Viscoplastic Flow Research Articles

Dendrite initiation and propagation in lithium metal solid-state batteries.

All-solid-state batteries with a Li anode and ceramic electrolyte have the potential to deliver a step change in performance compared with today's Li-ion batteries1,2. However, Li dendrites (filaments) form on charging at practical rates and penetrate the ceramic electrolyte, leading to short circuit and cell failure3,4. Previous models of dendrite penetration have generally focused on a single process for dendrite initiation and propagation, with Li driving the crack at its tip5-9. Here we show that initiation and propagation are separate processes. Initiation arises from Li deposition into subsurface pores, by means of microcracks that connect the pores to the surface. Once filled, further charging builds pressure in the pores owing to theslow extrusion of Li (viscoplastic flow) back to the surface, leading to cracking. By contrast, dendrite propagation occurs by wedge opening, with Li driving the dry crack from the rear, not the tip. Whereas initiation is determined by the local (microscopic) fracture strength at the grain boundaries, the pore size, pore population density and current density, propagation depends on the (macroscopic) fracture toughness of the ceramic, the length of the Li dendrite (filament) that partially occupies the dry crack, current density, stack pressure and the charge capacity accessed during each cycle. Lower stack pressures suppress propagation, markedly extending the number of cycles before short circuit in cells in which dendrites have initiated.

Pipe Flow of Viscoplastic Fluids and Analytical Predictions of Concrete Pumping Based on the Shear-Stress-Dependent Parabolic Model

This study investigates the Hagen–Poiseuille pipe flow of viscoplastic fluids, focusing on analytical predictions of concrete pumping using the shear-stress-dependent parabolic model, extending analytical studies to a nonlinear rheological model with easily accessible experimental parameters. Research novelty and highlights encompass solving the steady laminar pipe flow for viscoplastic fluids described by the parabolic model, presenting detailed results for the two-fluid parabolic model, and introducing a computational app implementing theoretical findings. The parabolic model outperforms linear models, such as the Bingham model, in accuracy by accounting for the nonlinearity in the flow curves (i.e., shear stress and shear rate relations) of pumped concrete. The influence of rheological parameters on these relations is analyzed, and their versatility is demonstrated by a Wolfram Mathematica-based application program. The analytical approach developed in this work is adaptable for other models with shear stress as the independent variable, offering valuable insights into viscoplastic fluid flows.

Obstructed free-surface viscoplastic flow on an inclined plane

The interaction of steady free-surface flows of viscoplastic material with a surface-piercing obstruction of square cross-section on an inclined plane is investigated theoretically. The flow thickness increases upstream of the obstruction and decreases in its lee. The flow depends on two dimensionless parameters: an aspect ratio that relates the flow thickness, the obstruction width and the plane inclination; and a Bingham number that quantifies the magnitude of the yield stress relative to the gravitationally induced stresses. Flows with a non-vanishing yield stress always form a static ‘dead’ zone in a neighbourhood of the upstream and downstream stagnation points. For relatively wide obstructions, a deep ‘ponded’ region develops upstream with a small dead zone, while the deflected flow reconnects over relatively long distances downstream. The depth of the upstream pond increases with both the dimensionless yield stress and width of the obstruction, while the unyielded dead zone varies primarily with the yield stress. Both are predicted asymptotically by balancing the volume flux of fluid into and out of the ponded region. When the obstruction is narrow, the perturbation to the depth of the oncoming flow is reduced. It exhibits fore–aft antisymmetry, while the dead zone is symmetric to leading order. Increasing the yield stress leads to larger dead zones that eventually encompass all of the upstream- and downstream-facing boundaries of the obstruction and fully divert the flow. Results for obstructions with circular and rhomboidal cross-sections are also presented and illustrate the effects of boundary shape on the properties of the steady flow.

Multilayer models for hydrostatic Herschel-Bulkley viscoplastic flows

Multilayer models for hydrostatic Herschel-Bulkley viscoplastic flows

A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity

We propose a stabilized linear tetrahedral finite element method for static, finite elasticity problems involving compressible and nearly incompressible materials. Our approach relies on a mixed formulation, in which the nodal displacement unknown filed is complemented by a nodal Jacobian determinant unknown field. This approach is simple to implement in practical applications (e.g., in commercial software), since it only requires information already available when computing the Newton–Raphson tangent matrix associated with irreducible (i.e., displacement-based) finite element formulations. By nature, the proposed method is easily extensible to nonlinear models involving visco-plastic flow. An extensive suite of numerical tests in two and three dimensions is presented, to demonstrate the performance of the method.

