformation (–) \({\sigma }_{Y}\): plasticity constraint (\(\mathit{Pa}\)) \(H\): work hardening module (\(\mathit{Pa}\)) |
\(\mathit{LINEAIRE}\) 0.33 1.0 1.E8 0.0 |
1.3. Boundary conditions and loads#
On \(\mathrm{HAUT}\), conditions \(\sigma \cdot n=0\) and \(p=3.E6\) Pa are imposed.
On \(\mathrm{GAUCHE}\) and \(\mathrm{DROITE}\), the conditions \({u}_{x}=0\) and zero liquid flow \(\mathrm{M.n}=0\) are imposed.
On \(\mathrm{BAS}\), the conditions \({u}_{x}={u}_{y}=0\) and zero liquid flow \(M\cdot n=0\) are imposed.
1.4. Initial conditions#
The initial fluid pressure is taken to be equal to 2 \(\mathrm{MPa}\). The initial porosity is taken to be equal to 0.5.