MATH 559 Homework Assignment II
University of British Columbia
(due on Oct. 9, 2015 after class)
1. In class we showed by the simple-shear-on-a-turn-table setup that the linear Maxwell
model violates frame indifference. Prove that the upper convected Maxwell model satisfies frame indifference. If you need help, consult Bird et al. Vol. 1, Example 7.1-3.
2. Calculate the stress tensor of the Oldroyd-B model after abrupt startup of homogeneous
shear and purely elongational flow. Graph τxy (t) for the shear flow and τzz (t) for the
elongational flow. By abrupt startup, we mean that for t < 0, there is no deformation:
γ̇ = 0. But for t ≥ 0,


0 γ̇0 0
γ̇ = γ̇0 0 0
0 0 0
for the simple shear, and


−ǫ̇0 0
0
γ̇ =  0 −ǫ̇0 0 
0
0 2ǫ̇0
for the elongational flow.
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