Viscoplastic flows in thin superhydrophobic channels

Via numerical computations, we study plane Poiseuille flow of a viscoplastic fluid in channels with the presence of a superhydrophobic (SH) groovy lower wall, where air is trapped inside the SH wall cavities. We assume this liquid/air interface to be flat while it is pinned at the groove edges. Our main focus is on the thin channel limit, for which the channel height is typically smaller than the groove period. To quantify the viscoplastic rheological behaviour, we rely on the Bingham model, via the Papanastasiou regularization method. We consider a no-slip boundary condition at the liquid/solid contacts while we model the liquid/air interface boundary using the Navier slip law. Focusing on the creeping flow limit (i.e. the Reynolds number is fixed to R=0.01), our main flow parameters are the Bingham number (B), the slip number (b), the groove periodicity length (ℓ), and the slip area fraction (φ). Our computational results quantify the effects of these parameters on the flow velocity fields, the unyielded plug zones and their areas, the effective slip lengths, and the friction factors. The shape of the unyielded plug zones are captured, allowing us to classify our flows into four main regimes, based on the characteristics of the unyielded zones, in particular the presence/absence of a broken center plug and/or an SH wall plug. We also find that the effective slip length generally increases with an increase in b, converging to a profile once an SH wall plug appears. Finally, the friction factor decreases with an increase in b, especially at larger B.

Mixed convection Casson polymeric flow from a nonlinear stretching surface with radiative flux and non‐Fourier thermal relaxation effects: Computation with CSNIS

AbstractThermal non‐Newtonian polymer coating flows is growing as a major area in materials processing. Inspired by new developments in this field which require more sophisticated mathematical models, the current investigation examines the laminar viscoplastic boundary layer flow and mixed convective heat transfer over a power‐law nonlinear stretching surface. To simulate thermal relaxation effects the hyperbolic Cattaneo‐Christov heat flux model is deployed. The non‐Newtonian polymer characteristics are described by employing the Casson flow model. High temperature conditions invoke thermal radiation flux which is analyzed with an algebraic flux model. Via robust similarity transformations, the primitive partial differential conservation equations for momentum and energy equations are rendered into a system of coupled non‐linear ordinary differential equations with associated wall and free stream boundary conditions. The emerging boundary value problem is solved numerically with an efficient Chebyshev Spectral Newton Iterative scheme (CSNIS), in the MATLAB platform. The resulting solutions are discussed for different emerging parameters using graphs and tables. Validation is included with special cases from the literature. With increasing power law stretching index increases, the flow is decelerated, and temperatures are reduced. Increment in mixed convection parameter boosts the velocity but suppresses temperature and thermal boundary layer thickness. Increasing non‐Fourier Deborah number, temperatures are depleted whereas with increasing radiative flux parameter they are increased. With elevation in Casson non‐Newtonian parameter, velocity is decreased whereas temperature is enhanced and Nusselt number is suppressed.

Geophysical surveys for non‐invasive characterization of sinkhole phenomena: A case study of Murisengo

AbstractThe present research investigates the morphology and genetical mechanism of a sinkhole which occurred in 2019 in Murisengo (NW Italy). This landform is representative of several subsidence phenomena that often concern the Monferrato area (NW Italy). In concomitance with the appearance of the sinkhole at the surface, a cone of detrital material was found in the drifts of a nearby underground quarry. A geological survey was performed in the underground quarry in order to understand the interaction between the geological and geostructural features of the rock body and the generation of the sinkhole. Moreover, the underground sinkhole morphology was investigated through electrical resistivity tomography (ERT) surveys performed at the surface. The ERT outputs were combined to obtain a 3D image of the phenomenon and the 3D reconstruction was then compared with the geomorphological and structural setting of the area. Results suggest that a viscoplastic flow of clay‐rich sediments within a conduit in the gypsum bedrock (suffusion process) generated the sinkhole.

Anderson acceleration for a regularized Bingham model

AbstractThis article studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson acceleration (AA) applied to a Picard iteration, and we show accelerated convergence of the method by applying AA theory (recently developed by the authors) to the iteration, after showing sufficient smoothness properties of the associated fixed point operator. Numerical tests of spatial convergence are provided, as are results of the model for 2D and 3D driven cavity simulations. For each numerical test, the proposed nonlinear solver is also tested and shown to be very effective and robust with respect to the regularization parameter as it goes to zero.

