Cap model : elasto-plastic constitutive law for solid elements at constant temperature with thermoplasticity (A thermomechanical model of clays, CUI et al., 2000).
This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.
Prepro: LTSOIL.F
Lagamine: TSOIL2EA.F, TSOIL3D.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 | 169 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| Line 1 (14I5) | |
|---|---|
| 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=$1.10^{-5}$ | |
| 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 | |
| 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 | |
| ILY | = 0 : Evolution of the pre-consolidation pressure with temperature (ENPC, LY curve) \[p'_{cT} = p'_{c_0T_0}\exp(-\alpha_0\Delta T)\] |
| = 1 : Evolution of the pre)consolidation pressure with temperature (ACMEG-T) \[p'_{cT} = p'_{c_0T_0}\left[1-\gamma_T\log\left(\frac{T}{T_0}\right)\right]\] | |
| 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 PCONS0=0) |
| OCR | Over Consolidation Ratio (if PCONS0$\neq$0, see section 6.5) |
| AI1MIN | Minimum value of I$_{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 ITRACT$\neq$0) |
| Line 5 (4G10.0) | |
| POROS | Initial soil porosity ($n_0$) |
| 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) | |
| ALPHA2 | Volumetric thermal expansion coefficient of the solid |
| ALPHA0 | Shape parameter for LY curve (ILY=0 : formulation ENPC, for ACMEG-T see below) |
| BETA0 | Hardening parameter for TY curve (1/Pa) |
| TC | Critical temperature (TY curve) (°K) |
| T0 | Initial temperature (TY curve) (°K) \[TY \equiv T_{cT} - \left[(T_c-T_0)\exp(-\beta p')+T_0\right] = 0\] |
| Line 7 (4G10.0) | |
| C1 | Parameter for HC curve |
| C2 | Parameter for HC curve |
| A parameter | Parameter for the definition of the thermal volumetric plastic strain |
| GAMA | Shape parameter for LY curve according ACMEG-T (ILY = 1) \[HC\equiv p'-c_1 p'_{c0}\exp(c_2\Delta T) = 0\] |
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 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) | $\sigma_{zz}$ |
36 for 2D plane strain analysis with bifurcation criterion (ICBIF=1)
24 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°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) : $\alpha_1 = \dfrac{\Delta\dot{\varepsilon}_{eq}\;\Delta t}{\varepsilon_{eq1}}$ |
| 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 ALPHAP |
| Q(21) | Actualised value of temperature |
| Q(22) | ITESTALPHA : Variable for the calculation of ALPHAP |
| Q(23) | Actualised value of the pre-consolidation pressure as a function of the temperature (Pa) |
| Q(24) | Number of sub-intervals used for the integration |
| Q(25) | KSUMMITER |
| Q(26) | K (Pa) |
| Q(27) | G (Pa) |
| Q(28)$\rightarrow$Q(39) | Reserved for bifurcation |
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 = 2 : $p_0$ = $p_0$($\sigma$, cohesion, $\phi$) . OCR
Where : $p_0$($\sigma$, cohesion, $\phi$) = $\left[\dfrac{-II_{\hat{\sigma}}^2}{m^2\left(I_{\sigma}-\frac{3c}{\tan\phi}\right)}-I_{\sigma}\right]/3$