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laws:cloe
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CLOE
Description
Rate type constitutive law for sands.
The model
Rate type law (incremental non-linear) for mechanical analysis of soil like media, and especially of sands. Two tangent stiffness matrix, one obtained by directional linearisation and the other by numerical perturbations.
Files
Prepro: LPAR_CLOES.F
Lagamine: PIL_CLOES.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 | 75 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (4I5) | |
|---|---|
| NINTV | Number of sub steps used to integrate numerically the constitutive equation in a time step |
| = 0 : Number automatically computed (Default value : PNSIV = $10^{-4}$) | |
| < 0 : Number of sub steps based on PNSIV (given in PARAM (28 or 18) following ITYDO) | |
| ISOL | ≠ 0 : Use of effective stresses in constitutive law (See appendix 8) |
| = 0 : Use of total stresses in constitutive law | |
| ICLOC | = 0 : Nothing |
| = 1 : Rice's criterion | |
| = 2 : Vilotte's indicator | |
| = 4 : Future indicator 1 | |
| = 8 : Future indicator 2 | |
| = 3 : Rice's criterion + Vilotte's indicator | |
| … etc | |
| ITYDO | = 1 : Geotechnical type data |
| = 2 or 0 : Internal type data at CLoE | |
Real parameters
According to the prepro file, 3 lines of characters are read before the real parameters.
Geotechnical type data (ITYDO = 1)
No format is specified, parameters can all be written on the same line and must be separated by a blank space.
| Limit area | |
|---|---|
| P(1) | Friction angle in compression |
| P(2) | Friction angle in extension |
| P(3) | Van Eekelen exponent |
| P(4) | Cohesion |
| Triaxial compression | |
| P(5) | Stress ratio at the characteristic point (yrc) |
| P(6) | Axial strain at the characteristic point (xca) |
| P(7) | Volumetric strain at the characteristic point (yca) |
| P(8) | Final slope in compression (pfc) |
| Triaxial extension | |
| P(9) | Maximum volumetric contracting strain (ye) |
| P(10) | Axial strain at no volumetric strain (xd) |
| P(11) | Constant volumetric strain at epsilon (xm2) |
| P(12) | At epsilon (xc) |
| P(13) | Volumetric strain's final slope (pfe) |
| Isotropic state | |
| P(14) | Volumic modulus in semi-logarithmic axes (lc) |
| P(15) | Pseudo-isotropic modulus in compression (psimco) |
| P(16) | Pseudo-isotropic modulus in extension (psimex) |
| P(17) | Variation's parameter of the shear modulus in compression (omcisco) |
| P(18) | Variation's parameter of the shear modulus in extension (omcisex) |
| P(19) | Shear term OMCIS3: value of OMCIS ($\alpha_2$) |
| P(20) | Shear term OMCIS4: $\alpha_2$ = Corresponding Lode angle |
| P(21) | Shear term OMCIS5: value of OMCIS ($\alpha_3$) |
| P(22) | Shear term OMCIS6: $\alpha_3$ = Corresponding Lode angle |
| P(23) | Shear term OMCIS7: value of OMCIS ($\alpha_4$) |
| P(24) | Shear term OMCIS8: $\alpha_4$ = Corresponding Lode angle |
| P(25) | Temporal integration parameter (div) |
| P(26) | = RHO: Soil density |
Internal type data (ITYDO = 2 or 0)
No format is specified, parameters must be separated by a blank space.