A physically based elasto-viscoplastic constitutive model for modeling the hot deformation and microstructure evolution of a near α Ti alloy

In this work, a general elasto-viscoplastic constitutive model incorporating a finite strain viscoplastic flow law, the Kocks-Mecking dislocation density evolution, work hardening, stress softening due to dynamic recovery and dynamic recrystallization (DRX), and the Johnson-Mehl-Avarmi-Kolmogorov (JMAK) DRX kinetics was established for modeling the deformation and microstructure evolution of a near-α Ti alloy. A full-implicit stress integration scheme was proposed to implement the constitutive model into the commercial FEM solver ABAQUS/Standard. Isothermal hot compression experiments under various deformation conditions and detailed microstructure characterizations were conducted to study the deformation and DRX behaviors of the alloy, as well as to validate the developed material model. The alloy exhibits a typical discontinuous DRX behavior, macroscopically sensitive to various deformation conditions and microscopically strongly affected by the orientation of prior grains. The simulation results regarding the macroscopic flow stress curves and the local volume fractions of DRX in various regions in the specimen agree well with the experimental results. The proposed material model and the robust numerical implemental scheme can be extended to consider more physical deformation mechanisms and microstructure evolution of advanced structural metals and alloys.

Viscoplastic Flow in the Material of a Cylindrical Layer Suspended on a Rigid Shaft under the Conditions of Its Variable Rotation

Viscoplastic Flow in the Material of a Cylindrical Layer Suspended on a Rigid Shaft under the Conditions of Its Variable Rotation

Numerical investigation of thermo-hydraulic features of viscoplastic flow in wavy channels

In the present work, the thermo- hydraulic characteristics are studied for a laminar viscoplastic flow through raccoon and serpentine type wavy channels. The results are presented by varying Bingham number (Bn), power-law index (n), Reynolds number (Re), dimensionless amplitude, and wave number in the physically justified ranges. It is found that the size of the recirculatory zone decreases with Bn and the zone disappears at the higher Bn values. The topology of the yielded-unyielded region highly depends on the geometry and the range of Bn. Moreover, the value of average Nusselt number decreases with n. With the increase in Bn, average Nusselt number gradually decreases up to a critical Bn value and then increases sharply at higher Bn values. Interestingly, the wavy channel is only advantageous at smaller Bn values up to a critical limit. The variation of performance factor (PF) strongly depends on the combined effect of rheological and geometrical parameters. Besides, results for raccoon and serpentine channels are highly dependent on the ranges of amplitude, wave number, Bn, and n.

Viscoplastic flow between hinged plates

The incompressible motion of viscoplastic fluid between two semi-infinite rigid plates, hinged at their ends and rotating towards one another at constant angular velocity, generates self-similar flow fields because there is no externally imposed length scale in the absence of inertia. The magnitude of the strain rate scales with the angular velocity of the plates and the dimensionless deviatoric stresses are functions only of the polar angle and a dimensionless measure of the yield stress; they are independent of the radial distance from the corner. These flows feature unyielded regions adjacent to the boundaries for sufficiently large angles between the plates. Moreover, when the dimensionless yield stress is large, there are viscoplastic boundary layers that are attached to the boundary or the plug, the asymptotic structures of which are constructed.

A bounding surface viscoplastic damage model for time-dependent rock deformation

A novel bounding surface viscoplastic damage (BS-VPD) framework is proposed in this study for capturing the time-dependent rock deformation driven by subcritical cracking. Our constitutive creep model has been established via imposing effective control over stress-state evolution with respect to the characteristic surfaces while enforcing strictly the thermodynamic constraint. In particular, a new viscoplastic flow rule is first developed by upscaling the microscopic subcritical cracking towards macroscopic creep characterization based on the bounding surface concept. A continuum damage criterion has then been deduced from the maximum dissipation principle for capturing realistically the strain hardening and damage softening during sustained creep loading. By further completing the model with a novel strategy for regulating the interactive surface evolution, we have thus reproduced successfully the progressive transition from stable subcritical cracking characteristic of decelerating creep into unstable propagation during accelerating rupture. In addition, a hierarchical procedure has also been formulated in this study to facilitate straightforward calibration via conventional laboratory testing, and the applicability of our BS-VPD model is then verified against constant strain-rate and creep tests of brittle rocks representing distinct lithologies (i.e., granite, sandstone, and gneiss). The close agreement between model simulation and experimental measurement suggests that the proposed BS-VPD framework is able to capture faithfully the trimodal creep behaviour of brittle rocks across primary, secondary, and tertiary regimes.

