Effects of object ellipticity on strain, and implications for clast–matrix rocks

We examine the influence of object shape on strain, taking the example of an elliptical object in a matrix of different viscosity. The Eshelby–Bilby equation for the cross-sectional strain of circular cylindrical objects in a matrix of different viscosity is differentiated, to express the relationship of developing sectional ellipticity on incremental strain. This leads to an expression for the strain of initial elliptical objects whose axes are parallel or perpendicular to pure shearing. Graphs show that competent elliptical objects with axial ratios of Ri=3 or more, will strain significantly more than circular objects of the same viscosity; less if the objects are incompetent. While the effect is likely to be insignificant for competent objects with initial ellipticity of <2, which is indicated from statistics for undeformed pebbles in conglomerates, any clast with greater ellipticity, such as Ri=5 to 10, could deform significantly more than an equant clast, and thus appear to be materially less competent. These principles have implications for geological strain studies and for competence contrasts in rocks.