VISUALIZING DEFORMATION WITH AN INTERACTIVE COMPUTER PROGRAM: LINKING SHAPE CHANGE WITH GRAPHICAL AND MATHEMATICAL REPRESENTATIONS OF STRAIN

Deformed pebbles conglomerates are commonly used to introduce students to the concept of strain. It is relatively easy to visualize how strain will transform initially circular objects, but it is more challenging to grasp how deformation will affect a population of elliptical objects, and how a preferred-shape fabric corresponds to the intensity and orientation of the strain. Strain can be quantified as a linear transformation, and graphs of pebble axial ratios (Rf) vs. long axis orientations (Phi) can be used to estimate the orientation and magnitude of the strain ellipse. It is difficult for most students, however, to connect the 2x2 strain matrix to shape change, and to visualize how the deformation of pebbles will manifest in Cartesian and polar Rf-Phi plots. We developed a platform independent Java program that allows users to visually link a deforming set of pebbles with the corresponding strain matrix and Rf-Phi plots. The user creates or loads a set of ellipses and then deforms them by simple shear, pure shear, or rotation. As the shape and long axis orientation of ellipses change in one window, the Rf-Phi plot simultaneously tracks those changes in another, and the corresponding deformation matrix is displayed. Deformation can be specified precisely, altered in small increments using arrow keys, or controlled by click-and-drag with a mouse. The program shows both Cartesian and polar Rf-Phi plots. Elliptical objects can be loaded from a text file or quickly digitized from an imported photograph. When a population of naturally deformed ellipses is digitized, the ratio of the strain ellipse and the maximum initial ellipticity can be determined with the equations provided by Ramsay and Huber (1987). It is also possible to graphically un-strain the population to determine the inverse strain ellipse. This allows students to inspect the original shapes and orientations of pebbles, to evaluate the plausibility of the estimated strain values, and to assess the key assumption of no initial preferred orientation of pebble long axes. The source code and program are freely available for academic purposes.

The instantaneous visual feedback provides a critical link between deformation of a population of pebbles and changes in the graphical representation of the population via the linear algebraic description of strain.