Viscoplastic Flow in the Material of a Cylindrical Layer Suspended on a Rigid Shaft under the Conditions of Its Variable Rotation

The development of viscoplastic flow in the material of a cylindrical layer placed on a rigid cylindrical shaft and rotating with it around their common axis is calculated. Depending on the increasing speed of rotation up to the maximum, the place and time points of the beginning of the viscoplastic flow, the patterns of propagation of the flow area, the changing strains and stresses in the deformable material are determined. As a condition for viscoplastic flow, the corresponding generalization of the condition for maximum octahedral stresses is taken. For the purposes of testing the calculation programs, an exact solution of the problem of a steady viscoplastic flow of a material during rotation of a compound cylinder at a constant speed has been obtained.

Transient solute dispersion in electro‐osmotic viscoplastic flow in a microchannel

AbstractThe transport of a neutral solute in incompressible electro‐osmotic flow of Bingham plastic non‐Newtonian liquid flowing through a microchannel is studied theoretically. The flow is driven by a constant axially applied electric field. The non‐dimensional conservation equations with associated boundary conditions are solved with Gill's series expansion technique. The whole transport process is analyzed using three transport coefficients, namely, advection coefficient, dispersion coefficient and the apparent asymmetry coefficient, respectively. The mean concentration distribution of the solute is calculated via a third‐order approximation of the series expansion. The study investigates the collective effects of yield stress and electric double layer (EDL) thickness (inverse Debye length) on the transport of solute. The long‐term behaviour of mean concentration distribution is shown to be accurately predicted by second‐order approximations; however, utilizing third or higher order approximations in Gill's series expansion enables a more refined analysis of the small and moderate time behavior of transport coefficients. The present analysis is relevant to emerging applications in bio‐microfluidics exploiting electroviscous fluent media.

Numerical Study of Viscoplastic Flows Using a Multigrid Initialization Algorithm

In this paper, an innovative methodology to handle the numerical simulation of viscoplastic flows is proposed based on a multigrid initialization algorithm in conjunction with the SIMPLE procedure. The governing equations for incompressible flow, which consist of continuity and momentum equations, are solved on a collocated grid by combining the finite volume discretization and Rhie and chow interpolation for pressure–velocity coupling. Using the proposed solver in combination with the regularization scheme of Papanastasiou, we chose the square lid-driven cavity flow and pipe flow as test cases for validation and discussion. In doing so, we study the influence of the Bingham number and the Reynolds number on the development of rigid areas and the features of the vortices within the flow domain. Pipe flow results illustrate the flow’s response to the stress growth parameter values. We show that the representation of the yield surface and the plug zone is influenced by the chosen value. Regarding viscoplastic flows, our experiments demonstrate that our approach based on using the multigrid method as an initialization procedure makes a significant contribution by outperforming the classic single grid method. A computation speed-up ratio of 6.45 was achieved for the finest grid size (320 × 320).

К ВЫБОРУ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ДЛЯ КОРРЕКТНОГО РЕШЕНИЯ КРАЕВОЙ ЗАДАЧИ ТЕЧЕНИЯ ТОНКОГО СЛОЯ ПЛАСТИЧЕСКОГО МАТЕРИАЛА ПРИ СЖАТИИ ОБРАЗЦА В ВИДЕ КРУГОВОГО СЕКТОРА

The class of flow problems for a relatively thin layer of plastic metal includes most of the practical problems of rolling and forging and stamping production. With the difference that during rolling, rolling, rotary drawing and other similar processes, the deformation zone is localized, and in stamping processes, the entire volume of metal is redistributed in the cavity of the stream, flowing into its various elements, forming the necessary shape of the forging, often the shape is elongated and of small thickness. It is natural to believe that the same mathematical models can be used for the analysis of processes close in kinematics, but in different formulations. The article substantiates the choice of a mathematical model for the theoretical solution of the boundary value problem of constrained compression of a sample in the form of a circular sector based on the results of the experiment. The article presents the results of an analytical study of the boundary value problem of the viscoplastic flow of a thin layer of metal located between thin rough plates moving towards each other. Exact solutions based on the classical formulation in the framework of an "ideal fluid" and "viscoplastic fluid" are given. A real experiment is described for assessing the effect of shear stresses averaged over the layer thickness on the kinematics of the flow of a plastic layer. Comparison of the obtained experimental and analytical simulation results allows us to evaluate the correctness of the chosen mathematical model, which can be used to describe the flows. When designing and introducing into production most high-performance technological processes for processing materials by pressure, not only the numerical values of technological parameters are required, but also the prediction of the behavior of the material during loading. At present, problem-oriented software systems are available based on numerical methods for solving, for example, the finite element method (FEM), various problems of continuum mechanics (MCS). However, without the development of fundamental approaches to the formulation, schematization and analytical solution of boundary value problems, it would hardly be possible to create reliable mathematical models for modern computer systems. Therefore, the further development of theoretical approaches to solving boundary value problems of the MSS is relevant.

