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We study theoretically the formation of shear bands in time-dependent flowsof polymeric and wormlike micellar surfactant fluids, focussing on theprotocols of step shear stress, step shear strain (or in practice a rapidstrain ramp), and shear startup, which are commonly studied experimentally. Foreach protocol we perform a linear stability analysis to provide afluid-universal criterion for the onset of shear banding, following our recentLetter [Phys. Rev. Lett. 110 (2013) 086001]. In each case this criteriondepends only on the shape of the experimentally measured rheological responsefunction for that protocol, independent of the constitutive properties of thematerial in question. (Therefore our criteria in fact concern all complexfluids and not just the polymeric ones of interest here. A separate manuscript[in preparation] will explore them in a broad class of disordered soft glassymaterials including foams, dense emulsions, dense colloids, and microgel beadsuspensions.) An important prediction is that pronounced banding can arisetransiently in each of these protocols, even in fluids for which the underlyingconstitutive curve of stress as a function of strain-rate is monotonic and asteadily flowing state is accordingly unbanded. For each protocol we providenumerical results in the rolie-poly and Giesekus models that support ourpredictions. We comment on the ability of the rolie-poly model to capture theobserved experimental phenomenology, and on the failure of the Giesekus model.

Shear banding in time-dependent flows of polymers and wormlike micelles