The motion of deformable ellipsoids in power-law viscous materials: Formulation and numerical implementation of a micromechanical approach applicable to flow partitioning and heterogeneous deformation in Earth's lithosphere

Earth's lithosphere is heterogeneous in rheology on a wide range of observation scales. When subjected to a tectonic deformation, the incurred flow field can vary significantly from one rheologically distinct element to another and the flow field in an individual element is generally different from the bulk averaged flow field. Kinematic and mechanical models for high-strain zones provide the relations between prescribed tectonic boundary conditions and the resulting bulk flow field. They do not determine how structures and fabrics observed on local and small scales form. To bridge the scale gap between the bulk flow field and minor structures, Eshelby's formalism extended for general power-law viscous materials is shown to be a powerful means. This paper first gives a complete presentation of Eshelby's formalism, from the classic elastic inclusion problem, to Newtonian viscous materials, and to the most general case of a power-law viscous inhomogeneity embedded in a general power-law viscous medium. The formulation is then implemented numerically. The implications and potential applications of the approach are discussed. It is concluded that the general Eshelby formalism together with the self-consistent method is a powerful and physically sound means to tackle large plastic deformation of Earth's lithosphere.