A MODIFIED MODEL OF KARAGOZIAN & CASE CONCRETE IN LOGOS SOFTWARE PACKAGE

The paper describes a local model of concrete on the basis of Karagozian & Case (K&C) approach that is successfully used for computed description of the behavior of concrete and reinforced concrete constructions under dynamic loadings. A modified option of the K&C model is presented aiming at the expansion of functional capabilities of the model and providing the details of its computer realization, which is scarcely described in publications. Basic ratios of the model are provided: the equation of state of the environment with compacting; limiting surfaces of the initial yielding flow, maximum and residual strengths that depend on pressure; limiting surfaces as a function of the third invariant in the form of William-Vonke; evolution of the concrete damage; partially-associated plastic yielding to account for dilatancy; simplified regularization of the model at the stage of the loss of strength of the environment; account for isotropic reinforcement, the strain rate using the strengthening factor of the concrete; auto-generation of the model parameters. Besides, the following options have been introduced: degradation description of the elastic hardness of the concrete to simulate cyclic loading; account for the concrete behavior as a function of the strain rate by the mechanism of viscoplastic flow; model regularizing by the set energy of the concrete destruction. The represented modified model of K&C concrete is realized in explicit dynamic module of LOGOS software package for a supercomputer. The initial data and the scheme of the model algorithm are described. Model realization has been verified using test examples of simulation of the concrete samples behavior under quasi-static loading until destruction: uniaxial and triaxial compression, uniaxial and two-axial compression and stretching, cyclic uniaxial stretching. The considered problems show compliance of the K&C model and the behavior of the concrete in the experiments.

МОДЕЛИРОВАНИЕ И СРАВНЕНИЕ РЕЗУЛЬТАТОВ ТОЧНОГО АНАЛИТИЧЕСКОГО РЕШЕНИЯ КРАЕВОЙ ЗАДАЧИ ТЕЧЕНИЯ В ТОНКОМ СЛОЕ С ЭКСПЕРИМЕНТАЛЬНЫМИ ДАННЫМИ

Many technological processes of metal forming include deformation of an elongated workpiece by approaching tools, the contact surfaces of which have shallow grooved cavities. A common special case are stamps or part of their contact surfaces, which are planes: sites for draft and some types of harvesting streams. The article is devoted to mathematical modeling of the flow of a thin metal layer over rough surfaces. The article presents the results of an analytical study of the boundary value problem of the viscoplastic flow of a thin layer of metal located between thin rough plates moving towards each other. Exact solutions based on the classical formulation in the framework of an "ideal fluid" and "viscoplastic fluid" are given. A real experiment is described for assessing the effect of shear stresses averaged over the layer thickness on the kinematics of the flow of a plastic layer. In order to assess the effect of shear stresses averaged over the layer thickness on the flow kinematics, and, in particular, near fixed boundaries, experiments were carried out and the results on settlement between converging rigid plates of a thin plastic sample bounded by fixed walls and initially having the shape of a rectangle in plan are analyzed. . The fixed walls of the tool are located along the long sides of the rectangle. Experimental regularities have been established. Spreading of samples occurs as expected, i.e., along straight streamlines parallel to the long side of the rectangle, or along the rays of a circular sector. It was found that the longitudinal displacements near the immovable walls noticeably lag behind the displacements far from the boundary, and the maximum displacements are observed on the line of symmetry of the sample with respect to the immovable walls. This fact indicates the presence of nonzero shear stresses and (velocities) of deformations in the considered flows of a thin plastic layer. Comparison of the obtained experimental and analytical simulation results allows us to evaluate the correctness of the chosen mathematical model, which can be used to describe the flows.