Shear localization is the process by which deformation in a solid material becomes highly focused into narrow bands that weaken the material. Shear localization is apparent in many fields of physics, materials science and geoscience; at the largest scale, it plays an important role in how plate tectonics arises from thermal convection in the Earth's rocky mantle. In the last few decades, studies of how rocks deform (flow, break, bend, etc.) have shown that the long-term deformation of the lithosphere (the coldest strongest part of the mantle near the surface) is likely controlled by complex behavior such as simultaneous breaking and fluid-like flow; and reduction in the size of mineral grains inside of rocks. Such mechanisms are known to lead to focused or localized deformation and thus play a crucial role in the evolution and structure of boundaries between tectonic plates upon which most of the worlds volcanism and seismicity are focused. Thus, the development of a complete theory of tectonic plate boundary generation from microcrack generation and grainsize reduction in the lithosphere-mantle system is paramount for understanding how plate tectonics arises out of mantle convection. This project continues development of one such new theory called two-phase damage theory. This theory states that (1) a damaged material (with voids/microcracks, defects, grain boundaries) is, in its simplest form, a two-phase material (a rock phase, and a fluid phase representing void-filling or intergranular matter); and (2) the energy going into damage is deformational work that is stored as surface energy on the crack wall and/or grain boundary. The theory has been used to predict shear localization, failure envelopes in rocks, and generation of plate-like motion from simple fluid-dynamical models. These results stress the importance of, and competition between, crack- or void-generating damage and grainsize reducing damage in models of mantle-lithosphere dynamics. The ongoing project incorporates into the theory new important physics of (1) grain-grain boundaries; (2) mass exchange and chemical reactions between phases (e.g., for healing, melting, etc); and (3) evolution in grainsizes and grainsize distributions by coarsening and damage. Applications relevant to lithospheric compression, extension, shear, gravitational collapse, and convectively driven flow are constructed to test the various new physical effects that are added to the theory. This work furthers our understanding of the fundamental processes of mantle dynamics, lithospheric deformation and the origin of plate tectonics. Moreover, since the project involves a fundamental theory, it contributes to many problems of geological fluid mechanics (magma dynamics, glaciology, and hydrological systems), rock mechanics (small-scale damage zones, localization and failure), as well as general material science and engineering (e.g., elastodynamic damage, metallurgy, and complex fluids such as colloids and suspensions).