| Line 1 (*) | |
|---|---|
| P(1) | Coefficient AHC of the stress hyperbola in compression |
| P(2) | Coefficient CHC of the stress hyperbola in compression |
| P(3) | Coefficient APC of the strain hyperbola in compression |
| P(4) | Coefficient BPC of the strain hyperbola in compression |
| P(5) | Final slope PFC of strains in compression |
| P(6) | Abscissa XPC of the straight parabola transition in compression |
| P(7) | Coefficient AHE of the stress hyperbola in extension |
| P(8) | Coefficient CHE of the stress hyperbola in extension |
| P(9) | Coefficient A1 of the deformation cubicle in extension |
| P(10) | Coefficient B1 of the deformation cubicle in extension |
| P(11) | Coefficient C1 of the deformation cubicle in extension |
| P(12) | Abscissa XM2 of the 2nd maximum of strains in extension |
| P(13) | Abscissa XC of the end of the 2nd section of strains in extension |
| P(14) | Coefficient AB of the quadratic equation |
| P(15) | Coefficient CB of the quadratic equation |
| P(16) | Abscissa XT2 of the connection point n°3 |
| P(17) | Final slope of the quadratic equation PFE |
| P(18) | Initial isotropic modulus LAMBDC |
| P(19) | Compression's pseudo-isotropic modulus LAMLCO |
| P(20) | Extension's pseudo-isotropic modulus LAMLEX |
| P(21) | Slope of the ratio of strain rates and stresses in compression POINCO |
| P(22) | Slope of the ratio of strain rates and stresses in extension PSIMEX |
| P(23) | Coefficient of the boundary area 1 ASL |
| P(24) | Coefficient of the boundary area 2 BSL |
| P(25) | Exponent of the boundary area's equation NSL |
| P(26) | Cohesion CCOTF1 |
| P(27) | Shear term OMCIS1 : value of OMCIS ($\alpha_1$) |
| P(28) | Shear term OMCIS2 : $\alpha_1$ = Corresponding Lode angle |
| P(29) | Shear term OMCIS3 : value of OMCIS ($\alpha_2$) |
| P(30) | Shear term OMCIS4 : $\alpha_2$ = Corresponding Lode angle |
| P(31) | Shear term OMCIS5 : value of OMCIS ($\alpha_3$) |
| P(32) | Shear term OMCIS6 : $\alpha_3$ = Corresponding Lode angle |
| P(33) | Shear term OMCIS7 : value of OMCIS ($\alpha_4$) |
| P(34) | Shear term OMCIS8 : $\alpha_4$ = Corresponding Lode angle |
| P(35) | Shear term OMCIS9 : value of OMCIS ($\alpha_5$) |
| P(36) | Shear term OMCIS10 : $\alpha_5$ = Corresponding Lode angle |
| P(37) | DIV : Size of the sub-steps for the computation of NINTV |
| Line 2 (*) | |
| P(38) | RHOS: Specific mass of grains |
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
34
List of state variables
| Q(1) | = 1 : Plane strain state |
| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical state | |
| = 0 : 3D state | |
| Q(2) | Void ratio $e$ |
| Q(3) | Direction of the shear band (angle between the normal to the band and the first principal stress in radian) (first in the sense of the CLoE law module) for the first possible solution |
| Q(4) | Expansion angle (in radian) (angle between the characteristic vector $g$ and the first principal stress) for the first possible solution |
| Q(5) | Direction of the shear band (angle between the normal to the band and the first principal stress in radians) (first in the meaning of CLoE law module) for the second possible solution |
| Q(6) | Expansion angle (in radian) (angle between the characteristic vector $g$ and the first principal stress) for the second possible solution |
| Q(7) | Direction of the shear band (first in the sense of CLoE law module) for the first possible solution |
| Q(8) | Expansion angle in degree (angle between the characteristic vector $g$ and the first principal stress) for the first possible solution |
| Q(9) | Direction of the shear band (angle between the normal to the band and the first principal stress in degree) (first in the sense of the CLoE law module) for the second possible solution |
| Q(10) | Angle of expansion in degree (angle between the characteristic vector $g$ and the first principal stress) for the second possible solution |
| Q(11) | Angle between the Ox axis and the direction of the first principal stress |
| Q(12) | s: Band expansion index for the first solution |
| Q(13) | s: Band expansion index for the second solution |
| Q(14) | |
| Q(15) | |
| Q(16) | |
| Q(17) | ICRIT: corresponds to the number of solution |
| = 11 : theta = infinite | |
| = 12 : theta = 0 | |
| = 13 : General case | |
| = 20 + JROOT : Criterion of the standard (JROOT = number of real roots) | |
| Q(18) | |
| Q(19) | |
| Q(20) | |
| Q(21) | Reduced deviator (Q bar) |
| Q(22) | Sum of $\dot{\varepsilon}_v\;dt$ |
| Q(23) | Pore pressure (undrained analysis) |
| Q(24) | Vilotte indicator |
| Q(25) | Corresponding cumulative $\varepsilon_{eq}$ |
| Q(26) | Vilotte indicator n°2 |
| Q(27) | Corresponding cumulative $\varepsilon_{eq}$ |
| Q(28) | Vilotte indicator n°3 |
| Q(29) | Corresponding cumulative $\varepsilon_{eq}$ |
| Q(30) | Vilotte indicator n°4 |
| Q(31) | Corresponding cumulative $\varepsilon_{eq}$ |
| Q(32) | Actualised RHO-s |
| Q(33) | Major principal stress |
| Q(34) | Minor principal stress |
laws/cloe.txt · Last modified: 2020/08/25 15:46 (external edit)
