====== ACMEG ======

===== Description =====

Elasto-plastic constitutive law for saturated soils under non-isothermal conditions with two plastic mechanisms.\\

It can take into account :
  - linear or non-linear thermo-elasticity
  - the progressive plasticity inside the yield limit
  - the elasto-plasticity and thermo-plasticity
  - the critical state concept
  - the cyclic behaviour through the isotropic plastic mechanism
  - The suction effect on the evolution of pre-consolidation pressure (LC)\\

This constitutive model for unsaturated soil is developed based on the generalized effective stress framework (Bishop’s effective stress). So, if unsaturated states are considered (ISUC=1), the Bishop’s effective stress must be used (ISOL=7). Moreover, this mechanical constitutive model may be coupled with retention law 17 or 18 in [[laws:wavat|WAVAT]] (ISRW=17 or 18).

==== The model ====

This law is used for mechanical analysis of elasto-plastic saturated and unsaturated porous media undergoing large strains under non-isothermal conditions with possible cyclic isotropic loadings.  

==== Files ====

Prepro: LACMEG.F \\
Lagamine: PIL_ACMEG2D.F, PIL_ACMEG3D.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| 599|
|COMMNT| Any comment (up to 60 characters) that will be reproduced on the output listing|

==== Integer parameters ====

^ Line 1 (3I5) ^^
|NINTV| Number of sub-steps used to integrate numerically the constitutive equation in a time step |
|:::| = 0 : Number of sub-steps is based on the norm of the deformation increment and on DIV |
|ISOL| = 0 : Use of total stresses in the constitutive law |
|:::|≠ 0 : Use of effective stresses or independent stress variables in the constitutive law (See [[appendices:a8|appendix 8]]) |
|ITHERMO| = 0 : Isothermal computation, the five real parameters related to thermal effect will not be taken into account |
|:::| = 1 : Non-isothermal computation, a THM analyse must be done |
|:::| = 2 : Non-isothermal analyses with a constant volumetric thermal dilatation coefficient |
|ISUC| = 0 : Saturated computation, the last two real parameters will not be taken into account |
|:::| = 1 : Unsaturated computation, the Bishop’s effective stress must be used (ISOL=7) |
|NUMRET| $\in$ [0,18] : Number of the retention curve used in the WAVAT diffusive law |

==== Real parameters ====

^ Line 1 (7G10.0) ^^
|XKREF| Bulk modulus at reference pressure (PREF) |
|XGREF| Shear modulus at reference pressure (PREF) |
|PREF| Reference pressure for which the elastic modulus are defined |
|XN| Elastic exposant |
|PHI| Friction angle at critical state |
|BETA| Beta coefficient related to the slope of the consolidation line |
|ALPHA| Material parameter to enable a non-associated flow rule |
^ Line 2 (5G10.0) ^^
|A| Material parameter defining the evolution of the degree of mobilisation of the deviatoric mechanism |
|B| Material parameter defining the shape of the deviatoric yield limit |
|C| Material parameter defining the evolution of the degree of mobilisation of the isotropic mechanism |
|D| Distance between critical state line and the consolidation line in a logarithmic scale (pre-consolidation pressure = critical pressure * D) |
|PCI| Initial critical pressure |
^ Line 3 (4G10.0) ^^
|RAYELAD| Ratio between the extreme deviatoric yield limit and the initial deviatoric elastic domain |
|RAYELAI| Ratio between the extreme isotropic yield limit and the initial isotropic elastic domain |
|DIV| Size of sub-steps for computation of NINTV (if NINTV=0; Default value=5.D-3) |
|RHOS| Density of solid phase |
^ Line 4 (5G10.0) ^^
|TDILAS| Coefficient of thermal dilatation of the solid skeleton |
|XNTEM| Thermo-elastic exponent |
|DEV| Parameter for the evolution of the friction angle with temperature |
|GAMAT| Parameter for the evolution of the pre-consolidation pressure with temperature |
|TEMP0| Temperature for which the pre-consolidation pressure is defined |
^ Line 5 (2G10.0) ^^
|GAMAS| Parameter for the evolution of the pre-consolidation pressure with suction |
|OMEGA| Parameter for the evolution of the plastic compressibility with suction |
^ Line 6 (7G10.0) ^^
|ALPHABIO| Coefficient of biological dilatation of the solid skeleton |
|AKDMKG| (kd-kg) coefficient for the variation of porosity with concentration |
|AKHI| Multiplier factor for the concentration effect (bio + precipitation) |
|AKDM| Coefficient of linear attachement |
|OMEGAC| Effect of concentration on the plastic compressibility |
|GAMAC| Parameter for the evolution of the pre-consolidation pressure with concentration |
|CMIN| Minimal concentration to modify the pre-consolidation pressure |
^ Line 7 (1G10.0) ^^
|GC| Parameter for the evolution of the friction angle with concentration |

===== Stresses =====

==== Number of stresses ====

6 for 3D analysis \\ 4 for 2D plane strain and axisymmetric analysis

==== 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)|$\sigma_{xy}$|
|SIG(4)|$\sigma_{zz}$|
|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 ====

20

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

|Q(1)| Element thickness |
|:::| = 1 : Plane strain state |    
|:::|=	circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical state |
|:::| = 0 : 3D state |
|Q(2$\rightarrow$7)| Total strains |
|Q(2)| EPSxx |
|Q(3)| EPSyy |
|Q(4)| EPSzz |
|Q(5)| EPSxy |
|Q(6)| EPSxz (= 0 in plane strains and axisymmetric analyses) |
|Q(7)| EPSyz (= 0 in plane strains and axisymmetric analyses) |
|Q(8)| RAY(1) = Radius of the deviatoric mechanism |
|Q(9)| RAY(2) = Radius of the isotropic mechanism |
|Q(10)| IPEL(1) = Activity of the deviatoric mechanism |
|:::| = 1 : The deviatoric mechanism is active |
|:::| = -1 : The deviatoric mechanism is non-active |
|Q(11)| IPEL(2) = Activity of the isotropic mechanism |
|:::| = 1 : The isotropic mechanism is active |
|:::| = -1 : The isotropic mechanism is non-active |
|Q(12)| EPSVP = Volumetric plastic strain |
|Q(13)| PRECONS = Pre-consolidation pressure |
|Q(14)| LAMDA(1) = Plastic multiplier of the deviatoric mechanisms |
|Q(15)| LAMDA(2) = Plastic multiplier of the isotropic mechanisms |
|Q(16)| RHO = Density of the solid phase |
|Q(17)| Q = Deviatoric stress |
|Q(18)| TEMP = Temperature |
|Q(19)| SUCTION = Suction |
|Q(20)| PC = Critical pressure |