KINEMATICS OF DEFORMATION CONSTRUCTED FROM DEFORMED PLANAR AND LINEAR ELEMENTS: THE METHOD AND ITS APPLICATION

We illustrate the kinematics for flow and finite deformation by forward modeling of various steady-state progressive deformations on lower-hemisphere stereographic projections. On such projections, planar and linear material markers that undergo progressive shortening, progressive extension, shortening followed by extension, and extension followed by shortening are divided into fields separated by the non-material surfaces of zero stretching and the material surfaces defined by all material lines in the deformed state that originally constituted the surfaces of zero stretching. The models also include the fields of instantaneous shortening, instantaneous extension, and the surfaces defined by material lines with unit finite stretch. Natural examples from the literature are used to illustrate applications of our models.

We then present a revised approach to construct flow parameters and position gradient tensors from deformed planar and linear elements. The approach is particularly novel in its application in strain analysis of deformed veins. Typically, such strain analysis is carried out on a two-dimensional section. Three-dimensional analysis has previously been carried out by plotting poles to shortened and/or extended veins, which was somewhat limited as the direction of shortening/extension remained unknown. Our method of plotting shortened and/or extended linear sections within veins yields the most accurate information on the directions of shortening and extension, and in some cases on finite strain.