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laws:eptsoil
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EP-TSOIL
Description
Cap model : elasto-plastic constitutive law for solid elements at constant temperature with thermoplasticity (A thermomechanical model of clays, CUI et al., 2000).
The model
This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.
Files
Prepro: LTSOIL.F
Lagamine: TSOIL2EA.F, TSOIL3D.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 | 169 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| 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) \[p'_{cT} = p'_{c_0T_0}\left[1-\gamma_T\log\left(\frac{T}{T_0}\right)\right]\] | |
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 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) \[HC\equiv p'-c_1 p'_{c0}\exp(c_2\Delta T) = 0\] |
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 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 |
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 parameter
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, $\phi$) = $\left[\dfrac{-II_{\hat{\sigma}}^2}{m^2\left(I_{\sigma}-\frac{3c}{\tan\phi}\right)}-I_{\sigma}\right]/3$
laws/eptsoil.txt · Last modified: 2020/08/25 15:46 (external edit)
