Anisotropic Rheology Research Articles

Anisotropic rheology and friction of suspended graphene

Graphene is a powerful membrane prototype for both applications and fundamental research. Rheological phenomena including indentation, twisting, and wrinkling in deposited and suspended graphene are actively investigated to unravel the mechanical laws at the nanoscale. Most studies focused on isotropic setups, while realistic graphene membranes are often subject to strongly anisotropic constraints, with important consequences for the rheology, strain, indentation, and friction in engineering conditions. Graphene in particular is recognized as the thinnest solid lubricant material and a large amount of work has been dedicated to understanding the fundamentals mechanisms of this effect and to unravel parameters relevant to its technological development. Here, we experimentally show how graphene's frictional response to an external indenter is severely altered by conditions of anisotropic suspension, specifically when graphene is clamped across a long and narrow groove. Results show that the friction coefficient is significant when the tip is sliding parallel to the groove while becoming ultralow in the orthogonal direction. While the experimental data suggest that----rather unexpectedly----prestrain of the graphene sheet as a result of clamping is negligible, the key to understanding the underlying mechanism is provided by simulations. The paramount mechanism is provided by the extra anisotropic strain induced from indentation under anisotropic constraints, which in turn produces an anisotropic stiffening of the graphene. While the focus of this work is on graphene, we believe our experimental protocol and the physical mechanism uncovered by our model can be applicable to other 2D membranelike materials.

Influence of anisotropic rheology on wave processes in sea ice

Influence of anisotropic rheology on wave processes in sea ice

Numerical model for compression molding process of hybridly laminated thermoplastic composites based on anisotropic rheology

In this work, a numerical model is developed for simulating the compression molding process of a hybrid composite material, alternately laminated with continuous and discontinuous fiber-reinforced layers. Although various process simulation models are already available for plastic materials embedding each type of the reinforcements, they are incapable of simultaneously dealing with the continuity and discontinuity. Here, thermomechanical behavior of the continuous fiber-reinforced layer and rheological behavior of the discontinuous fiber-reinforced layer are separately modeled and eventually integrated assuming perfectly bonded interfaces. The unified process model is applied to the simulation of compression molding of a full-scale battery pack structure of an electric vehicle. A simple yet robust rheology test is utilized to measure rheological properties necessary for the numerical simulation. In the full-scale simulation, thermoforming process of the hybrid charge is successfully simulated and fiber direction changes due to the suspension flow are also predicted. It is found that the reoriented fibers significantly affect stress distributions at the final stage of the process. The process model developed in the present study can be implemented into either the Lagrangian or Eulerian framework.

On viscous propulsion in active transversely isotropic media

Very low Reynolds number propulsion is a topic of enduring interest due to its importance in biological systems such as sperm migration in the female reproductive tract. Motivated by the fibrous nature of cervical mucus, several recent studies have considered the effect of anisotropic rheology; these studies have generally employed the classical swimming sheet model of G. I. Taylor. The models of Cupples et al. (J. Fluid Mech. vol. 812, 2017, pp. 501–524) and Shi & Powers (Phys. Rev. Fluids vol. 2, 2017, 123102) consider related problems which in a common limit (passive, slightly anisotropic) make different predictions regarding how swimming speed depends on alignment angle. In the present paper we find that this discrepancy is due to missing terms in the analysis of Cupples et al., and that when these terms are correctly included, the models agree in their common limit. We further explore the predictions of the corrected model for both passive and active cases; it is found that for certain combinations of alignment angle and activity parameter, propulsion is halted; in other cases the small amplitude asymptotic expansion is no longer valid, motivating future numerical study.

Influences of transversely isotropic rheology and translational diffusion on the stability of active suspensions.

Suspensions of self-motile, elongated particles are a topic of significant current interest, exemplifying a form of ‘active matter’. Examples include self-propelling bacteria, algae and sperm, and artificial swimmers. Ericksen's model of a transversely isotropic fluid (Ericksen 1960 Colloid Polym. Sci. 173, 117–122 (doi:10.1007/bf01502416)) treats suspensions of non-motile particles as a continuum with an evolving preferred direction; this model describes fibrous materials as diverse as extracellular matrix, textile tufts and plant cell walls. Director-dependent effects are incorporated through a modified stress tensor with four viscosity-like parameters. By making fundamental connections with recent models for active suspensions, we propose a modification to Ericksen's model, mainly the inclusion of self-motility; this can be considered the simplest description of an oriented suspension including transversely isotropic effects. Motivated by the fact that transversely isotropic fluids exhibit modified flow stability, we conduct a linear stability analysis of two distinct cases, aligned and isotropic suspensions of elongated active particles. Novel aspects include the anisotropic rheology and translational diffusion. In general, anisotropic effects increase the instability of small perturbations, while translational diffusion stabilizes a range of wave-directions and, in some cases, a finite range of wavenumbers, thus emphasizing that both anisotropy and translational diffusion can have important effects in these systems.

