Γ-convergence for a fault model with slip-weakening friction and periodic barriers
We consider a three-dimensional elastic body with a plane fault under a slip-weakening friction. The fault has e-periodically distributed holes, called (small-scale) barriers. This problem arises in the modeling of the earthquake nucleation on a large-scale fault. In each e-square of the e-lattice on the fault plane, the friction contact is considered outside an open set T∈ (small-scale barrier) of size r∈ 0, then the fault behaves as a fault under a slip-dependent friction. The slip weakening rate of the equivalent fault is smaller than the undisturbed fault. Since the limit slip-weakening rate may be negative, a slip-hardening effect can also be expected. iii) if the barriers are too small (i.e. c = 0), then the presence of the barriers does not affect the friction law on the limit fault.