CMG: Rheology of Damaged Materials with Applications to Deformation in the Earth's Crust

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The investigators are exploring new methods for representing damage mechanics in the Earth's crust using a continuum rheology. Using a method that has been developed for understanding phase transitions in liquid crystals, they are developing a new model of damage in a continuum material undergoing shear flow. They model crustal deformation using a fluid phase with anisotropic properties, in which some elastic energy is stored according to the direction of an alignment vector. The undamaged state is characterized by random alignment of the directional vectors (director). Defects can be introduced in various configurations with appropriate alignment of the directors. In response to shear, point defects can develop and merge to trigger spikes in the velocity, that is, slip events. This slip mechanism, followed by subsequent healing, provides a model for the formation of microcracks and stick-slip behavior on faults.Intellectual Merit: Deformation of the Earth's crust and upper mantle has implications for the origins of earthquakes and the mechanisms for plate tectonics. This study of the behavior of this system will address the origins of damage, formation of faults, fault slip, and healing, in the Earth's crust.Broader Impacts: By developing new models of damage rheology, this project will address the underlying mechanisms leading to earthquakes, a scientific problem of fundamental societal importance. A theory of damage in a continuum has potential implications well beyond geophysics, and could be applicable to damage in other continuum materials. In addition, this project establishes a new collaboration between geophysics and applied mathematics, leading to the development of new methods in both fields, while educating a graduate student and a postdoctoral scholar.