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MWAT2
Plane or axisymmetric state
Description
Complete coupled analysis soil mechanics-3 fluids. Couplings: Mechanical-Water-Air-Temperature in large deformations.
Type: 205
The element is defined by 3, 4, 6, 8, 15 or 25 nodes indicated in NODES in the order indicated in the figure.
The flow (water, air, temperature) description can be different from the mechanical description: pressure/temperature could be linearly interpolated in a 3 or 4 nodes configurations, while the mechanical DoFs would be parabolically interpolated in a 6 or 8 nodes configuration. In that case, the fluid DoF must be fixed for the non-used nodes.
The “fluid” constitutive laws that can be used with this element are, for now:
15-node element (12 I.P.)
For the element with 15 nodes, the interpolation functions are the following:
\[N_1=\zeta(4\zeta-1)(4\zeta-2)(4\zeta-3)/6 \\ N_2=\xi(4\xi-1)(4\xi-2)(4\xi-3)/6 \\ N_3=\eta(4\eta-1)(4\eta-2)(4\eta-3)/6 \\ N_4=4\zeta\xi(4\zeta-1)(4\xi-1) \\ N_5= 4\xi\eta(4\xi-1)(4\eta-1) \\ N_6= 4\eta\zeta(4\eta-1)(4\zeta-1) \\ N_7=\xi\zeta(4\zeta-1)(4\zeta-2)*8/3 \\ N_8=\zeta\xi(4\xi-1)(4\xi-2)*8/3 \\ N_9=\eta\xi(4\xi-1)(4\xi-2)*8/3 \\ N_{10}=\xi\eta(4\eta-1)(4\eta-2)*8/3 \\ N_{11}=\zeta\eta(4\eta-1)(4\eta-2)*8/3 \\ N_{12}=\eta\zeta(4\zeta-1)(4\zeta-2)*8/3 \\ N_{13}=32\eta\xi\zeta(4\zeta-1) \\ N_{14}=32\eta\xi\zeta(4\xi-1) \\ N_{15}=32\eta\xi\zeta(4\eta-1) \]
25-node element (16 I.P.)
For the element with 25 nodes, the interpolation functions are expressed from the following functions:
\[\begin{align*}
N_1&=N_1(\xi)N_1(\eta) & N_{14}&=N_1(\xi)N_4(\eta) \\
N_2&=N_2(\xi)N_1(\eta) & N_{15}&=N_1(\xi)N_3(\eta) \\
N_3&=N_3(\xi)N_1(\eta) & N_{16}&=N_1(\xi)N_2(\eta) \\
N_4&=N_4(\xi)N_1(\eta) & N_{17}&=N_2(\xi)N_2(\eta) \\
N_5&=N_5(\xi)N_1(\eta) & N_{18}&=N_3(\xi)N_2(\eta) \\
N_6&=N_5(\xi)N_2(\eta) & N_{19}&=N_4(\xi)N_2(\eta) \\
N_7&=N_5(\xi)N_3(\eta) & N_{20}&=N_4(\xi)N_3(\eta) \\
N_8&=N_5(\xi)N_4(\eta) & N_{21}&=N_4(\xi)N_4(\eta) \\
N_9&=N_5(\xi)N_5(\eta) & N_{22}&=N_3(\xi)N_4(\eta) \\
N_{10}&=N_4(\xi)N_5(\eta) & N_{23}&=N_2(\xi)N_4(\eta) \\
N_{11}&=N_3(\xi)N_5(\eta) & N_{24}&=N_2(\xi)N_3(\eta) \\
N_{12}&=N_2(\xi)N_5(\eta) & N_{25}&=N_3(\xi)N_3(\eta) \\
N_{13}&=N_1(\xi)N_5(\eta)
\end{align*}\]
With:
\[N_1(X)=1/6X-1/6X^2-2/3X^3+2/3X^4 \\ N_2(X)=-4/3X+8/3X^2+4/3X^3-8/3X^4 \\ N_3(X)=1-5X^2+X^4 \\ N_4(X)=4/3X+8/3X^2-4/3X^3-8/3X^4 \\ N_5(X)=-1/6X-1/6X^2+2/3X^3+2/3X^4 \]
Implmented by: J.P. Radu & J.D. Barnichon, 1986
Files
Prepro: MWAT2A.F
Lagamine: MWAT2B.F
Input file
| Title (A5) | |
|---|---|
| TITLE | “MWAT2” in the first 5 columns |
| Control data (4I5) | |
| NELEM | Number of elements |
| ISPSMAS | = 0 → Nothing = 1 → Take into account the specific mass if and only if NTANA<0 |
| INSIG | = 0 → No initial stress = 1 or 2 → Initial stresses |
| INBIO | = 0 → No Biot coefficient = 1 → Isotropic Biot coefficient |
| Specific mass in dynamic analysis - Only if ISPMAS = 1 (1G10.0) | |
| SPEMAS | Specific mass |
| Initial stresses - Only if INSIG > 0 (4G10.0) | |
| If INSIG=1: $\sigma_y=\sigma_{y0}+yd\sigma_{y}$ If INSIG=2: $\sigma_y=min(\sigma_{y0}+yd\sigma_y,0)$ |
|
| SIGY0 | $\sigma_{y0}$ effective stress $\sigma_y$ at the axes origin |
| DSIGY | Effective stress gradient along Y axis |
| AK0X | $k_0$ ratio $\sigma_x/\sigma_y$ |
| AK0Z | $k_0$ ratio $\sigma_z/\sigma_y$ (if AK0Z=0, AK0Z=AK0X) |
| The computation of SIGY0 and DSIGY must take into account the apparent specific mass, defined as \[\rho_a'=[(1-n)\rho_s+nS_w\rho_w]-\rho_w\] where: $\rho_s$ is the solid specific mass - this represents the specific mass of a fictive sample where ther is no porosity, i.e. where the grains occupy the whole volume of the sample $\rho_w$ is the fluid specific mass $n$ is the porosity defined in the flow law related to the element $S_w$ fluid saturation, ∈ [0,1] |
|
| Biot coefficient - Only if INBIO = 1 (1G10.0) | |
| CBIOT | Biot coefficient |
| Definition of the elements (6I5/16I5(/9I5)) | |
| NNODM | Number of nodes for the mechancial description: 3, 4, 6, 8, 15, or 25 |
| NINTM | Number of integration point (1, 3, 4, 7, 9, 12, or 16) for the mechanical description |
| LMATM | Mechanical material |
| NNODP | Number of nodes for the flow description: 3, 4, 6, 8, 15, or 25 |
| NINTP | Number of integration points (1, 3, 4, 7, 9, 12, or 16) for the flow description Must be equal to NINTM |
| LMATF | Flow material |
| NODES(NNODEM) | List of nodes |
Results
- Stresses (in global axes)
- Mechanical stresses $\sigma_x$, $\sigma_y$, $\sigma_{xy}$, $\sigma_z$
- Flow in water $f_{wx}$, $f_{wy}$, $f_{w,stored}$, 0
- Flow in air $f_{ax}$, $f_{ay}$, $f_{a,stored}$, 0
- Thermal flow $f_{tx}$, $f_{ty}$, $f_{t,stored}$, 0
- Internal variables:
- Internal variables of the mechanical law
- Internal variables of the flow law
