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laws:epchemsol
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EP-CHEMSOL
Description
Cap model : elasto-plastic constitutive law for solid elements at constant temperature with effect of contaminant concentration.
The model
This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.
Files
Prepro: LCHEM.F
Lagamine: CHEM.F
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | NO |
| Generalized plane state | NO |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 570 |
| COMMNT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (11I5) | |
|---|---|
| NINTV | > 0 : Number of sub-steps used to integrate numerically the constitutive equation in a time step |
| = 0 : NINTV will be calculated in the law with DIV=$5.10^{-3}$ | |
| ISOL | = 0 : Use of total stresses in the constitutive law |
| $\neq$ 0 : Use of effective stresses in the constitutive law (See annex 8) | |
| IELA | = 0 : Linear elasticity |
| > 0 : Non-linear elasticity | |
| IELAS | = 0 : Constant BETA |
| > 0 : Variable BETA | |
| ILODEF | Shape of the yield surface in the deviatoric plane |
| = 1 : Circle in the deviatoric plane | |
| = 2 : Smoothed irregular hexagon in the deviatoric plane | |
| ILODEG | Not used : Associated plasticity |
| ITRACT | = 0 : No traction limitation |
| $\neq$ 0 : Traction stresses limitation | |
| IECPS | = 0 : $\psi$ is defined with PSIC and PSIE |
| = 1 : $\psi$ is defined with PHMPS | |
| ICBIF | Computation indice of bifurcation criterion |
| = 0 : Non computed | |
| = 1 : Computed (plane strain state only) | |
| KMETH | = 2 : Actualised VGRAD integration |
| = 3 : Mean VGRAD integration (Default value) | |
| IPCONS | = 0 :Definition of pre-consolidation pressure |
| $\neq$ 0 : Definition of OCR | |
Real parameters
| Line 1 (5G10.0) | |
|---|---|
| E_PAR1 | First elastic parameter |
| E_PAR2 | Second elastic parameter |
| E_PAR3 | Third elastic parameter |
| E_PAR4 | Fourth elastic parameter |
| HARD | Hardening parameter |
| Line 2 (6G10.0) | |
| PCONS0 | Pre-consolidation pressure (if IPCONS=0) |
| OCR | Over Consolidation Ratio (if IPCONS<>0, see section 6.5) |
| AI1MIN | Minimum value of $I_{\sigma}$ for non-linear elasticity |
| PSIC | Coulomb's angle (in degrees) for compressive paths |
| PSIE | Coulomb's angle (in degrees) for extensive paths |
| PHMPS | Van Eekelen exponent (default value=-0.229) |
| Line 3 (6G10.0) | |
| PHIC0 | Initial Coulomb's angle (in degrees) for compressive paths |
| PHICF | Final Coulomb's angle (in degrees) for compressive paths |
| BPHI | Only if there is hardening/softening |
| PHIE0 | Initial Coulomb’s angle (in degrees) for extensive paths |
| PHIEF | Final Coulomb’s angle (in degrees) for extensive paths (ssi ILODEF = 2) |
| AN | Van Eekelen exponent (default value=-0.229) |
| Line 4 (4G10.0) | |
| COH0 | Initial value of cohesion |
| COHF | Final value of cohesion |
| BCOH | Only if there is hardening/softening |
| TRACTION | Limit of the traction stress (only if ITRACT$\neq$0) |
| Line 5 (3G10.0) | |
| POROS | Initial soil porosity ($n_o$) |
| RHO | Specific mass |
| DIV | Parameter for the computation of NINTV in the law (for NINTV = 0 only) |
| Line 6 (3G10.0) | |
| C0 | Yield limit in term of concentration. This is not used at present in the model, so C0 should be given a large value (>1) so that yielding never takes place |
| A | Chemical softening parameter |
| BETA | Chemo-elastic expansion coefficient BETA if it is constant (IELAS=0) |
| Line 7 (3G10.0) | |
| k | Evolution of cohesion with concentration ($c(c) = c(0) + k.c$) |
| BETA0 | First parameter of chemo-elastic expansion coefficient BETA |
| F0 | Second parameter of chemo-elastic expansion coefficient BETA |
Stresses
Number of stresses
6 for 3D state
4 for the other cases
Meaning
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
For the 3-D state:
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{zz}$ |
| SIG(4) | $\sigma_{xy}$ |
