Numerical models of shear-induced melt band formation with anisotropic matrix viscosity

Abstract

When a system of partial melt is subjected to an externally driven strain-rate, an instability can occur whereby bands of low and high porosity form. Theory and numerical simulations have shown that if the matrix viscosity is isotropic and strain-rate independent, the bands grow fastest when parallel to the direction of maximum compression of the externally imposed flow. However, experiments indicate that bands form at angles that differ by roughly 25° from the direction of maximum compression even when the matrix viscosity is strain-rate independent. Recently, Takei and Holtzman (2009c) have argued that the matrix viscosity is likely to be anisotropic when partial melt is present because of the anisotropic arrangement of melt at the grain scale. These authors also presented a theoretical expression for the stress tensor in the presence of this anisotropy and a linear theory of band formation that indicated that bands would form at angles that are in accord with the results of experiments. In this contribution, I present the results of linear theory and full nonlinear simulations of band formation under simple shear with anisotropic viscosity. I show that, even when the viscosity is strain-rate independent, the resulting bands form at low angles in accord with experiments if the anisotropy reflects a distribution of melt in pockets aligned parallel to the direction of maximum compression. If instead the anisotropy represents melt that is aligned at low angles to the shear plane, as seen in highly deformed experiments, the melt bands rapidly rotate to high angles. In that case, another mechanism is required to maintain the bands at low angles. The effects of buoyant melt are also investigated and bands are shown to grow at the same rate as when buoyancy is absent, but with an additional secondary preferred orientation.