Onset Of Elastic Instability Research Articles

Quantum confinement effect in nanotwinned diamond

The success in enhancing diamond by introducing nanotwins opens a new frontier in the development of superhard materials. However, the underlying hardening mechanism of nanotwinned diamond (nt-diamond) remains elusive and a persistent research focus. In this study, we employ first-principles calculations to unveil the performance enhancement in nt-diamond mediated by quantum confinement effect. This effect is characterized by the non-uniform valence charge density of C-C bonds near the twin boundary, leading to incomplete bond breakage at the onset of elastic instability and identified as the key factor in delaying cracking. These findings not only contribute to establishing the theory of hardness in superhard materials, but also suggest new avenues for enhancing their mechanical performance through the introduction of heterogeneous structures and dopant atoms aligned with the principle of quantum confinement effect.

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate or the flow in a Taylor–Couette geometry, can become unstable to a three-dimensional time-dependent instability at conditions exceeding a critical Weissenberg ( $Wi$ ) number. However, the combined effects of fluid elasticity, shear thinning and finite inertia (as quantified by the Reynolds number $Re$ ) on the onset of elasto-inertial instabilities are not fully understood. Using a set of cone–plate geometries, we experimentally explore the entire $Wi$ – $Re$ phase space for a series of nonlinear viscoelastic fluids (with the dependence on shear rate $\dot{\gamma}$ quantified using a shear-thinning parameter $\beta _P(\dot {\gamma })$ ). We tune $\beta _P(\dot {\gamma })$ by varying the dissolved polymer concentration in solution. This progressively reduces shear thinning but leads to finite inertial effects before the onset of elastic instability, and thus naturally results in elasto-inertial coupling. Time-resolved rheometric measurements and flow visualization experiments allow us to investigate the effects of flow geometry, and document the combined effects of varying $Wi, Re$ and $\beta _P(\dot {\gamma })$ on the emergence of secondary motions at the onset of instability. The resulting critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and the destabilizing effects of inertia. We extend the curved streamline instability criterion of Pakdel & McKinley (Phys. Rev. Lett., vol. 77, no. 12, 1996, p. 2459) for the onset of purely elastic instability in curvilinear geometries by using scaling arguments to incorporate shear thinning and finite inertial effects. The augmented condition facilitates predictions of the onset of instability over a broader range of flow conditions, and thus bridges the gap between purely elastic and elasto-inertial curved streamline instabilities.

Out-of-Plane Instability and Vibrations of a Flexible Circular Arch Under a Moving Load

Flexible lightweight arched structures are finding increasing use as components in smart engineering applications. Such structures are prone to various types of instability under moving transverse loads. Here, we study deformation and vibration of a hinged circular arch under a uniformly moving point load using geometrically-exact rod theory to allow for large pre- and post-buckling deformations. We first consider the quasi-statics problem, without inertia. We find that for arches with relatively large opening angle ([Formula: see text]160[Formula: see text]) a sufficiently large traversing load will induce an out-of-plane flopping instability, instead of the in-plane collapse (snap-through) that dominates failure of arches with smaller opening angle. In a subsequent dynamics study, with full account of inertia, we then explore the effect of the speed of the load on this lateral buckling. We find speed to have a delaying (or even suppressing) effect on the onset of three-dimensional bending–torsional vibrations and instability. Based on numerical computations we propose a power law describing this effect. Our results highlight the role of inertia in the onset of elastic instability.

Towards Predicting the Onset of Elastic Turbulence in Complex Geometries

Flow of complex fluids in porous structures is pertinent in many biological and industrial processes. For these applications, elastic turbulence, a viscoelastic instability occurring at low Re—arising from a non-trivial coupling of fluid rheology and flow geometry—is a common and relevant effect because of significant over-proportional increase in pressure drop and spatio-temporal distortion of the flow field. Therefore, significant efforts have been made to predict the onset of elastic turbulence in flow geometries with constrictions. The onset of flow perturbations to fluid streamlines is not adequately captured by Deborah and Weissenberg numbers. The introduction of more complex dimensionless numbers such as the M-criterion, which was meant as a simple and pragmatic method to predict the onset of elastic instabilities as an order-of-magnitude estimate, has been successful for simpler geometries. However, for more complex geometries which are encountered in many relevant applications, sometimes discrepancies between experimental observation and M-criteria prediction have been encountered. So far these discrepancies have been mainly attributed to the emergence from disorder. In this experimental study, we employ a single channel with multiple constrictions at varying distance and aspect ratios. We show that adjacent constrictions can interact via non-laminar flow field instabilities caused by a combination of individual geometry and viscoelastic rheology depending (besides other factors) explicitly on the distance between adjacent constrictions. This provides intuitive insight on a more conceptual level why the M-criteria predictions are not more precise. Our findings suggest that coupling of rheological effects and fluid geometry is more complex and implicit and controlled by more length scales than are currently employed. For translating bulk fluid, rheology determined by classical rheometry into the effective behaviour in complex porous geometries requires consideration of more than only one repeat element. Our findings open the path towards more accurate prediction of the onset of elastic turbulence, which many applications will benefit.Article HighlightsWe demonstrate that adjacent constrictions “interact” via the non-laminar flow fields caused by individual constrictions, implying that the coupling of rheological effects and fluid geometry is more complex and implicit.The concept of characterizing fluid rheology independent of flow geometry and later coupling back to the geometry of interest via dimensionless numbers may fall short of relevant length scales, such as the separation of constrictions which control the overlap of flow fields.By providing direct experimental evidence illustrating the cause of the shortcoming of the status-quo, the expected impact of this work is to challenge and augment existing concepts that will ultimately lead to the correct prediction of the onset of elastic turbulence.

