Rheologica Acta

, Volume 47, Issue 7, pp 719–725 | Cite as

A physical decomposition of the stress tensor for complex flows

  • P. C. BolladaEmail author
  • T. N. Phillips
Original Contribution


Traditionally, the components of the stress with respect to a relevant coordinate system are used for the purpose of stress visualisation and interpretation. A case for using a flow dependent measure to interpret and visualise stress is made for two dimensional flow, together with a suggestion for extending the idea to three dimensions. The method is illustrated for Newtonian and Oldroyd B fluids in both the eccentrically rotating cylinder and flow past a cylinder benchmark problems. In the context of a generalised Newtonian fluid, the relation between the flow-dependent stress measure to other field variables under certain flow conditions, is examined and is indicative of its importance in complex flow.


Stress invariant Principal stress Stress visualisation Shear stress Normal stress difference Stress decomposition 



We gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council of the United Kingdom through a Portfolio Partnership award (EP/C513037).

My thanks to Rene Vargas, Universidad Nacional Autonoma de Mexico UNAM and Nat Inkson, Cardiff University for their help with flow past a cylinder computations.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of MathematicsCardiff UniversityCardiffUK

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