Shape preferred orientation of rigid particles in a viscous matrix: reevaluation to determine kinematic parameters of ductile deformation

The development of the shape preferred orientation of rigid elliptical bodies during non-coaxial deformation is theoretically simulated in a two-dimensional Newtonian matrix. The angular velocity of a rigid elliptical body (φ) can be expressed as φ = caseVR2 + 1 [R2 sin2 φ cos Θ + cos2 φ cos Θ − (R2 − 1) sin2 φ sin Θ] where φ is the angle between the shear plane and the longest axis of the ellipse, R is the aspect ratio of the ellipse, V is a constant, and Θ is the newly introduced index angle to describe degree of non-coaxiality between simple shear and pure shear defined as tan Θ = φ̇g3φ̇gg · φ̇gg and φ̇g3 are simple shear strain rate and pure shear strain rate, respectively. The initial distribution pattern of the elliptical bodies is assumed to be random in an R/φ diagram, and a series of the distribution patterns was calculated using the above equation with increasing deformation at varying Θ. When deformation is simple shear (i.e. Θ = 0 dg), all elliptical bodies rotate with various angular velocities, resulting in a skewed distribution in the R/φ diagram. In contrast, for pure shear (i.e. Θ = 90 °) all of them asymptotically settle their longest axes on a plane perpendicular to the compression axis, resulting in strongly concentrated and symmetric distribution patterns in the R/φ diagram. When deformation is general non-coaxial (0 ° < Θ < 90 °), distribution patterns in the R/φ diagram change systematically from the pattern similar to that of Θ = 0 ° to that of Θ = 90 ° with increasing Θ. These R/φ diagrams can be used for estimating the degree of non-coaxiality. We analyzed shape preferred orientation of porphyroclasts in two mylonites, and concluded that deformation within the mylonites contain a certain amount of pure shear component that superimposes on a simple shear component.