Characterization of Effective Diffusion within Viscoelastic Fluids with Elastic Instabilities

We considered effective diffusion, characterized by magnitudes of effective diffusion coefficients, in order to quantify mass transport due to the onset and development of elastic instabilities. Effective diffusion coefficient magnitudes were determined using different analytic approaches, as they were applied to tracked visualizations of fluorescein dye front variations, as circumferential advection was imposed upon a flow environment produced using a rotating Couette flow arrangement. Effective diffusion coefficient results were provided for a range of flow shear rates, which were produced using different Couette flow rotation speeds and two different flow environment fluid depths. To visualize the flow behavior within the rotating Couette flow environment, minute amounts of fluorescein dye were injected into the center of the flow container using a syringe pump. This dye was then redistributed within the flow by radial diffusion only when no disk rotation was used, and by radial diffusion and by circumferential advection when disk rotation was present. Associated effective diffusion coefficient values, for the latter arrangement, were compared to coefficients values with no disk rotation, which were due to molecular diffusion alone, in order to quantify enhancements due to elastic instabilities. Experiments were conducted using viscoelastic fluids, which were based on a 65% sucrose solution, with different polymer concentrations ranging from 0 ppm to 300 ppm. Associated Reynolds numbers based on the fluid depth and radially averaged maximum flow velocity ranged from 0.00 to 0.5. The resulting effective diffusion coefficient values for different flow shear rates and polymer concentrations quantified the onset of elastic instabilities, as well as significant and dramatic changes to local mass transport magnitudes, which are associated with the further development of elastic instabilities.

Effects of rheological properties on heat transfer enhancements by elastic instability in von-Karman swirling flow

Elastic instability is proposed as a promising method to intensify heat transfer under very low Reynolds number conditions. However, the onset of elastic instability and its influence on heat transfer is highly dependent on the rheological properties of polymer solution, which has not been revealed. By varying polymer concentration, sucrose proportion and the degree of salinity, the heat transfer performance due to the variations of rheology is investigated in a swirling flow configuration between parallel plates. The results indicate that both the increase of polymer concentration and the reduction of the salinity can induce elastic instability easily, leading to a better heat transfer performance when the swirling velocity is fixed. However, the salinity effects become weakened as the swirling velocity continually increases and the maximum enhancement becomes independent on salinity. In particular, the heat transfer performance based on pure elastic instability shows larger enhancement than that of inertial-elastic instability at low Reynolds number.

Effects of salinity on the onset of elastic turbulence in swirling flow and curvilinear microchannels

Elastic turbulence, which is sensitive to geometry and polymer rheology, has shown great potential for improving the performance of mixing, heat transfer, and even oil recovery. Recent studies showed the importance of the rheological properties of polymer solutions on the onset of elastic turbulence. However, variations of rheological properties based on polymer sensitivities such as salinity and its corresponding effects on the elastic turbulence have not been revealed. This work investigated systematically the effects of salinity on the onset of elastic turbulence in both swirling flow and curvilinear microchannels. The variations of statistical properties, such as probability distribution functions (PDFs) and power spectral density of injected power (PSD), were analyzed for characterization. The onset conditions of elastic turbulence are postponed by high salinity, which is consistent with the mixing performance in a curvilinear microchannel. A salinity independent power-law exponent at a value of −4.3 is observed in a fully developed elastic regime for all polymer solutions. Particularly, the diffusion of fluorescein at a low flow rate in the microchannel is possible due to the existence of a steady secondary flow before the onset of elastic instability.

Wing twisting by elastic instability: A purely passive approach

The design of morphing structures requires attaining concurrently light-weight, load-carrying and shape adaptable systems that minimize complexity, actuation requirements and part count. Exploiting the external loads to produce local stiffness variations induced by elastic instabilities offers the potential to activate shape deformations purely passively. Following this approach, we present the structural response study of wings capable of attaining compliant buckling-induced twisting deformations. The structure is designed such that a specific level of aerodynamic load triggers the elastic instability in a shear web part of the wing box. The buckling-induced variation in effective shear stiffness, resulting from the development of a stable, reversible diagonal tension field, leads to a twisting deformation. The structural behaviour is characterized by two drastically different mechanical responses, delimited by the onset of elastic instability. The influence of the buckling component design on the attainable change in spanwise angle of attack is investigated for the specific case of a finite composite wing structure under aerodynamic loads. The type of composite material, its thickness, and the fibre orientation are the considered design parameters. The buckling-induced variation in twist angle, and the corresponding aerodynamic pressure redistribution on the wing, is exploited for achieving load alleviation, reducing the global lift coefficient and decreasing the wing root bending moment.

Electro-elastic instabilities in cross-shaped microchannels

Purely-elastic flow instabilities have been extensively investigated in pressure-driven systems, but little attention has been paid to electrically-driven systems. This work attempts to fill this gap by investigating the electroosmotic flow of viscoelastic fluids in cross-slot and flow-focusing micro-devices, with a special focus on the onset of elastic instabilities. Relying on the visualization of dye patterns, the onset of electro-elastic instabilities for dilute and semi-dilute polyacrylamide solutions was observed at a low bulk Weissenberg number, O(10−2), through a direct transition from a steady symmetric flow to a time-dependent asymmetric flow. Time-series analysis of the dye interface patterns revealed a broad range of excitation frequencies with a power-law decay. The elastic instabilities observed seem not to improve significantly the mixing efficiency, contrarily to what has been previously reported for unstable pressure-driven flows. Numerical simulations of the electroosmotic flows were also carried out with a finite-volume method, showing that the observed electro-elastic instabilities can be predicted numerically. Both the experimental and numerical results suggest that the large stresses developed inside the electric double layer, coupled with the streamline curvature around the geometry corners, play a fundamental role in the onset and in the dynamics of the observed electro-elastic instabilities. However, further research is needed to clarify the mechanism of electro-elastic instabilities, and, in general, to improve our understanding of the complex behavior of polymeric fluids in electroosmotic flows.

Analytic analysis of auxetic metamaterials through analogy with rigid link systems.

In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite-element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson's ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling-induced auxetic metamaterials.

Extra dissipation and flow uniformization due to elastic instabilities of shear-thinning polymer solutions in model porous media.

We study flows of hydrolized polyacrylamide solutions in two dimensional porous media made using microfluidics, for which elastic effects are dominant. We focus on semi-dilute solutions (0.1%-0.4%) which exhibit a strong shear thinning behavior. We systematically measure the pressure drop and find that the effective permeability is dramatically higher than predicted when the Weissenberg number is greater than about 10. Observations of the streamlines of the flow reveal that this effect coincides with the onset of elastic instabilities. Moreover, and importantly for applications, we show using local measurements that the mean flow is modified: it appears to be more uniform at high Weissenberg number than for Newtonian fluids. These observations are compared and discussed using pore network simulations, which account for the effect of disorder and shear thinning on the flow properties.

Conditions for the onset of elastic and material instabilities in hyperelastic materials

Several constitutive inequalities have been proposed in the literature to quantify the notion that ‘stress increases with strain’ in an elastic material. Due to some inherent shortcomings in them, which we discuss, we propose a new tensorial criterion for isotropic materials. We also present necessary conditions in terms of elasticity tensors for the onset of elastic instabilities.

Atomic pattern formation at the onset of stress-induced elastic instability: Fracture versus phase change

A systematic theoretical study is presented of the stress-induced structural response of initially cubic single crystals to uniaxial [100] loading based on elastic stability analysis and isostress molecular-dynamics simulations through a classical description of interatomic interactions in model metallic crystals. Special emphasis is placed on the study of the atomic pattern formation characteristics in the crystal's structural response to loading at and beyond the onset of elastic instability. The instability is reached at a rigorously defined critical stress level that occurs in association with the vanishing of a shear modulus, i.e., when ${C}_{22}∕{C}_{23}\ensuremath{-}1=0$, where ${C}_{rs}$ are stress-dependent elastic moduli. Although the atomic mechanism for the onset of instability is invariant, two divergent atomic processes are found to occur beyond the onset of instability, depending on subtle differences in the elastic properties of the crystals. Our analyses and simulations of a crystal model with the relatively small initial value of ${C}_{22}∕{C}_{23}\ensuremath{-}1=0.41$ (based on the elastic moduli of copper) reveal an inhomogeneous structural transformation mechanism, through the creation of individual rotating domains that lead to formation of a new hexagonal single crystal without loss of strength. This theoretical result is consistent with what is known experimentally for metals with relatively small values of $({C}_{22}∕{C}_{23}\ensuremath{-}1)$, e.g., certain copper alloys and the alkali metals, which can undergo various cubic-to-hexagonal structural transformations. However, a crystal model based on the elastic moduli of nickel, with the larger initial value of ${C}_{22}∕{C}_{23}\ensuremath{-}1=0.73$, fails to exhibit domain rotation beyond the onset of elastic instability and, as a result, the initial destabilization of the crystal structure then leads to fracture.