Static Mohr-Coulomb

Mohr-Coulomb failure criterion with static (constant) friction angle [Franceschini et al.,2016].

Theory

At the Interface Elmenet (IE), the acting strength can be decomposed into two components, \(\sigma_N\) and \(\tau_S\), orineted normally and tangetially to the contact surface, respectively. the Mohr-Coulomb failure criterion prescribes that the continuity of the displacements across the IE is preserved if:

\(\tau_S <= \tau_L = c - \sigma_N tan(\phi)\)

where \(\phi\) and \(c\) are the fault friction angle and cohesion, respectively, and \(\tau_L\) is the limit shear strength. A \(\sigma_N < 0\) means compression and \(\sigma_N\) cannot be positive. When \(\tau_S = \tau_L\) the shear stress can no longer increase and a relative surface displacement along the IE plane,\(\boldsymbol{u}_r\), can occur. An opening, i.e. a relative displacement in the direction normal to the IE plane can occur if \(\sigma_N = 0\) (in this case also \(\tau_S = \tau_L = 0\)).

The Mohr-Coulmob criterion gives no information about the direction of the shear vector \(\boldsymbol{\tau}_L\). To this aim, is used the “Principle of Maximum Plastic Dissipation” [Simo and Hughes, 2000] (MPD):

\(\boldsymbol{\tau}_L = \tau_L \frac{\boldsymbol{u}_r}{||\boldsymbol{u}_r||_2}\)

When the relative displacement is smaller then a given tolerance \(||\boldsymbol{u}_r||_2 < tol_{MPD}\), the direction are computed according to the elastic tangential stress \(\boldsymbol{\tau}_e\) at the failure (\(||\boldsymbol{\tau}_e||_2 >= \tau_L\)):

\(\boldsymbol{\tau}_L = \tau_L \frac{\boldsymbol{\tau}_e}{||\boldsymbol{\tau}_e||_2}\)

Initialization

The initialization can be done using the tab_file or the restart file.

Input Notes

In the input file interf_materials must be set:

• The material type IEMAT_TYPE = 1.

• The integer parameters IEMAT_IPAR[NI_IEMAT_TYPE] with NI_IEMAT_TYPE = 3:

• The real parameters IEMAT_RPAR[NR_IEMAT_TYPE] with NR_IEMAT_TYPE = 6: