Constraints on deformation path from finite strain gradients

We present a methodology for analyzing finite strain gradients in high-strain zones in order to place constraints on the zone's possible deformation path. To accomplish this, the high-strain zone is divided into several sub-zones, within each of which finite strain is described by a single ellipsoid. Based on knowledge of the spatial and temporal evolution of deformation, strain observed in less deformed sub-zones is then mathematically removed from more deformed sub-zones to calculate incremental finite strains. The mean kinematic vorticity number of each of these increments must be constant if deformation was steady-state. We use the methodology to analyze two natural examples of high-strain zones at different scales. Both natural examples have non-steady-state likely deformation paths, which may be a common characteristic of high-strain zones. Although results of the methodology are not unique, identification of likely paths considerably narrows the range of possible deformation paths. Consequently, useful kinematic information can be extracted from finite strain data even in instances where the detailed spatial and temporal evolution of a high-strain zone cannot be determined conclusively.