Linear Rayleigh–Bénard stability of a transversely isotropic fluid

Suspended fibres significantly alter fluid rheology, as exhibited in for example solutions of DNA, RNA and synthetic biological nanofibres. It is of interest to determine how this altered rheology affects flow stability. Motivated by the fact thermal gradients may occur in biomolecular analytic devices, and recent stability results, we examine the problem of Rayleigh–Bénard convection of the transversely isotropic fluid of Ericksen. A transversely isotropic fluid treats these suspensions as a continuum with an evolving preferred direction, through a modified stress tensor incorporating four viscosity-like parameters. We consider the linear stability of a stationary, passive, transversely isotropic fluid contained between two parallel boundaries, with the lower boundary at a higher temperature than the upper. To determine the marginal stability curves the Chebyshev collocation method is applied, and we consider a range of initially uniform preferred directions, from horizontal to vertical, and three orders of magnitude in the viscosity-like anisotropic parameters. Determining the critical wave and Rayleigh numbers, we find that transversely isotropic effects delay the onset of instability; this effect is felt most strongly through the incorporation of the anisotropic shear viscosity, although the anisotropic extensional viscosity also contributes. Our analysis confirms the importance of anisotropic rheology in the setting of convection.

Effects of crystal preferred orientation on upper-mantle flow near plate boundaries: rheologic feedbacks and seismic anisotropy

Insight into upper-mantle processes can be gained by linking flow-induced mineral alignment to regional deformation and seismic anisotropy patterns. Through a series of linked micro–macro scale numerical experiments, we explore the rheologic effects of crystal preferred orientation (CPO) and evaluate the magnitude of possible impacts on the pattern of flow and associated seismic signals for mantle that includes a cooling, thickening young oceanic lithosphere. The CPO and associated anisotropic rheology, computed by a micromechanical polycrystal model, are coupled with a large scale flow model (Eulerian Finite Element method) via a local viscosity tensor field, which quantifies the stress:strain rate response of a textured polycrystal. CPO is computed along streamlines throughout the model space and the corresponding viscosity tensor field at each element defines the local properties for the next iteration of the flow field. Stable flow and CPO distributions were obtained after several iterations for the two dislocation glide cases tested: linear and nonlinear stress:strain rate polycrystal behaviour. The textured olivine polycrystals are found to have anisotropic viscosity tensors in a significant portion of the model space. This directional dependence in strength impacts the pattern of upper-mantle flow. For background asthenosphere viscosity of ∼1020 Pa s and a rigid lithosphere, the modification of the corner flow pattern is not drastic but the change could have geologic implications. Feedback in the development of CPO occurs, particularly in the region immediately below the base of the lithosphere. Stronger fabric is predicted below the flanks of a spreading centre for fully coupled, power-law polycrystals than was determined using prior linear, intermediate coupling polycrystal models. The predicted SKS splitting is modestly different (∼0.5 s) between the intermediate and fully coupled cases for oceanic plates less than 20 Myr old. The magnitude of azimuthal anisotropy for surface waves, on the other hand, is predicted to be twice as large for fully coupled power-law flow/polycrystals than for linear, intermediate coupled flow/polycrystal models.

Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations.

The flow of glaciers and polar ice sheets is controlled by the highly anisotropic rheology of ice crystals that have hexagonal symmetry (ice lh). To improve our knowledge of ice sheet dynamics, it is necessary to understand how dynamic recrystallization (DRX) controls ice microstructures and rheology at different boundary conditions that range from pure shear flattening at the top to simple shear near the base of the sheets. We present a series of two-dimensional numerical simulations that couple ice deformation with DRX of various intensities, paying special attention to the effect of boundary conditions. The simulations show how similar orientations of c-axis maxima with respect to the finite deformation direction develop regardless of the amount of DRX and applied boundary conditions. In pure shear this direction is parallel to the maximum compressional stress, while it rotates towards the shear direction in simple shear. This leads to strain hardening and increased activity of non-basal slip systems in pure shear and to strain softening in simple shear. Therefore, it is expected that ice is effectively weaker in the lower parts of the ice sheets than in the upper parts. Strain-rate localization occurs in all simulations, especially in simple shear cases. Recrystallization suppresses localization, which necessitates the activation of hard, non-basal slip systems.This article is part of the themed issue 'Microdynamics of ice'.

Modelled stress distributions at the Dome Summit South borehole, Law Dome, East Antarctica: a comparison of anisotropic ice flow relations

AbstractIn this study we compare the anisotropic flow relations for polycrystalline ice of Azuma and Goto-Azuma (1996), Thorsteinsson (2002), Placidi and others (2010) and Budd and others (2013). Observations from the Dome Summit South (DSS) ice-coring site at Law Dome, East Antarctica, are used to model the vertical distribution of deviatoric stress components at the borehole site. The flow relations in which the anisotropic rheology is parameterized by a scalar function, so that the strain-rate and deviatoric stress tensor components are collinear, provide simple shear and vertical compression deviatoric stress profiles that are most consistent with laboratory observations of tertiary creep in combined stress configurations. Those flow relations where (1) the anisotropy is derived from the magnitude of applied stresses resolved onto the basal planes of individual grains and (2) the macroscopic deformation is obtained via homogenization of individual grain responses provide stress estimates less consistent with laboratory observations. This is most evident in combined simple shear and vertical compression flow regimes where shear is dominant. Our results highlight the difficulties associated with developing flow relations which incorporate a physically based description of microdeformation processes. In particular, this requires that all relevant microdeformation, recrystallization and recovery processes are adequately parameterized.

Sea ice volume and age: Sensitivity to physical parameterizations and thickness resolution in the CICE sea ice model

New dynamics parameterizations in Version 5 of the Los Alamos Sea Ice Model, CICE, feature an anisotropic rheology and variable drag coefficients. This study investigates their effect on Arctic sea ice volume and age simulations, along with the effects of several pre-existing model options: a parameter that represents the mean cumulative area of ice participating in ridging, the resolution of the ice thickness distribution, and the resolution of the vertical temperature and salinity profiles.By increasing shear stress between floes, the anisotropic rheology slows the ice motion, producing a thicker, older ice pack. The inclusion of variable drag coefficients, which depend on modeled roughness elements such as deformed ice and melt pond edges, leads to thinner ice and a more realistic simulation of sea ice age. Several feedback processes act to enhance differences among the runs. Notably, if less open water is produced mechanically through ice deformational processes, the simulated ice thins relative to runs with more mechanically produced open water. Thermodynamic processes can have opposing effects on ice age and volume; for instance, growth of new ice increases the volume while decreasing the age of the pack. Therefore, age data provides additional information useful for differentiating among process parameterization effects and sensitivities to other model parameters.Resolution of thicker ice types is crucial for proper modeling of sea ice volume, because the volume of ice in the thicker ice categories determines the total ice volume. Model thickness categories tend to focus resolution for thinner ice; this paper demonstrates that 5 ice thickness categories are not enough to accurately resolve the ice thickness distribution for simulations of ice volume.

Impact of a new anisotropic rheology on simulations of Arctic sea ice

AbstractA new rheology that explicitly accounts for the subcontinuum anisotropy of the sea ice cover is implemented into the Los Alamos sea ice model. This is in contrast to all models of sea ice included in global circulation models that use an isotropic rheology. The model contains one new prognostic variable, the local structure tensor, which quantifies the degree of anisotropy of the sea ice, and two parameters that set the time scale of the evolution of this tensor. The anisotropic rheology provides a subcontinuum description of the mechanical behavior of sea ice and accounts for a continuum scale stress with large shear to compression ratio and tensile stress component. Results over the Arctic of a stand‐alone version of the model are presented and anisotropic model sensitivity runs are compared with a reference elasto‐visco‐plastic simulation. Under realistic forcing sea ice quickly becomes highly anisotropic over large length scales, as is observed from satellite imagery. The influence of the new rheology on the state and dynamics of the sea ice cover is discussed. Our reference anisotropic run reveals that the new rheology leads to a substantial change of the spatial distribution of ice thickness and ice drift relative to the reference standard visco‐plastic isotropic run, with ice thickness regionally increased by more than 1 m, and ice speed reduced by up to 50%.

Anisotropic rheology during grain boundary diffusion creep and its relation to grain rotation, grain boundary sliding and superplasticity

The response of periodic microstructures to deformation can be analysed rigorously and this provides guidance in understanding more complex microstructures. When deforming by diffusion creep accompanied by sliding, irregular hexagons are shown to be anisotropic in their rheology. Analytic solutions are derived in which grain rotation is a key aspect of the deformation. If grain boundaries cannot support shear stress, the polycrystal viscosity is extremely anisotropic. There are two orthogonal directions of zero strength: sliding and rotation cooperate to allow strain parallel to these directions to be accomplished without any dissolution or plating. When a linear velocity/shear stress relationship is introduced for grain boundaries, the anisotropy is less extreme, but two weak directions still exist along which polycrystal strength is controlled only by the grain boundary “viscosity”. Irregular hexagons are characterised by four parameters. A particular subset of hexagons defined by two parameters, which includes regular hexagons as well as some elongate shapes, shows singular behaviour. Grain shapes that are close to that of the subset may exhibit large grain rotation rates and have no well-defined rheology unless there is a finite grain boundary viscosity. This new analysis explains why microstructures based on irregular but near equiaxed grains show high rotation rates during diffusion creep and it provides a framework for understanding strength anisotropy during diffusion creep.

Microstructures and rheology of the Earth's upper mantle inferred from a multiscale approach

Abstract The strongly anisotropic rheology of olivine polycrystals, associated to their microstructure, constitutes a key feature affecting the dynamics of the Earth's upper mantle. High pressure deformation experiments carried out on olivine single crystals under synchrotron radiation, together with estimations of lattice friction based on first-principle calculations, show a transition from easy [100] to easy [001] slips as pressure and temperature (thus depth) increases. We input these data at the slip system level into the second-order extension of the self-consistent scheme to assess microstructure evolution along a typical flow pattern beneath an oceanic spreading center.

On the effects of anisotropic rheology on ice flow, internal structure, and the age‐depth relationship at ice divides

We use numerical modeling with a full‐system Stokes solver to elucidate the effects of nonlinear rheology and strain‐induced anisotropy on ice flow at ice divides. We find that anisotropic rheology profoundly affects the shape of both isochrone layering and surface topography. Anisotropic effects cause the formation of a downward curving fold, i.e., a syncline, in isochrones in the lower central area beneath the ice divide. When the resulting syncline is superimposed on the well‐known Raymond anticline, a double‐peaked Raymond bump is formed. Furthermore, to each side of the Raymond bump, flanking synclines are formed. In addition, anisotropic effects are found to give rise to a subtle concavity in the surface profile to both sides of the summit. The lower center syncline, the flanking synclines, and the near‐summit surface concavity have all previously been observed in nature, but hitherto no explanation for the genesis of these features has been given. We compare modeling results with radiograms collected from Fuchs Ice Piedmont and Kealey Ice Rise, Antarctica. Good overall agreement is found. In particular, we are able to reproduce all observed qualitative features of surface geometry and internal layering by including, and only by including, the effects of induced nonlinear rheological anisotropy on flow. Rheological anisotropy has the potential to profoundly affect the age distribution with depth, and caution must be exercised when estimating age of ice from ice cores with an isotropic model. The occurrence of linear features parallel to the ridge of ice divides, often seen in satellite imagery, is indicative of long‐term stability rather than signs of ongoing ice divide migration as previously suggested. Such ice divides are ideal locations for extracting ice cores.

Anisotropic rheology and directional mechanotransduction in vascular endothelial cells

Adherent cells remodel their cytoskeleton, including its directionality, in response to directional mechanical stimuli with consequent redistribution of intracellular forces and modulation of cell function. We analyzed the temporal and spatial changes in magnitude and directionality of the cytoplasmic creep compliance (Gamma) in confluent cultures of bovine aortic endothelial cells subjected to continuous laminar flow shear stresses. We extended particle tracking microrheology to determine at each point in the cytoplasm the principal directions along which Gamma is maximal and minimal. Under static condition, the cells have polygonal shapes without specific alignment. Although Gamma of each cell exhibits directionality with varying principal directions, Gamma averaged over the whole cell population is isotropic. After continuous laminar flow shear stresses, all cells gradually elongate and the directions of maximal and minimal Gamma become, respectively, parallel and perpendicular to flow direction. This mechanical alignment is accompanied by a transition of the cytoplasm to be more fluid-like along the flow direction and more solid-like along the perpendicular direction; at the same time Gamma increases at the downstream part of the cells. The resulting directional anisotropy and spatial inhomogeneity of cytoplasmic rheology may play an important role in mechanotransduction in adherent cells by providing a means to sense the direction of mechanical stimuli.

