In the present paper a mathematical theory is given for a viscoelastic fluid exhibiting a hysteresis loop in the shear stress versus shear rate plane. The main rheological idea is to introduce a constitutive equation of rate type whose steady shear stress versus shear rate locus is nonmonotone. The main mathematical idea is to use a local shock structure theory to pick out the admissible solutions in loading and unloading of the applied driving force.
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Hunter et al. (1983) studied this question.
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