We study theoretically the necking dynamics of a filament of complex fluid or soft solid in uniaxial tensile stretching at constant imposed Hencky strain rate ˙ , by means of linear stability analysis and nonlinear (slender filament) simulations. We demonstrate necking to be an intrinsic flow instability that arises as an inevitable consequence of the constitutive behaviour of essentially any material (with a possible rare exception, which we outline), however carefully controlled the experimental conditions. We derive criteria for the onset of necking that are reportable simply in terms of characteristic signatures in the shapes of the experimentally measured rheological response functions, and should therefore apply universally to all materials. As evidence of their generality, we show them to hold numerically in six popular constitutive models: the Oldroyd B, Giesekus, FENE-CR, Rolie-Poly and Pom-pom models of polymeric fluids, and a fluidity model of soft glassy materials. Two distinct modes of necking instability are predicted. The first is relatively gentle, and sets in when the tensile stress signal first curves downward as a function of the time t (or accumulated strain = ˙ t) since the inception of the flow. The second is more violent, and sets in when a carefully defined 'elastic derivative' of the tensile force first slopes down as a function of t (or ˙ ). In the limit of fast flow ˙ τ → ∞, where τ is the material's characteristic stress relaxation time, this second mode reduces to the Considère criterion for necking in solids. However we show that the Considère criterion fails to correctly predict the onset of necking in any viscoelastic regime of finite imposed ˙ τ , despite being widely discussed in the complex fluids literature. Finally, we elucidate in detail the way in which these modes of instability manifest themselves in entangled polymeric fluids (linear polymers, wormlike micelles and branched polymers). In particular we demonstrate four distinct regimes of necking behaviour as a function of imposed strain rate, consistent with master curves in the experimental literature.

Reprinted with permission from the American Physical Society: Physical Review Letters 114, 158301 c 2015 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Publisher's copyright statement:This document is the Accepted Manuscript version of a Published Work that appeared in nal form in ACS macro letters, copyright c American Chemical Society after peer review and technical editing by the publisher. ACS macro letters.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. SynopsisIn this paper, the predictions of the Pompom constitutive model in medium and large amplitude oscillatory shear (LAOS) are examined using Fourier transform rheology (FTR). FTR is commonly used in combination with small amplitude oscillatory shear to fit linear Maxwell parameters to dynamic moduli, and in this paper, this process is expanded to larger strain amplitudes and to further terms in the Fourier series. For both small and large amplitudes, these higher harmonics are dependent on the nonlinear Pompom parameters and the Pompom parameter space is explored to see how experimental oscillatory shear data can infer molecular detail. In the regime of small and medium strain amplitude, there exists an asymptotic solution to the Pompom equations which depends only on the ratio of the orientation and stretch relaxation times,

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. SynopsisThis work analyses the high-strain extensional behavior of long-chain branched polyethylenes, employing two novel extensional rheometer devices, the filament stretching rheometer and the crossslot extensional rheometer. The filament stretching rheometer uses an active feedback loop to control the imposed strain rate on a filament, allowing Hencky strains of around 7 to be reached. The cross-slot extensional rheometer uses optical birefringence patterns to determine the steady-state extensional viscosity from planar stagnation point flow. The two methods probe different strain-rate regimes and in this paper we demonstrate the agreement when the operating regimes overlap and explore the steadystate extensional viscosity in the full strain-rate regime that these two complimentary techniques offer. For long-chain branched materials, the cross-slot birefringence images show a double cusp pattern around the outflow centre line (named W-cusps). Using constitutive modeling of the observed transient overshoot in extension seen in the filament stretching rheometer and using finite element simulations we show that the overshoot explains the W-cusps seen in the cross-slot extensional rheometer, further confirming the agreement between the two experimental techniques. V C 2013 The Society of Rheology.[http://dx