Two-phase damage and tectonic plate generation

The two-phase theory for compaction and damage employs a nonequilibrium relation between interfacial surface energy, pressure, and viscous deformation, thereby providing a model for damage (void generation and microcracking) and a continuum description of weakening, failure, and shear localization. Here we examine the application of this theory to the problem of generating plate-like behavior from convective-type divergent (poloidal) motion through a source-sink formulation. We extend the previous damage theory to consider two possible damage effects: (1) growth and nucleation of voids associated with dilation of the host matrix, and (2) increasing fineness (i.e., reducing coarseness) of the mixture by, for example, grainsize reduction. Void-generating damage is found to be poor at plate generation because of the predominance of dilational motion that is adverse to the development of plate-like flow. Fineness-generating damage is found to be very efficient at generating plate-like behavior if we assume that the matrix viscosity is a simple function of grain/void size, as is typical for diffusion creep. The implied grainsize reduction mechanism is different than that of dynamic recrystallization, and appears highly capable of generating the requisite shear-localization for forming tectonic plates from mantle flow.