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ISRN Polymer Science
Volume 2013 (2013), Article ID 952379, 22 pages
Review Article

50 Years of the K-BKZ Constitutive Relation for Polymers

School of Mining Engineering and Metallurgy, National Technical University of Athens, Zografou, 157 80 Athens, Greece

Received 13 November 2012; Accepted 1 January 2013

Academic Editors: Y. Chen, X. Colin, H. Kaddami, and S. Yamazaki

Copyright © 2013 Evan Mitsoulis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The K-BKZ constitutive model is now 50 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experiment, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction a historical perspective is given on developments in the last 50 years of the K-BKZ model. Then a section follows on mathematical modeling of polymer flows, including governing equations of flow, rheological constitutive equations (with emphasis on viscoelastic integral constitutive equations of the K-BKZ type), dimensionless numbers, and boundary conditions. The Method of Solution section reviews the major developments of techniques necessary for particle tracking and calculation of the integrals for the viscoelastic stresses in flow problems. Finally, selected examples are given of successful application of the K-BKZ model in polymer flows relevant to rheology.