Plate generation and two-phase damage theory in a model of mantle convection

The formation of narrow, rapidly deforming plate boundaries separating strong plate interiors are integral components of the generation of plate tectonics from mantle convection. The development of narrow plate boundaries requires the interaction of a non-linear rheology and convection. One such non-linear rheology is two-phase damage theory which employs a non-equilibrium relation between interfacial surface energy, pressure and viscous deformation, thereby forming a theoretical model for void generation. Two-phase damage theory was recently extended to allow for deformational work to increase the fineness (reduce the grain size) of the matrix phase. We present results testing two-phase damage theory in a 2-D convectively driven system where we allow for (1) pure void-generating damage, (2) pure fineness-generating damage and (3) combined void- and fineness-generating damage. Pure void-generating damage is found to be unsuccessful at producing plate-like features. Fineness-generating damage is successful at inducing plate-like behaviour in certain circumstances, including increasing viscosity sensitivity to fineness and certain regimes of damage input and healing rate. Cases with combined void- and fineness-generating damage produce significantly more localization than the end-members due to the apparent increase of deformational work input into fineness generation. The interaction of microcracks and grain size reduction in two-phase damage theory suggests a rheological model for shear localization necessary for the formation of plate tectonic boundaries.