Prediction of anisotropy from flow models: A comparison of three methods

Observations of anisotropy in Earth are used regularly as constraints for models of deformation, using various assumptions about the relationship between deformation and the resulting anisotropic fabric. We compare three methods for calculating fabric from velocity fields: tracking of finite strain ellipses, a kinematic crystallographic code, and the evolution of directors. We find that the use of the finite strain ellipse provides only limited prediction capabilities, as it cannot reproduce experimental observations that involve recrystallization. The crystallographic code we tested (a variant of the popular code D‐Rex) provides a more complete fabric prediction, but at a much higher computational cost. The directors method provides an intermediate solution: while it does not include some of the more complex crystallographic processes that D‐Rex does, the results of this method closely resemble those of D‐Rex, at a lower computational cost. The directors are also capable of tracking anisotropy at much larger strains than D‐Rex. We conclude that when computation speed is important, for example, in self‐consistent geodynamic models with anisotropic rheology, the directors method provides an appropriate approximation.

The rise of Newtonian drops in a nematic liquid crystal

We simulate the rise of Newtonian drops in a nematic liquid crystal parallel to the far-field molecular orientation. The moving interface is computed in a diffuse-interface framework, and the anisotropic rheology of the liquid crystal is represented by the Leslie–Ericksen theory, regularized to permit topological defects. Results reveal interesting coupling between the flow field and the orientational field surrounding the drop, especially the defect configuration. The flow generally sweeps the point and ring defects downstream, and may transform a ring defect into a point defect. The stability of these defects and their transformation are depicted in a phase diagram in terms of the Ericksen number and the ratio between surface anchoring and bulk elastic energies. The nematic orientation affects the flow field in return. Drops with planar anchoring on the surface rise faster than those with homeotropic anchoring, and the former features a vortex ring in the wake. These are attributed to the viscous anisotropy of the nematic. With homeotropic anchoring, the drop rising velocity experiences an overshoot, owing to the transformation of the initial surface ring defect to a satellite point defect. With both types of anchoring, the drag coefficient of the drop decreases with increasing Ericksen number as the flow-alignment of the nematic orientation reduces the effective viscosity of the liquid crystal.

Anisotropic rheology of a cubic medium and implications for geological materials

Dislocation creep, which is the dominant deformation mechanism in the upper mantle, results in a non-Newtonian anisotropic rheology. The implication of non-Newtonian rheology has been quite extensively studied in geodynamic models but the anisotropic aspect remains poorly investigated. In this paper, we propose to fill this gap by (1) introducing a simple mathematical description of anisotropic viscosity and (2) illustrating the link between plastic crystal deformation and bulk material rheology. The study relies on the highest symmetry of the anisotropic tensor, a cubic symmetry, for which anisotropy is characterized by one parameter only, δ. First-order implications of anisotropy are quantitatively explored as a function of δ. The effective rheology of the material is described as a function of the orientation of the crystals and of the imposed stress and the validity of the isotropic approximation is discussed. The model, applied to ringwoodite, a cubic crystal with spinel-type structure, predicts that the dynamics of the transition zone in the Earth's mantle is going to be strongly affected by mechanical anisotropy.

Rheological anisotropy of the Earth’s mantle and attenuation of seismic waves

The nonlinear integral (having memory) model previously proposed by the author for the description of the dislocation rheology of mantle rocks is generalized to the case of crystals with anisotropic rheology. The latter is caused by a large difference between the effective viscosities associated with dislocation glide and dislocation climb (in the crystallographic coordinate system, the dislocation glide governs simple shear, whereas the dislocation climb governs pure shear). Since the mantle is polycrystalline and crystal grains an order of a millimeter in size are oriented chaotically, anisotropy vanishes with volume averaging. However, convective flows in the mantle produce large strains and lead to a preferred orientation of grains and, thereby, anisotropy of the upper mantle. The lower mantle is dominated by diffusion rheology, which cannot cause anisotropy. The mantle rheological anisotropy gives rise to anisotropic attenuation of seismic waves. It is shown that the attenuation depends on the polarization and direction of seismic waves and on the parameters of the rheological model.

Rheological characterization of continuous fibre composites in oscillatory shear flow

Abstract The anisotropic rheology of a model composite consisting of a temperature-sensitive viscous liquid matrix reinforced by aligned and virtually inextensible fibres of nylon has been studied experimentally using a custom-built linear oscillator. The composite was characterized dynamically both along and transverse to the fibre direction over a wide frequency range and for different fibre volume concentrations. Towards the limit of zero shear the composite was found to exhibit a yield stress. The temperature dependence of the matrix dynamic viscosity was used to study the dependence of the longitudinal and transverse dynamic viscosities of the composite on the dynamic viscosity of the matrix. The dependence of the composite dynamic viscosities on fibre volume concentration is compared with models of the steady shear dependence for aligned fibre systems that have been reported in the literature.