= Solution
A plain <material derivative> of the <conformation tensor> is not an <objective time derivative>: an observer undergoing a time-dependent rigid rotation would infer a different constitutive response, and even rigid-body rotation could appear to change polymer deformation. The <upper-convected derivative> subtracts deformation and rotation carried by the velocity gradient and is frame indifferent.
The <Oldroyd-B model> is often inadequate because its Hookean dumbbells are infinitely extensible. It predicts constant shear viscosity rather than shear thinning, zero second <normal-stress difference>, and an unbounded extensional viscosity at a finite extension rate. Real polymer chains have finite extensibility and commonly exhibit shear thinning, bounded extensional stress, multiple relaxation times, and nonlinear solvent or concentration effects.
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