Table of Contents
DAFA2
Description
Full law name : EVP-DAFALIAS-KALIAKIN
DAFALIAS-KALIAKIN elasto-visco-plastic constitutive law for isotropic cohesive soils.
The model
This law is used for mechanical analysis of elasto-visco-plastic isotropic porous media undergoing large strains according to DAFALIAS-KALIAKIN “bounding surface model”.
Use ISTRA(3) = -1 in the loading file.
Files
Prepro: LDAFA.F
Lagamine: INT2DA.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 | 89 |
| 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 |
| ISOL | = 0 : Use of total stresses in the constitutive law |
| $\neq$ 0 : Use of effective stresses in the constitutive law (See annex 8) | |
| ICBIF | = 0 : Nothing |
| = 1 : Compute the bifurcation criterion | |
| ISTRAIN | = 0 : Use of “CAUCHY” strains |
| = 1 : Use of natural strains | |
Real parameters
| Line 1 (7G10.0) | |
|---|---|
| $\lambda$ | Slope of the consolidation line in a plot of $e$ vs. $\ln(p)$ |
| $\kappa$ | Slope of the swell/recompression line in a plot of $e$ vs. $\ln(p)$ |
| $\phi_c$ | Frictional angle in triaxial compression path |
| $\phi_e$ | Frictional angle in triaxial extension path |
| G | Elastic shear modulus (if $\nu > 0$, G is useless in the simulation) |
| $\gamma$ | Without signification for the moment (= 0) |
| $I_l$ | Non-zero limiting value of $I$ and $I_0$ below which the relation between $I$ (or $I_0$) and void ratio changes continuously from logarithmic to linear (usually $I_l$ = $P_a$) |
| Line 2 (7G10.0) | |
| $P_a$ | Atmospheric pressure |
| $R_c$ | Parameter defining the shape of the bounding surface for ellipse 1 (corresponding to a state of triaxial compression, it may assume any value in the range $1.0\leq R\leq\infty$. Typical values : 2.00-3.00) |
| $A_c$ | Parameter defining the shape of the hyperbolic portion of the bounding surface (corresponding to a state of triaxial compression. In theory, $0$\leq$A_c<\infty$, experimentally : 0.02-0.2) |
| t | Parameter defining the shape of the ellipse 2 portion of the bounding surface ($0.05\leq t\leq 0.95$) |
| $R_e/R_c$ | Ratio of the values of the shape parameter associated with ellipse 1 in extension ($R_e$) and in compression ($R_c$) |
| $A_e/A_c$ | Ratio of the values of the shape parameter associated with hyperbola in extension ($A_e$) and in compression ($A_c$) |
| c | Projection center parameter ($0.0\leq c < 1.0$) |
| Line 3 (7G10.0) | |
| $S_p$ | Parameter controlling the size of elastic nucleus associated with plastic strains |
| $H_c$ | Primary hardening parameter $H$ in a state of triaxial compression (typical values: 5-50) |
| m | Secondary hardening parameters which applies to both extension and compression (m=0.02 is recommended) |
| $H_e/H_c$ | Ratio of the values of the primary hardening parameter $H$ in extension ($H_e$) and in compression ($H_c$) |
| s | Hardening parameter used only for the single ellipse version of the bounding surface (not available now) |
| w | Hardening parameter used only for the single ellipse version of the bounding surface (not available now) |
| $S_v$ | Parameter controlling the size of elastic nucleus associated with visco-plastic response |
| < 0 : The effect of viscosity will not be considered | |
| Line 4 (7G10.0) | |
| V | Visco-plastic parameter (typical values : $10^7-10^8$ kPa-min) |
| n | Visco-plastic parameter (typical values : 0.7-10) |
| $e_{in}$ | Initial void ratio |
| $\nu$ | Poisson's ratio (if $\nu$ < 0, G is specified explicitly) |
| $p_c$ | Initial size of the bounding surface ($p_c$ is the effective pre-consolidation pressure) |
| OCR | Over consolidation ratio (if OCR = 0 : we give $p_c$) |
| RHO | Specific mass |
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
22 (11 for axisymmetric state)
List of state variables
| Q(1) | Element thickness (t) in plane stress state |
| = 1 : Plane strain state | |
| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical state | |
| = 0 : 3D state | |
| Element thickness (t) in generalized plane state | |
| Q(2) | e : Void ratio |
| Q(3) | $I_0$ : Intersection of the bounding surface with the positive $I$-axis |
| Q(4) | $\varepsilon_{kk}$ : Accumulated volumetric strain |
| Q(5) | $I$ : First invariant of the effective stress (corresponding to the current state) |
| Q(6) | J : Square root of the second deviatoric stress invariant (corresponding to the current state) |
| Q(7) | An index to projection zone |
| = 1 : Indicates that the “image” state is on the ellipse 1 | |
| = 2 : Indicates that the “image” state is on the hyperbola | |
| = 3 : Indicates that the “image” state is on the ellipse 2 | |
| Q(8) | $\sin(3\alpha)$ where $\alpha$ is the “Lode” angle |
| Q(9) | b : Projection parameter (b$\geq$1, if b=1 the current state is on the bounding surface) |
| Q(10) | Sum of $\dot{\varepsilon}_V \;dt$ |
| Q(11) | Actualised specific mass |
| Q(12)$\rightarrow$Q(23) | Modulus for the analysis of bifurcation |
