Development of anisotropic contiguity in deforming partially molten aggregates: 1. Theory and fast multipole boundary elements method

The microstructure of partially molten rocks strongly influences the macroscopic physical properties. Contiguity, a geometric parameter, is a tensorial quantity that describes the area fraction of intergranular contact in a partially molten aggregate. It is also a key parameter that controls the effective elastic strength of the grain network. As the shape of the grains evolves during deformation, so does the contiguity of each grain. In this article, we present the first set of numerical simulations of evolution of grain‐scale contiguity of an aggregate during matrix deformation using a fast multipole boundary elements method‐based model. We simulate a pure shear deformation of an aggregate of 1200 grains up to a shortening of 0.47 and a simple shear deformation of 900 grains up to a shear strain of 0.75, for solid‐melt viscosity ratios of 1 and 50. Our results demonstrate that the initially isotropic contiguity tensor becomes strongly anisotropic during deformation. We also observe that the differential shortening, the normalized difference between the major and minor axes of grains, is inversely related to the ratio between the principal components of the contiguity tensor. In pure shear, the principal components of the contiguity tensor remain parallel to the irrotational principal axes of the applied strain. In simple shear, however, the principal components of the contiguity tensor rotate continually during the course of deformation in this study. In the companion article we present the seismic anisotropy resulting from the anisotropic contiguity and the implications for the Earth's lithosphere‐asthenosphere boundary.