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Constitutive mechanical relations of a partially molten rock in terms of grain boundary contiguity: an approach with an internal state variable

Presented by: 
Yasuko Takei
Tuesday 12th April 2016 - 11:30 to 12:30
INI Seminar Room 1
Mechanical and transport properties of a partially molten rock strongly depend on the grain scale melt geometry. To quantify the microstructural effects, constitutive mechanical relations for elasticity (Takei, 1998) and diffusion creep viscosity (Takei and Holtzman, 2009) are derived theoretically by considering a realistic microstructural model. The essential geometrical factor which determines these properties was found to be the ``grain boundary contiguity’’ which represents the area of grain-to-grain contacts relative to the total surface area of each grain. One of the most striking results is that while contiguity affects both elasticity and viscosity, the effect on viscosity is about 100 times larger than that on elasticity. When partially molten rock is texturally equilibrated, contiguity is determined as a function of melt fraction and dihedral angle. However, when it is deformed under a deviatoric stress, contiguity deviates from the equilibrium value an d evolves, resulting in a significant change in the matrix viscosity. Possible consequences of these microstructural evolution on the macroscopic dynamics can be studied within the framework of continuum mechanics by solving the governing equations of two phase flow together with the viscous constitutive relation which includes contiguity as an internal state variable. By applying this approach to the formation of stress-driven, melt-enriched channels, I will demonstrate the important role of microstructural processes in the macroscopic dynamics.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons