arXiv subjects

Suzanne M. Fielding

Publications and source records attributed to Suzanne M. Fielding.

At least 37 records · Page 2Linked to original sources

arXiv2020

Aging in a mean field elastoplastic model of amorphous solids

We construct a mean-field elastoplastic description of the dynamics of amorphous solids under arbitrary time-dependent perturbations, building on the work of Lin and Wyart [Phys. Rev. X 6, 011005 (2016)] for steady shear. Local stresses are driven by power-law distributed mechanical noise from yield events throughout the material, in contrast to the well-studied Hébraud-Lequeux model where the noise is Gaussian. We first use a mapping to a mean first passage time problem to study the phase diagram in the absence of shear, which shows a transition between an arrested and a fluid state. We then introduce a boundary layer scaling technique for low yield rate regimes, which we first apply to study the scaling of the steady state yield rate on approaching the arrest transition. These scalings are further developed to study the aging behaviour in the glassy regime, for different values of the exponent $μ$ characterizing the mechanical noise spectrum. We find that the yield rate decays as a power-law for $1<μ<2$, a stretched exponential for $μ=1$ and an exponential for $μ<1$, reflecting the relative importance of far-field and near-field events as the range of the stress propagator is varied. Comparison of the mean-field predictions with aging simulations of a lattice elastoplastic model shows excellent quantitative agreement, up to a simple rescaling of time.

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arXiv2020

Interplay of edge fracture and shear banding in complex fluids

We explore theoretically the interplay between shear banding and edge fracture in complex fluids, by performing a detailed simulation study within two constitutive models: the Johnson-Segalman model and the Giesekus model. We consider separately parameter regimes in which the underlying constitutive curve is monotonic and non-monotonic, such that the bulk flow (in the absence of any edge effects) is respectively homogeneous and shear banded. Phase diagrams of the levels of edge disturbance and of bulk (or quasi-bulk) shear banding are mapped as a function of the surface tension of the fluid-air interface, the wetting angle where this interface meets the walls of the flow cell, and the imposed shear rate. In particular, we explore in more detail the basic result recently announced in Hemingway et al. (2018): that precursors to edge fracture can induce quasi-bulk shear banding. We also appraise analytical predictions that shear banding can induce edge fracture, Skorski and Olmsted (2011). Although a study of remarkable early insight, that study made some strong assumptions about the nature of the "base state", which we examine using direct numerical simulation. The basic prediction that shear banding can cause edge fracture remains valid, but with qualitatively modified phase boundaries.

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arXiv2020

Ductile and brittle yielding in thermal and athermal amorphous materials

We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In thermal systems we find a gradual progression, with increasing annealing, from smoothly "ductile" yielding, in which the sample remains homogeneous, to abruptly "brittle" yielding, in which it becomes strongly shear banded. This progression arises from an increase with annealing in the size of an overshoot in the underlying stress-strain curve for homogeneous shear, which causes a shear banding instability that becomes more severe with increasing annealing. "Ductile" and "brittle" yielding thereby emerge as two limiting cases of a continuum of yielding transitions, from gradual to catastrophic. In contrast, athermal systems with a stress overshoot always show brittle yielding at low shear rates, however small the overshoot.

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arXiv2020

Elastoviscoplastic rheology and ageing in a simplified soft glassy constitutive model

Yield stress fluids display a rich rheological phenomenology. Beyond the defining existence of a yield stress in the steady state flow curve, this includes in many materials rather flat viscoelastic spectra over many decades of frequency in small amplitude oscillatory shear; slow stress relaxation following the sudden imposition of a small shear strain; stress overshoot in shear startup; logarithmic or sublinear power law creep following the imposition of a shear stress below the yield stress; creep followed by yielding after the imposition of a shear stress above the yield stress; richly featured Lissajous-Bowditch curves in large amplitude oscillatory shear; a Bauschinger effect, in which a material's effective yield strain is lowered under straining in one direction, following a preceding strain in the opposite direction; hysteresis in up-down shear rate sweeps; and (in some materials) thixotropy and/or rheological ageing. A key challenge is to develop a constitutive model that contains enough underlying mesoscopic physics to have meaningful predictive power for the full gamut of rheological behaviour just described, with only a small number of model parameters, and yet is simple enough for use in computational fluid dynamics to predict flows in complicated geometries, or complicated flows that arise due to spontaneous symmetry breaking instabilities even in simple geometries. Here we introduce such a model, motivated by the widely used soft glassy rheology model, and show that it captures all the above rheological features.

