Constitutive law for layered rocks at constant temperature
This law is only used for elasto‑plastic constitutive law for mechanical analysis of layered rocks, with only one family of parallel joints. Rocks are elastic and joints have a COULOMB rigid plastic behaviour.
Prepro: LROCK.F
Lagamine: ELP1.F (2D), ELP3DT.F (3D)
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | NO |
| 3D state | YES (?) |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 10 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| Line 1 (I5) | |
|---|---|
| NINTV | number of sub‑steps used to integrate numerically the constitutive equation in a time step. |
| Line 1 (6G10.0) | |
|---|---|
| E | Young's elastic modulus |
| ANU | Poisson's ratio |
| CO | material cohesion between layers |
| FI | friction angle (in degrees) between layers |
| ST | stratigraphy angle (in degrees), that is the angle of the layers with respect to an horizontal plane |
| PSI | dilatancy angle (in degrees) |
= 6 for the 3-D state
= 4 for the other cases.
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) | $\sigma_{zz}$ |
2
| Q(1) | = element thickness (t) in plane stress state |
| = 1 in plane strain state | |
| = circumferential strain rate ($\dot{\varepsilon}_\theta$) in axisymmetrical state | |
| = 0 in 3‑D state | |
| = element thickness (t) in generalized plane state. | |
| Q(2) | = 0 if the current state is elastic |
| = 1 if the current state in elasto‑plastic (i.e., sliding between joints has occurred) |