Kinematic and mechanical discontinuity at a coherent interface

Abstract

Across a coherent interface, displacements are continuous, but some components of large strain, rotation, stretching, spin, stress and rheology need not be so. This accounts for refraction of cleavage and other geological structures. The general theory of deformation and motion is used to analyze how discontinuities develop. A measure of discontinuity in total deformation gradients (strain and rotation) is the ratio, ( K), of amounts of shear above and below the interface and in directions parallel to it. It is shown that ( K) is equal to the ratio of simple shearings above and below the interface provided (i) the latter ratio is constant in time and (ii) no volume changes occur. These kinematic conditions are shown to hold in Newtonian fluids and incompressible neo-Hookean solids, where ( K) is exactly equal to the inverse viscosity ratio, or to the inverse rigidity ratio. The conditions do not hold in general in Reiner-Rivlin fluids. In power-law fluids, the ratio of simple shearings is constant for two special classes of motion, one with little simple shearing along the interface, the other with simple shearing alone; therefore, the rheological contrast can be determined. The theoretical results can be used to determine rheological contrasts in nature or experiment, provided there is some knowledge of the nature of the flow laws that operate. Under these conditions, an interface is an inbuilt rheometer.