Rheological and kinematical responses to flow of two-phase rocks

Numerical simulations have been performed to investigate the strain-dependent behaviour of rheological and kinematical responses to flow of two-phase rocks using the commercial finite-difference program FLAC2D. It was assumed that the two phases have Maxwell rheology. Plane strain and velocity boundary condition, which produces a simple shear deformation, were also assumed. Two types of geometries were considered: strong phase supported (SPS) and weak phase supported (WPS). We calculated strain-dependent variations of effective viscosity and partitioning of strain rate, vorticity and kinematic vorticity number during deformation in both SPS and WPS structure models.The results show that the strain-dependent behaviour is largely influenced by the geometry of the composite. SPS models show both strain hardening and strain softening during the simulations, with strain hardening preceding strain softening. A critical shear strain is necessary to begin the strain softening behaviour. Strain hardening and strain softening are accompanied by a reduction and an increase of the partition of strain rate into the weak phase, respectively. On the other hand, WPS models show only weak strain hardening and strain softening, being the strain-dependent behaviour close to a steady state flow. In addition, the following results are obtained on vorticity and kinematic vorticity number; (1) in both SPS and WPS models the partition of vorticity into weak phase increases with progressive shear strain, i.e. the strong phase becomes less rotational, (2) in SPS models weak inclusions changes from sub-simple shear to super-simple shear with progressive strain, whereas the strong matrix changes from super-simple shear to sub-simple shear, (3) in WPS models the strong inclusions with high viscosity contrasts are less rotational but can be in super-simple shear condition to high strains.The observed strain-dependent behaviours have been compared with previous proposed analytical models. The degree of agreement is variable. Balshin and Ryshkewitch–Duckworth models are only applicable to SPS models. Ji-generalized mixture rule model is applicable to both models.The results suggest that polyphase rocks with SPS structure during ductile shear deformation respond as strain softening materials, after an initial strain hardening stage that may drive to the strain localization into the material.