We develop a steady-state fluid-mechanical analysis describing the effect of strain partitioning on viscous energy dissipation. As observed in experimental studies of shear deformation of partially molten rocks, strain partitions when melt segregates because viscosity is reduced in regions of elevated melt fraction. The equations derived here are based on parameters measured in experiments, describing the evolution of melt distribution and rheological properties. We find that the dissipation depends strongly on the configuration of the melt-rich network of shear zones, including the average angle, volume fraction of melt and amplification of strain rate in the melt-rich bands. Minima in energy dissipation as a function of band angle develop, corresponding to configurations of melt networks that minimize the difference in mean stress between the band and the non-band regions. We propose that the organization of band networks occurs by the interplay between strain localization and viscosity variations associated with melt segregation. The band networks maintain a steady-state angle during shear by continuously pumping melt through the network. The development of strain partitioning in melt-rich networks will modify the energetics of melting and melt transport by efficiently extracting melt and reducing effective viscosity.
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