Numerical modeling of the motion of deformable ellipsoidal objects in slow viscous flows

An algorithm for modeling the strain and rotation of deformable ellipsoidal objects in viscous flows based on Eshelby's (1957. Proceedings of the Royal Society of London A241, 376–396) theory is presented and is implemented in a fully graphic mathematics application (Mathcad®, http://www.mathsoft.com). The algorithm resolves all singular cases encountered in modeling large finite deformations. The orientation of ellipsoidal objects is specified in terms of polar coordinate angles which are easily converted to the trend and plunge angles of the three principal axes rather than the Euler angles. With the Mathcad worksheets presented in the supplementary data associated with this paper, one can model the strain and rotation paths of individual deformable objects and the development of preferred orientation and shape fabrics for a population of deformable objects in any homogeneous viscous flow. The shape and preferred orientation fabrics for a population of deformable objects can be presented in both a three-dimensional form and a two-dimensional form, allowing easy comparison between field data and model predictions. The full graphic interface of Mathcad® makes using the worksheets as easy as using a spreadsheet. The modeler can interact fully with the computation and customize the type and format of the output data to best fit the purpose of the investigation and to facilitate the comparison of model predictions with geological observations.