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arXiv2019

Slow coarsening in jammed athermal soft particle suspensions

We simulate a densely jammed, athermal assembly of repulsive soft particles immersed in a solvent. Starting from an initial condition corresponding to a quench from a high temperature, we find non-trivial slow dynamics driven by a gradual release of stored elastic energy, with the root mean squared particle speed decaying as a power law in time with a fractional exponent. This decay is accompanied by the presence within the assembly of spatially localised and temporally intermittent `hot-spots' of non-affine deformation, connected by long-ranged swirls in the velocity field, reminiscent of the local plastic events and long-ranged elastic propagation that have been intensively studied in sheared amorphous materials. The pattern of hot-spots progressively coarsens, with the hot-spot size and separation slowly growing over time, and the associated velocity correlation length increasing as a sublinear power law. Each individual spot however exists only transiently, within an overall picture of strongly intermittent dynamics.

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arXiv2019

Linear instability of shear thinning pressure driven channel flow

We study theoretically pressure driven planar channel flow of shear thinning viscoelastic fluids. Combining linear stability analysis and full nonlinear simulation, we study the instability of an initially one-dimensional base state to the growth of two-dimensional perturbations with wavevector in the flow direction. We do so within three widely used constitutive models: the microscopically motivated Rolie-Poly model, and the phenomenological Johnson-Segalman and White-Metzner models. In each model, we find instability when the degree of shear thinning exceeds some level characterised by the logarithmic slope of the flow curve at its shallowest point. Specifically, we find instability for $n<n^*$, with $n^*\approx 0.21, 0.11$ and $0.30$ in the Rolie-Poly, Johnson-Segalman and White-Metzner models respectively. Within each model, we show that the critical pressure drop for the onset of instability obeys a criterion expressed in terms of this degree of shear thinning, $n$, together with the derivative of the first normal stress with respect to shear stress. Both shear thinning and rapid variations in first normal stress across the channel are therefore key ingredients driving the instability. In the Rolie-Poly and Johnson-Segalman models, the underlying mechanism appears to involve the destabilisation of a quasi-interface that exists in each half of the channel, across which the normal stress varies rapidly. In the White-Metzner model, no such quasi-interface exists, but the criterion for instability nonetheless appears to follow the same form as in the Rolie-Poly and Johnson-Segalman models. This presents an outstanding puzzle concerning any possibly generic nature of the instability mechanism. We finally make some briefly comments on the Giesekus model, which is rather different in its predictions from the other three.

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arXiv2019

Edge fracture instability in sheared complex fluids: onset criterion and possible mitigation strategy

We perform a detailed theoretical study of the edge fracture instability, which commonly destabilises the fluid-air interface during strong shear flows of entangled polymeric fluids, leading to unreliable rheological measurements. By means of direct nonlinear simulations, we map out phase diagrams showing the degree of edge fracture in the plane of the surface tension of the fluid-air interface and the imposed shear rate, within the Giesekus and Johnson-Segalman models, for different values of the nonlinear constitutive parameters that determine the dependencies on shear rate of the shear and normal stresses. The threshold for the onset of edge fracture is shown to be relatively robust against variations in the wetting angle where the fluid-air interface meets the hard walls of the flow cell, whereas the nonlinear dynamics depend strongly on wetting angle. We perform a linear stability calculation to derive an exact analytical expression for the onset of edge fracture, expressed in terms of the shear-rate derivative of the second normal stress difference, the shear-rate derivative of the shear stress (sometimes called the tangent viscosity), the jump in shear stress across the interface between the fluid and the outside air, the surface tension of that interface, and the rheometer gap size. Full agreement between our analytical calculation and nonlinear simulations is demonstrated. We also elucidate in detail the mechanism of edge fracture, and finally suggest a new way in which it might be mitigated in experimental practice. Some of the results in this paper were first announced in an earlier letter. The present manuscript provides additional simulation results, calculational details of the linear stability analysis, and more detailed discussion of the significance and limitations of our findings.

