= Solution
An <objective time derivative> transforms as a tensor under every superposed time-dependent rigid translation and rotation of the observer. A constitutive prediction using it is therefore frame-indifferent. The <upper-convected derivative>, <lower-convected derivative>, and <Jaumann derivative> are objective; the componentwise partial time derivative, and generally the uncorrected <material derivative> of a tensor, are not objective under rotating observers.
The <Johnson--Segalman--Oldroyd model> uses the <Gordon--Schowalter derivative>
$$
\overset{\square}{\boldsymbol\sigma}
=\overset{\triangledown}{\boldsymbol\sigma}
+\frac a2(\dot{\boldsymbol\gamma}\boldsymbol\sigma
+\boldsymbol\sigma\dot{\boldsymbol\gamma}).
$$
Here $\eta$ is the zero-shear viscosity, $\lambda_1$ is the stress-relaxation time, and $\lambda_2$ is the retardation time associated with the more rapidly responding viscous contribution. Passive Oldroyd-type materials normally have $0\leq\lambda_2\leq\lambda_1$.
A low-rate steady-shear experiment measures $\eta$. A step strain followed by stress relaxation determines $\lambda_1$ from the exponential decay. Creep and recovery, or a frequency sweep in <small-amplitude oscillatory shear>, then separates $\lambda_2$ from $\lambda_1$; fitting both <storage modulus> and <loss modulus> is especially direct.
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