Measure of non-coaxiality

Abstract

The kinematical vorticity number (W_k) can be a measure of instantaneous non-coaxiality of geologic deformations. In order to determine the degree of non-coaxiality from finite deformation structures, an entity W'_k is defined. W'_k = 2Ω/D, where (Ω) is the amount of rotation of a rigid equant grain embedded in a ductile matrix, D=[2ε^-2₁+ε^-2₂+ ε^-2₃]^½ and εⁱ are the principal natural strains. For different values of W_k the progressive variation of 2Ω with D is plotted graphically. The gradient of each curve at the origin is equal to W_k. The gradient of the curves and the values of W_k increase with progressive deformation. If Ω and D are independently determined from the rock fabric, then the plots of the data on the 2ωD diagram will enable us to identify a curve for a particular W_k. The analysis is carried out for plane equivoluminal strain and the method is applicable for the case in which the instantaneous character of deformation remains unchanged in progressive deformation.