The behaviour of deformable ellipsoidal particles in three-dimensional slow flows: implications for geological strain analysis

Abstract

Eshelby's equations governing the motion of a viscous inclusion embedded in a matrix of contrasting viscosity are solved numerically for arbitrarily shaped and arbitrarily oriented ellipsoidal particles. The theory has important implications for geological strains and strain analysis. Specifically, it predicts that particles more competent than their matrix will have deformed shapes with larger k-values than equivalently shaped and oriented passive markers. The effect is significant even for viscosity ratios as low as r = 1.5 and increases with increase in r. For general applications numerical solutions must be sought, nevertheless, there are useful exceptions. 1. (1) The two-dimensional deformed shape of viscous particles can be computed graphically provided the matrix strain is irrotational pure shear and the section ellipse is a principal plane of the particle ellipsoid. For sections through a three-dimensional system with arbitrarily oriented particles this method (and those based on sections through an elliptic cylinder) is inaccurate. The reliability is further diminished for simple shear. 2. (2) Irrotational deformations in three-dimensions can be computed on transformed Flinn plots if the particle or average particle axial orientations are parallel with the applied flow. Similar diagrams may be used to make independent estimates of viscosity contrasts in polymict conglomerates.