Finite strain estimation using the mean radial length of elliptical objects with bootstrap confidence intervals

Abstract

A new method for calculating finite sectional strain from distributions of elliptical objects is presented. The only assumptions required are that before deformation (1) long axis orientations are uniformly distributed and (2) the distribution of axial ratios is independent of orientation. Importantly, an estimate of the orientation of the long axis of the strain ellipse is not required before the method can be applied. The method is based on the conceptually simple fact that the mean radial length of a set of uniformly oriented ellipses in the unstrained state equates to that of a circle, so that after strain, the mean radial length evaluates to the strain ellipse. Errors associated with the method are calculated from the bootstrap, and a simulation study verifies both the applicability of the new method for finite strain estimation and the accuracy of errors calculated with the bootstrap. The method is applied to a large set of sandstone quartz clast data from the Irish Variscides, whilst cross-checking of results with those from established methods also validates the approach taken.