Viscous constitutive relations of solid-liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model

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Shearing Melt Out of the Earth: An Experimentalist's Perspective on the Influence of Deformation on Melt Extraction (2009, methodology): “Takei & Holtzman (2009b) showed that asymmetry in the distribution of melt around a grain can develop due to the effects of deviatoric stress on melt composition.”
Organized melt, seismic anisotropy, and plate boundary lubrication (2010, methodology): “[48] Recent studies show that the effect of melt on rheological properties may be more dramatic than previously believed [Takei and Holtzman, 2009a, 2009b, 2009c].”
Polycrystal anelasticity at near‐solidus temperatures (2016, background): “One of our major concerns in this study is whether or not the formation of the connected melt network at T = Tm discontinuously increases the matter diffusivity, which causes a discontinuous change in the mechanical properties [Takei and Holtzman, 2009a, 2009b].”
Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust (2013, methodology): “We use an inverse melt fraction law to relate the compaction viscosity to the shear viscosity of the host rock (Takei & Holtzman 2009; Simpson et al. 2010a; Schmeling et al. 2012): ξ = η0φ−p. (51) The melt fraction exponent is taken as p = 1 in this study, consistent with theoretical work…”