====== PREVOST ======

===== Description =====

Nested surface model.

==== The model ====

This law is used for mechanical analysis of the cyclic behaviour of soils, with or without cohesion.

==== Files ====

Prepro: LPREVO.F \\
Lagamine: PREVOST.F

===== Availability =====

|Plane stress state| NO |
|Plane strain state| YES |
|Axisymmetric state| YES |
|3D state| YES |
|Generalized plane state| NO |

===== Input file =====

==== Parameters defining the type of constitutive law ====

^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 612|
|COMMNT| Any comment (up to 60 characters) that will be reproduced on the output listing|

==== Integer parameters ====

^ Line 1 (6I5) ^^
|NINTV| = 0 : by default |
|ISOL| = 0 : Use of total stresses in the constitutive law |
|:::| $\neq$ 0 : Use of effective stresses in the constitutive law (See annex 7) |
|KRES| Resolution method (=1, 2 is not available any more) |
|ILODEF| Not used any more |
|ILODEG| Not used any more |
|ISURF| Surface type and hardening direction |
|:::| = 1 : Von Mises shape |
|:::| = 2 : Drucker Prager shape and Mroz hardening rule |
|:::| = 3 : Drucker Prager shape and Prager hardening rule |
|KMETH| = 2 : Actualised vgrad method |
|:::| = 3 : Mean vgrad method (default) |

==== Real parameters ====

^ Line 1 (5G10.0) ^^
|E| YOUNG's elastic modulus |
|ANU| POISSON's ratio |
|RHO| Specific mass |
|NSURF| Number of nested surfaces |
|DIV| DIV parameter |
^ Line 2 (5G10.0) ^^
|ACOH|$p'_0$ : Cohesion parameter (see Cerfontaine’s thesis) |
|IPVOL| = 0 : Basic volumetric hardening direction (P") (default) |
|:::| = 1 : Modified hardening direction |
|ETA1| First parameter of P" |
|ETA2| Second parameter of P" |
|ETA3| Third parameter of P" |
^ Line 3 (5G10.0) ^^
|ANMAT| $p$-dependency of the stiffness, exponent $n$ |
|PREF| Reference pressure for the p-dependency |
|FMIN| Minimum pressure for the p-dependency |
|ARRET1| First criterion of the local iterative process (variation/relative residual) |
|ARRET2| Second criterion of the local iterative process (absolute residual) |
**If IANA ≠ 4 (2D state)**
^ Line 4 (6G10.0) - Repeated NSURF times ^^
|AH| Plastic modulus associated to surface i |
|AM| Radius associated to surface i |
|ALPHA(1)| Component of the backstress tensor ($\alpha_{11}$) |
|ALPHA(2)| Component of the backstress tensor ($\alpha_{22}$) |
|ALPHA(3)| Component of the backstress tensor ($\alpha_{33}$) |
|ALPHA(4)| Component of the backstress tensor ($\alpha_{12}$) |

**Else if IANA = 4 (3D state)**
^ Line 4 (8G10.0) - repeated NSURF times^^
|AH| Plastic modulus associated to surface i |
|AM| Radius associated to surface i |
|ALPHA(1)| Component of the backstress tensor ($\alpha_{11}$) |
|ALPHA(2)| Component of the backstress tensor ($\alpha_{22}$) |
|ALPHA(3)| Component of the backstress tensor ($\alpha_{33}$) |
|ALPHA(4)| Component of the backstress tensor ($\alpha_{12}$) |
|ALPHA(5)| Component of the backstress tensor ($\alpha_{13}$) |
|ALPHA(6)| Component of the backstress tensor ($\alpha_{23}$) |

===== 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 ====

7

==== List of state variables ====

|Q(1)| Element thickness ($t$) in plane stress state |
|:::| = 1 : Plane strain state |
|:::| Circumferential strain rate ($\varepsilon_r$) in axisymmetrical state |
|:::| = 0 : 3D state |
|:::| Element thickness ($t$) in generalized plane state |
|Q(2)| Nothing |
|Q(3)| IYIELD : Active surface |
|Q(4)| ALIQU : Liquefaction indicator |
|:::| = 1 if liquefaction |
|:::| = 0 otherwise |
|Q(5)| TESTQM : $\rvert\rvert Q'_{n+1}\rvert\rvert$ |
|Q(6)| VOLUM : Volumetric deformation |
|Q(7)| DGAMMA |
|Q(8)| $\varepsilon_{xx}$ |
|Q(9)| $\varepsilon_{yy}$ |
|Q(10)| $\varepsilon_{zz}$ |
|Q(11)| $\varepsilon_{xy}$ |
|Q(12)| $\varepsilon_{xz}$ (if 3D) |
|Q(13)| $\varepsilon_{yz}$ (if 3D) |
|Q(14)| Previous time step |
|Q(15)| $\eta=\frac{q}{p'}$ |
|Q(16:)| AH(i) : Does not change but might |
|Q(17:)| AM(i) : Does not change but might |
|Q(18:)| ALPHA(i,1) |
|Q(19:)| ALPHA(i,2) |
|Q(20:)| ALPHA(i,3) |
|Q(21:)| ALPHA(i,4) |
|Q(22:)| ALPHA(i,5) if 3D |
|Q(23:)| ALPHA(i,6) if 3D |