Constitutive models elastic media

Each block is modeled as linear, isotropic, homogeneous and elastic medium and subdivided with a mesh of constant-strain triangle finite-difference elements. Key factors affecting the hydraulic behaviour of fractures such as opening, closure, sliding and dilation of fractures are modeled by an elasto-perfectly plastic constitutive model of a fracture. A step-wise non-linear normal stress-normal closure relationship is adopted with a linear Mohr-Coulomb failure for shear (Figure 3). 

The equivalent force system of an earthquake depends on the constitutive law used to compute the model stress s,y in Eq. 2. This means that a fault in an anisotropic elastic medium has a different equivalent force system than it would if the medium were isotropic, and in particular that a shear fault in an anisotropic medium generally has a non-DC moment tensor, which can be determined, for example, from Eq. 11 (Vaviycuk 2005). Most rocks are anisotropic, because of layering on a scale smaller than seismic wavelengths, preferential orientation of crystals, and the presence of cracks and inclusirms, so most earthquakes are affected by anisotropy. 

---