Plate generation and damage theory

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 nonlinear rheology and convection. One such nonlinear 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 both a two- dimensional convectively driven system and two-dimensional simple shear calculations 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 behavior 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 lead to a spectrum of localized and distributed deformation results. The interaction of micro-cracks and grain size reduction in two-phase damage theory suggests a rheological model for shear localization necessary for the generation of plate tectonic boundaries. We also find that the interplay of damage and the thermal state of the lithosphere as influenced by surface temperatures may have a profound influence on the development of plate tectonics.