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arXiv2019

Long-term memory and delayed shear localisation in soft glassy materials

We study theoretically the dynamics of soft glassy materials during the process of stress relaxation following the rapid imposition of a shear strain. By detailed numerical simulations of a mesoscopic soft glassy rheology model and three different simplified continuum fluidity models, we show that a dramatic shear localisation instability arises, in which the strain field suddenly becomes heterogeneous within the sample, accompanied by a precipitous drop in the stress. Remarkably, this instability can arise at extremely long delay times after the strain was applied, due to the long-term memory inherent to glassy systems. The finding that a catastrophic mechanical instability can arise long after any deformation could have far reaching consequences for material processing and performance, and potentially also for delayed geophysical phenomena.

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arXiv2018

Dynamic vorticity banding in discontinuously shear thickening suspensions

It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions, because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show however that the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. We furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.

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arXiv2018

Edge-induced shear banding in entangled polymeric fluids

Despite decades of research, the question of whether solutions and melts of highly entangled polymers exhibit shear banding as their steady state response to a steadily imposed shear flow remains controversial. From a theoretical viewpoint, an important unanswered question is whether the underlying constitutive curve of shear stress $σ$ as a function of shear rate $\dotγ$ (for states of homogeneous shear) is monotonic, or has a region of negative slope, $dσ/d\dotγ<0$, which would trigger banding. Attempts to settle the question experimentally via velocimetry of the flow field inside the fluid are often confounded by an instability of the free surface where the sample meets the outside air, known as "edge fracture". Here we show by numerical simulation that in fact even only very modest edge disturbances - which are the precursor of full edge fracture but might well, in themselves, go unnoticed experimentally - can cause strong secondary flows in the form of shear bands that invade deep into the fluid bulk. Crucially, this is true even when the underlying constitutive curve is monotonically increasing, precluding true bulk shear banding in the absence of edge effects.

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arXiv2018

Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of soft glassy materials

We study theoretically shear banding in soft glassy materials subject to large amplitude time-periodic shear flows, considering separately the protocols of large amplitude oscillatory shear strain, large amplitude square or triangular or sawtooth strain rate, and large amplitude oscillatory shear stress. In each case, we find shear banding to be an important part of the material's flow response for a broad range of values of the frequency $ω$ and amplitude of the imposed oscillation. Crucially, and highly counterintuitively, in the glass phase this persists even to the lowest frequencies accessible numerically (that seems consistent with it persisting even when $ω\to 0$), although the soft glassy rheology model we use has an underlying monotonic constitutive curve of shear stress as a function of shear rate, and is therefore unable to support shear banding as its steady state response at constant shear rate. We attribute this to the repeated competition, within each flow cycle, of glassy aging and flow rejuvenation. Besides reporting significant banding in the glass phase, where the flow curve has a yield stress, we also observe it at noise temperatures just above the glass point, where the flow curve is of power law fluid form. Thus, our results suggest a predisposition to shear banding in flows of even extremely slow time-variation, for both aging yield stress fluids, and for power law fluids with sluggish relaxation timescales. We show that shear banding can have a pronounced effect on the shape of the Lissajous-Bowditch curves that are commonly used to fingerprint complex fluids rheologically. We therefore counsel caution in seeking to compute such curves calculations that impose upfront a homogeneous shear flow, discarding the possibility of banding. We also analyze the stress response to the imposed strain waveforms in terms of a `sequence of physical processes'.