| SIG(5) | $\sigma_{xz}$ |
| SIG(6) | $\sigma_{yz}$ |
For the other cases:
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{xy}$ |
| SIG(4) | $\sigma_{zz}$ |
State variables
Number of state variables
= 36 for 2D plane strain analysis with bifurcation criterion (ICBIF=1)
= 24 in all the other cases
List of state variables
| Q(1) | =1 : Plane strain state |
| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical state | |
| Q(2) | Actualised specific mass |
| Q(3) | = 0 : Current state is elastic |
| = 1 : Current state is elasto-plastic (Friction mechanism) | |
| = 2 : Current state is elasto-plastic (Pore collapse mechanism) | |
| = 3 : Current state is elasto-plastic (Traction mechanism) | |
| = 4 : Current state is elasto-plastic (Friction + pore mechanisms) | |
| = 5 : Current state is elasto-plastic (Friction + traction mechanisms) | |
| Q(4) | Plastic work per unit volume ($W^p$) |
| Q(5) | Actualised value of porosity |
| Q(6) | Equivalent strain n°1 : $\varepsilon_{eq1}=\int\Delta\dot{\varepsilon}_{eq}\;\Delta t$ |
| Q(7) | Updated value of pre-consolidation pressure $p_c$ |
| Q(8) | Equivalent strain indicator n°1 (Villote n°1) : $\alpha_1=\frac{\Delta\dot{\varepsilon}_{eq}\;\Delta t}{\varepsilon_{eq1}}$ |
| Q(9) | X deformation |
| Q(10) | Y deformation |
| Q(11) | Z deformation |
| Q(12) | XY deformation |
| Q(13) | Volumetric strain |
| Q(14) | Deviatoric strain |
| Q(15) | Actualised value of cohesion |
| Q(16) | Actualised value of frictional angle in compression path ($\phi_C$) |
| Q(17) | Actualised value of frictional angle in extension path ($\phi_E$) |
| Q(18) | Apex criterion |
| Q(19) | Actualised value of BETA |
| Q(20) | Actualised value of C0 (NOT USED AT PRESENT) |
| Q(21) | Updated value of pre-consolidation pressure at zero concentration $p_c^*$ |
| Q(22) | Number of sub-intervals used for the integration |
| Q(23) | Number of iteration used for the integration |
| Q(24) | Memory of localisation calculated during the re-meshing |
| Q(25)$\rightarrow$Q(36) | Reserved for bifurcation |
Hardening forms
ITYLA=2 : Volumetric strain hardening : \[dp_0=-ECRO\;p_0\;\varepsilon_v^p\] where the sign is dependent on the consolidation stress. Softening is possible.
Elastic forms
IELA = 0 : Linear elasticity
| E_PAR1 | E : Young's Elastic modulus |
| E_PAR2 | ANU : Poisson's ratio |
| E_PAR3 | Not used |
| E_PAR4 | Not used |
| HARD | ECRO : Hardening parameter |
IELA = 1 : Non Linear elasticity
| E_PAR1 | KAPPA : Elastic slope in oedometer path |
| E_PAR2 | ANU : Poisson's ratio |
| E_PAR3 | Not used |
| E_PAR4 | Not used |
| HARD | LAMBDA : Plastic slope in oedometer path |
\[ECRO=\frac{1+e_0}{\lambda-\kappa}\]
IELA = 2 : Non Linear elasticity
|E_PAR1| KAPPA : Elastic slope in oedometer path |
| E_PAR2 | G0 : Shear modulus |
| E_PAR3 | Not used |
| E_PAR4 | Not used |
| HARD | LAMBDA : Plastic slope in oedometer path |
\[ECRO=\frac{1+e_0}{\lambda-\kappa}\]
IELA = 3 : Non Linear elasticity
| E_PAR1 | KAPPA : Elastic slope in oedometer path |
| E_PAR2 | K0 : Minimum value of the bulk modulus |
| E_PAR3 | G0 : Shear modulus |
| E_PAR4 | ALPHA2 |
| HARD | LAMBDA : Plastic slope in oedometer path |
\[ECRO=\frac{1+e_0}{\lambda-\kappa}\]
IELA = 4 : Non Linear elasticity
|E_PAR1| K0: Minimum value of the bulk modulus |
| E_PAR2 | n : n parameter |
| E_PAR3 | G0 : Shear modulus |
| E_PAR4 | Patm : Atmospheric pressure |
| HARD |
\[ECRO = HARD\]
IELA = 5 : Non Linear elasticity
|E_PAR1| $\nu$ : Poisson’s ratio |
| E_PAR2 | n : n parameter |
| E_PAR3 | G0 : Shear modulus |
| E_PAR4 | Patm : Atmospheric pressure |
| HARD |
\[ECRO = HARD\]
IPCONS parameters
IPCONS = 0 : \[p_0 = PCONS0\]
IPCONS = 1 : \[p_0=\sigma_v\;OCR\]
IPCONS = 2 : \[p_0=p_0(\sigma,cohesion,\phi)\;OCR\] where \[p_0(\sigma,cohesion,\phi) = \left[\frac{-II_{\hat{\sigma}}^2}{m^2\left(I_{\sigma}-\frac{3c}{\tan\phi}\right)}-I_{\sigma}\right]/3\]
laws/epchemsol.txt · Last modified: 2020/08/25 15:46 (external edit)
