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laws:epsucsol
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EP-SUCSOL
Description
Cap model : elasto-plastic constitutive law for solid elements at constant temperature with effect of suction.
The model
This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.
Files
Prepro: LSUC.F
Lagamine: SUC2EA.F, SUC3D.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 | 90 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (11I5) | |
|---|---|
| NINTV | $\geq 0$ : 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 Appendix 8) | |
| IELA | = 0 : Linear elasticity |
| > 0 : Non-linear elasticity | |
| IELAS | = 0 : Constant KAPPAS |
| > 0 : Variable KAPPAS | |
| 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 |
| <> 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 |
| <> 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 Ration (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 (iff 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 TRACT<>0) |
| Line 5 (3G10.0) | |
| POROS | Initial soil porosity ($n_0$) |
| RHO | Specific mass |
| DIV | Parameter for the computation of NINTV in the law (for NINTV=0 only) |
| Line 6 (7G10.0) | |
| S0 | Yield limit in term of suction (SI curve) |
| PCrel | Relative Reference pressure PCONS0/PC for the definition of the LC curve |
| RRATIO | |
| BETA | |
| LAMBDA-S | Plastic suction coefficient |
| KAPPA-S | Elastic suction coefficient |
| PATM | Atmospheric pressure |
| Line 7 (3G10.0) | |
| k | Evolution of cohesion with suction ($c(s) = c(0)+k.s$) |
| AKAPPAS1 | First parameter of KAPPAS formulation |
| AKAPPAS2 | Second parameter of KAPPAS formulation |
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
39 for 2D plane strain analysis with bifurcation criterion (ICBIF=1)
28 in all the other cases
List of state variables
| Q(1) | = 1 in plane strain state |
| = circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical state | |
| Q(2) | actualised specific mass |
| Q(3) | = 0 if the current state is elastic |
| = 1 if the current state is elasto-plastic (Friction mechanism) | |
| = 2 if the current state is elasto-plastic (Pore collapse mechanism) | |
| = 3 if the current state is elasto-plastic (Traction mechanism) | |
| = 4 if the current state is elasto-plastic (Friction + pore mechanisms) | |
| = 5 if the current state is elasto-plastic (Friction + traction mechanisms) | |
| Q(4) | Plastic work per unite 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 $p_0$ |
| 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 ALAMBDAS |
| Q(20) | Actualised value of AKAPPAS |
| Q(21) | Actualised value of $S_0$ |
| Q(22) | Absolute value of reference pressure $P_C$ |
| Q(23) | Number of sub-intervals used for the integration |
| Q(24) | Number of iterations used for the integration |
| Q(25) | Cubic modulus |
| Q(26) | Shear modulus |
| Q(27) | Memory of localisation calculated during the re-meshing |
| Q(28)$\rightarrow$Q(39) | Reserved for bifurcation |
Hardening forms
| ITYLA = 2 | Volumetric strain hardening |
| $dp_0 = -ECRO\;p_0\varepsilon_v^p$ | |
| Sign 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 $$ ECRO = \frac{1+e_0}{\lambda-\kappa} $$ | |
| 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 | |
| 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 | |
| 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 | |
| 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 : Hardening parameter $$ ECRO = \frac{1+e_0}{\lambda-\kappa} $$ | |
| IELA = 5 | Non-linear elasticity |
| E_PAR1 = $\nu$ (ANU ???) : Poisson's ratio | |
| E_PAR2 = n : $n$ parameter | |
| E_PAR3 = G0 : Shear modulus | |
| E_PAR4 = Patm : Atmospheric pressure | |
| HARD = ECRO : Hardening parameter $$ ECRO = \frac{1+e_0}{\lambda-\kappa} $$ |
IPCONS Parameters
| IPCONS = 0 | $p_0$ = PCONS0 |
| IPCONS = 1 | $p_0$ = $\sigma_v.$OCR |
| IPCONS = 2 | $p_0$ = $p_0(\sigma, \text{cohesion}, \phi).$OCR |
where $p_0(\sigma, \text{cohesion}, \phi) = \left[\frac{-II_{\sigma}^2}{m^2\left(I_{\sigma}-\frac{3c}{\tan\phi)}\right)}-I_{\sigma}\right]/3 $
laws/epsucsol.txt · Last modified: 2020/08/25 15:46 (external edit)
