Visualizing strain and the Rf– Φ method with an interactive computer program

Abstract

The R f– Φ method is a powerful graphical approach for estimating finite strain of deformed elliptical objects, but one that students commonly find difficult to understand. We developed a program that allows users to explore visually how deforming a set of elliptical objects appears on R f– Φ plots. A user creates or loads the ellipses and then deforms them by simple shear, pure shear, or rigid rotation. As the ratio of the long to short axis of the ellipses ( R f) and long-axis orientations ( Φ) change in one window, the R f– Φ plot continuously and instantaneously updates in another. Users can save snapshots of the deformed elliptical objects and the R f– Φ plots to record graphical experiments. The program provides both R f vs. Φ and polar ln( R f) vs. 2( Φ) plots. The user can ‘undeform’ ellipses quickly and easily, making it possible to inspect the ‘original’ shapes and orientations of objects, and to evaluate the plausibility of the determined strain values. Users can export information about the pebbles' shape and orientation to spreadsheets for rigorous statistical analysis. This program is written in Java and so can run on virtually any operating system. Both the source code and the application will be freely available for academic purposes.