Cap model : elasto‑viscoplastic constitutive law for solid elements at constant temperature with effect of suction
This law is used for mechanical analysis of elasto‑viscoplastic isotropic porous media undergoing large strains.
Prepro: LVISU.F
Lagamine: VIS2EA.F
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | NO |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 41 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| Line 1 (12I5) | |
|---|---|
| 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 |
| ≠ 0 : use of effective stresses in the constitutive law. See annex 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 | |
| ILC | = 0: Barcelona LC curve |
| $\neq$ 0: Pasachalk LC curve | |
| 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 | Preconsolidation pressure (If IPCONS0=0) |
| OCR | Over Consolidation Ratio (If IPCONS0<>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 (psi 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 <>0 ) |
| Line 5 (4G10.0) | |
| POROS | Initial soil porosity ($n_o$) |
| RHO | Specific mass |
| DIV | Parameter for the computation of NINTV in the law (for NINTV=0 only) |
| BIOPT | Bifurcation computation parameter |
| 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 | Max soil stiffness |
| BETA | Beta soil stiffness parameter |
| 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 |
| Line 8 (3G10.0) | |
| Visco_parameters for Cap | |
| ALPHAC | Viscoplastic parameter for $\Phi_C = ( f_c /p())* * \alpha_c$ |
| OMEGA | Viscosity parameter for $\gamma_c$ |
| AIOT | Viscosity parameter for $\gamma_c$ |
| Line 9 (2G10.0) | |
| Visco_parameters for friction | |
| ALPHAD | parameter $\alpha_d$ for $\Phi_d = \left( \frac{f_d}{p_0} \right)^{\alpha_d}$ |
| A2D | parameter $\alpha_d$ for $\gamma_d = a_2 \gamma_c$ |
= 6 : for 3D state
= 4 : for the other cases.
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
For the other cases :
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{xy}$ |
| SIG(4) | $\sigma_{zz}$ |
= 40 : for 2D plane strain analysis with bifurcation criterion (ICBIF=1)
= 29 : in all the other cases
| 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 unit volume ($W^p$) |
| Q(5) | Actualised value of porosity |
| Q(6) | equivalent strain $n^o$1 $\varepsilon_{eq1} = \int \Delta \dot{\varepsilon}_{eq}\Delta t$ |
| Q(7) | Updated value of preconsolidation pressure $p_0$ |
| Q(8) | equivalent strain indicator $n^o 1$ (Villote $n^o 1$) $\alpha_1 = (\Delta\dot{\varepsilon}_{eq}\Delta t ) / \varepsilon_{eq1}$ |
| 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 compression 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) | PCONS0 |
| Q(24) | number of sub-intervals used for the integration |
| Q(25) | number of interation used for the integration |
| Q(26) | Cubic modulus |
| Q(27) | Shear modulus |
| Q(28) | OVERS |
| Q(29) → Q(40) | reserved for bifurcation |
ITYLA = 2 : Volumetric strain hardening
$dp_0$ = ECRO $p_0\varepsilon_v^p$
Sign depedent on the consolidation stress.
Softening is possible.
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 = 0 : $p_0 = PCONS0$
IPCONS = 1 : $p_0 = \sigma_v . OCR$
IPCONS = 0 : $p_0 = p_0(\sigma,\text{cohesion}, \phi) . OCR$
Where $p_0(\sigma,\text{cohesion},\phi) = \left[ \frac{-II_{\widehat{\sigma}}^2}{m^2(I_{\sigma}-\frac{3c}{tg\phi})} - I_{\sigma} \right] / 3$