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arXiv2017

Edge fracture in complex fluids

We study theoretically the edge fracture instability in sheared complex fluids, by means of linear stability analysis and direct nonlinear simulations. We derive an exact analytical expression for the onset of edge fracture in terms of the shear-rate derivative of the fluid's second normal stress difference, the shear-rate derivative of the shear stress, the jump in shear stress across the interface between the fluid and the outside medium (usually air), the surface tension of that interface, and the rheometer gap size. We provide a full mechanistic understanding of the edge fracture instability, carefully validated against our simulations. These findings, which are robust with respect to choice of rheological constitutive model, also suggest a possible route to mitigating edge fracture, potentially allowing experimentalists to achieve and accurately measure stronger flows than hitherto.

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arXiv2017

Necking after extensional filament stretching of complex fluids and soft solids

We perform linear stability analysis and nonlinear slender filament simulations of extensional necking in complex fluids and soft solids, during the stress relaxation process following an interrupted strain ramp. We start by deriving analytical criteria for necking within a highly simplified and generalised scalar constitutive model. Here, we find two different possible modes of necking: one associated with an upward curvature in the stress relaxation function on a log-linear plot, and another related to a carefully defined `elastic' derivative of the tensile force with respect to an imagined sudden strain increment. We showed these two criteria to agree fully with simulations of the Oldroyd B and Giesekus models of polymeric solutions, and with the RoliePoly model of more concentrated polymeric solutions and melts, without polymer chain stretch. With chain stretch included, we find a slightly more complicated analytical criterion for necking during the stress relaxation, with key ingredients that closely mirror counterpart ingredients of the simpler criteria obtained within the scalar model. We show this criterion to agree fully with slender filament simulations of the RoliePoly model with chain stretch, and with the scenario discussed by the Copenhagen group in Refs. [1, 2]. In particular, we see delayed necking after strain ramps with an accumulated strain exceeding ~ 0.7, for ramp rates exceeding the inverse chain stretch relaxation timescale. We discuss finally an analogy between this delayed necking following an interrupted extensional strain ramp and delayed shear banding following an interrupted shear strain ramp [3]. This work provides the counterpart, for interrupted extensional strain ramps, to earlier papers giving criteria for necking in the protocols of constant imposed Hencky strain rate [4] and of constant imposed tensile stress or constant imposed tensile force [5].

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arXiv2017

Shear Reversal in Dense Suspensions: The Challenge to Fabric Evolution Models from Simulation Data

Despite the industrial importance of dense suspensions of hard particles, few constitutive models for them have been proposed or tested. Most of these are effectively "fabric evolution models" (FEMs) based on a stress rule connecting the bulk stress to a rank-2 microstructural fabric tensor Q and a closed time-evolution equation for Q. In dense suspensions most of the stress comes from short-ranged pairwise steric or lubrication interactions at near-contacts, so a natural choice for Q is the deviatoric 2nd moment of the distribution P(p) of the near-contact orientations p. Here we test directly whether a closed time-evolution equation for such a Q can exist for inertialess non-Brownian hard spheres in a Newtonian solvent. We perform extensive numerical simulations for the evolution of P(p) under shear reversal, providing a stringent test for FEMs. We consider a generic class of these as defined by Hand (1962) constrained only by frame indifference. Motivated by the small microstructural anisotropy in the dense regime, we start with linear models and successively consider increasingly nonlinear ones. Based on these results we suggest that no closed FEM properly describes the dynamics of Q under reversal. We attribute this to the fact that Q gives a poor description of the microstructure during large parts of the microstructural evolution following shear reversal. Specifically, the truncation of P(p) at 2nd spherical harmonic level describes two-lobed distributions of near-contact orientations, whereas on reversal we observe distributions that are markedly four-lobed; moreover dP/dt (p) has oblique axes, not collinear with those of Q in the shear plane. This structure likely precludes any adequate closure at second-rank level. Instead, our numerical data suggest that closures involving the coupled evolution of both a fabric tensor and a fourth-rank tensor might be reasonably accurate.

