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INTME2/INTME3
Description
Constitutive law for mechanical contact for interface elements (FAIL2B/FAIN2B/FAIF2B or FAIL3B/FAIN3B/FAIF3B).
The model
This law is similar to the Coulomb's Law in 2D/3D and is used in mechanical analysis of problems involving unilateral contact between two bodies. Coulomb dry friction law is used. The contact condition is enforced via a penalty method or augmented Lagrangian method according to ISTRA(4).
The fault behaviour can be expressed according to two formulations:
- Classical formulation (IFRAC = 0) : \[\Delta \sigma = K_p\;\Delta V\]
- Goodman formulation (IFRAC = 1) : \[\Delta\sigma = \frac{K_p}{\left(1+\frac{V}{D_0}\right)^{\gamma}}\Delta V \leftrightarrow V = D_0\left[\sqrt[1-\gamma]{\left(\frac{(1-\gamma)}{D_0\;K_n}\sigma'+1\right)}-1\right] \quad\text{and}\quad d-V=D_0\]
Thus:
- if contact pressure $\sigma'=0$ : Hydraulic aperture = $d = D_0$ and Fault closure = $V=0$
- if contact pressure $\sigma'=-\infty$ : Hydraulic aperture = $d = 0$ and Fault closure = $V = -D_0$ (negative value)
Files
Prepro: LINTME.F
Lagamine: INTME2.F, INTME3.F
Availability
| Plane stress state | YES |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | YES |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 86 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (6I5) | |
|---|---|
| ISOL | = 0 : use of total stresses in the constitutive law |
| $\neq$ 0 : use of effective stresses in the constitutive law. See Appendix 8 | |
| IFRAC | = 0 : Classical formulation of fault behaviour |
| = 1 : Goodman formulation of fault behaviour | |
| NINTV | Only in 3D : number of sub-steps used to integrate numerically the constitutive equation in a time step (useful only in dynamic) |
| INDIC | Only in 3D : 0 or 1 to define the outside pressure used in case of no contact (see “Use” paragraph) |
| IREDUC | = 1 : Phi-C reduction method |
| = 0 : nothing | |
| ITYPEL | = 0 : for DAIL3 element (Nsig_meca = 6) |
| $\neq$ 0 : for FAIN3 or FAIF3 element (Nsig_meca = 4) | |
Real parameters
| Line 1 (6G10.0) | |
|---|---|
| AKP | Penalty coefficient on the contact pressure $K_p$ |
| AKTAU | Penalty coefficient on the shear frictional stress $K_{\tau}$Â |
| PHI | Coulomb's friction coefficient $\tan\phi$ |
| B | Cohesion |
| TAUMAX | Maximum contact friction (only for 2D state) (default value = $10^{20}$) |
| PRESID | Residual pressure |
| Line 2 (3G10.0) | |
| GAMMA | Exponent value of Goodman formulation (useful if IFRAC = 1 ) |
| D0 | Maximal fault closure in absolute value for $\sigma'=-\infty$ (useful if IFRAC = 1) |
| RHO | Specific mass (useful if element is FAIF2 and IENTH = 1 in INTFL2 law) |
Stresses
Number of stresses
4 for both the 2-D and 3-D states
Meaning
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
For the 2-D state:
| SIG(1) | normal contact pressure (> 0 if contact and < 0 if no contact) |
| SIG(2) | tangent contact stress |
| SIG(3) | meaningless |
| SIG(4) | meaningless |
For the 3-D state:
| SIG(1) | normal contact pressure |
| SIG(2) | tangent contact stress in the $\xi$ direction |
| SIG(3) | tangent contact stress in the $\eta$ direction |
| SIG(4) | reduced deviatoric stress = $\frac{||\tau||}{p'}$ if $p' > 0$ |
The $\xi$ and $\eta$ correspond to the intrinsic co-ordinates of the contact element FAIL3.
State variables
Number of state variables
4 (+6 for 2D state, +4 for FAIL3, +2 for FAIN3/FAIF3B)
These are the 4 state variables related to the law, they are the first ones printed. After them, you find the state variables related to the contact geometry, 6 for the FAIL2B/FAIN2B/FAIF2B, 4 for the FAIL3B and 2 for FAIN3B/FAIF3B their meaning are explained in the element section.
List of state variables
| Q(1) | = 0 if the current state is elastic (no sliding) |
| = 1 if the current state is elastoplastic (sliding at contact) | |
| = -1 if no mechanical, nor thermal contact | |
| Q(2) | amount of mechanical energy dissipated per unit area, due to friction |
| Q(3) | Fault closure (V : < 0 for closed fracture, > 0 for opened fracture) (useful if IFRAC = 1) |
| Q(4) | Hydraulic aperture $d$ (>0) (useful if IFRAC = 1) |
For FAIL2B/FAIN2B/FAIF2B element :
| Q(5) | Number of foundation segment |
| Q(6) | Relative interpenetration distance $\Delta V = V-V_{ini}$ (<0 for compression cases and >0 for extension cases) |
| Q(7) | Jacobian |
| Q(8) | NOCO contact indicator given by CALFON subroutine |
| Q(9) | Relative tangential speed |
| Q(10) | Relative sliding |
For FAIL3 element :
| Q(5) | Number of foundation segment |
| Q(6) | Interpenetration distance $\lambda_c=\Delta V$ |
| Q(7) | Relative tangential speed n°1 |
| Q(8) | Relative tangential speed n°2 |
For FAIN3 element :
| Q(5) | Number of foundation segment |
| Q(6) | Interpenetration distance $\lambda_c=\Delta V$ |
