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{{main|Oldroyd-B model}}
The Oldroyd-B model is an extension of the [[Upper Convected Maxwell model]] and is interpreted as a solvent filled with elastic bead and spring dumbbells.
The model is named after its creator [[James G. Oldroyd]].<ref name="a">{{cite journal|last=Oldroyd|first=James|title=On the Formulation of Rheological Equations of State|journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences|date=February 1950|volume=200|issue=1063|pages=523–541|bibcode=1950RSPSA.200..523O| doi=10.1098/rspa.1950.0035| s2cid=123239889}}</ref><ref name="b">{{cite book | last1=Owens |first1=R. G. |last2=Phillips |first2=T. N.| title=Computational Rheology| publisher=Imperial College Press | year=2002 | isbn=978-1-86094-186-3}}</ref><ref name="c">{{cite journal| last=Poole|first=Rob| journal=Physical Review Letters |title=Purely elastic flow asymmetries|date=October 2007|volume=99| number=16|
The model can be written as:
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