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arXiv2017

Understanding rheological hysteresis in soft glassy materials

Motivated by recent experimental studies of rheological hysteresis in soft glassy materials, we study numerically strain rate sweeps in simple yield stress fluids and viscosity bifurcating yield stress fluids. Our simulations of downward followed by upward strain rate sweeps, performed within fluidity models and the soft glassy rheology model, successfully capture the experimentally observed monotonic decrease of the area of the rheological hysteresis loop with sweep time in simple yield stress fluids, and the bell shaped dependence of hysteresis loop area on sweep time in viscosity bifurcating fluids. We provide arguments explaining these two different functional forms in terms of differing tendencies of simple and viscosity bifurcating fluids to form shear bands during the sweeps, and show that the banding behaviour captured by our simulations indeed agrees with that reported experimentally. We also discuss the difference in hysteresis behaviour between inelastic and viscoelastic fluids. Our simulations qualitatively agree with the experimental data discussed here for four different soft glassy materials.

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arXiv2016

Triggers and signatures of shear banding in steady and time-dependent flows

This precis is aimed as a practical field-guide to situations in which shear banding might be expected in complex fluids subject to an applied shear flow. Separately for several of the most common flow protocols, it summarises the characteristic signatures in the measured bulk rheological signals that suggest the presence of banding in the underlying flow field. It does so both for a steady applied shear flow, and for the time-dependent protocols of shear startup, step stress, finite strain ramp, and large amplitude oscillatory shear. An important message is that banding might arise rather widely in flows with a strong enough time-dependence, even in fluids that do not support banding in a steadily applied shear flow. This suggests caution in comparing experimental data with theoretical calculations that assume a homogeneous shear flow. In a brief postlude, we also summarise criteria in similar spirit for the onset of necking in extensional filament stretching.

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arXiv2016

Criteria for extensional necking instability in complex fluids and soft solids. Part I: imposed Hencky strain rate protocol

We study the necking dynamics of a filament of complex fluid or soft solid in uniaxial tensile stretching at constant imposed Hencky strain rate $\dot\varepsilon$, 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). 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 numerically show them to hold in six popular constitutive models of polymers and soft glasses. Two distinct modes of necking instability are predicted. The first is relatively gentle, and sets in when the tensile stress signal first curves down as a function of the time $t$ (or accumulated strain $ε=\dot\varepsilon t$) 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 $\dot\varepsilon$). In the limit of fast flow $\dot\varepsilonτ\to\infty$, where $τ$ is the material's characteristic stress relaxation time, this second mode reduces to the Considére criterion for necking in solids. However we show that the Considére criterion fails to correctly predict the onset of necking in any viscoelastic regime of finite imposed $\dot\varepsilonτ$. Finally, we elucidate the way these modes of instability manifest themselves in entangled linear polymers, wormlike micelles and branched polymers. We demonstrate four distinct regimes as a function of imposed strain rate, consistent with experimental master curves.

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arXiv2016

Criteria for extensional necking instability in complex fluids and soft solids. Part II imposed tensile stress and force protocols

We study the necking of a filament of complex fluid or soft solid subject to uniaxial tensile stretching, under conditions of constant imposed stress and force, by means of linear stability analysis and nonlinear simulations. We demonstrate necking to be a flow instability that is an unavoidable consequence of the constitutive behaviour of essentially any viscoelastic material. We derive criteria for the onset of necking that can be reported in terms of characteristic signatures in the shapes of the experimentally measured material functions, and that should therefore apply universally to all materials. To confirm their generality, we show them to hold numerically in six constitutive models. Under conditions of constant stress, we find two distinct dynamical regimes as a function of time. In the first regime the strain rate quickly attains a value prescribed by the fluid's underlying homogeneous constitutive curve, at the given stress. In this first regime, no appreciable necking arises. A second regime then ensues in which the homogeneous flow destabilises to form a neck. This necking instability can occur via two distinct modes. The first mode is relatively gentle and arises in any regime where the slope of the constitutive curve is positive. It has a rate of necking per accumulated strain unit set by the inverse of the slope of the constitutive curve. The second mode sets in when a carefully defined `elastic derivative' of the tensile force first slopes down as a function of the time. We discuss the way in which these modes of instability manifest themselves in entangled polymeric fluids, demonstrating four distinct regimes of necking behaviour as a function of stress. Under conditions of constant imposed force, typically the flow sweeps up the underlying constitutive curve of the fluid in question, with instability to necking in any regime where that curve is positively sloping.

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