Paulo R. Souza Mendes
Dept. of Mechanical Engineering, Pontifícia Universidade Católica, Rio de Janeiro, Brasil

Classification of Motions based on the Persistence-of-Straining Concept

In 1979, Astarita proposed a local and objective criterion to classify flows. His criterion is not restricted to MWCSH, and is essentially an attempt to quantify the stress-relieving rotation experienced by the flowing material. In 1980, Huilgol analyzed Astarita's work and showed, through examples, some inconsistencies which rendered it useless as a general flow criterion. The present work revisits Huilgol's examples and discusses in detail the underlying physics that make Astarita's criterion to fail for certain flows. This analysis leads to a new criterion for flow classification involving the concept of persistence of straining. A key kinematic entity introduced in the proposed criterion is the pi-plane, a plane that is normal to the relative-rate-of-rotation vector. For a more comprehensive criterion,
other parameters are needed in addition to a persistence-of-straining parameter. One of them is a measure of the deformation rate in the p-plane. Although emphasis is given to isochoric motions, a compressibility parameter is also introduced to encompass non-isochoric flows. The proposed kinematic criterion is local, frame-indifferent and is not restricted to particular classes of flows. Its robustness is shown through detailed analyses of some representative flows.

Acknowledgments
The author strongly appreciates the contribution of Mr. Roney L. Thompson, leading researcher of the project wich provides the ground for the present talk.