Effect Of Shear Stress Research Articles

Shear Stress Markedly Alters the Proteomic Response to Hypoxia in Human Pulmonary Endothelial Cells.

Blood flow produces shear stress that homeostatically regulates the phenotype of pulmonary endothelial cells, exerting antiinflammatory and antithrombotic actions and maintaining normal barrier function. Hypoxia due to diseases, such as chronic obstructive pulmonary disease (COPD), causes vasoconstriction, increased vascular resistance, and pulmonary hypertension. Hypoxia-induced changes in endothelial function play a central role in the development of pulmonary hypertension. However, the interactive effects of hypoxia and shear stress on the pulmonary endothelial phenotype have not been studied. Human pulmonary microvascular endothelial cells were cultured in normoxia or hypoxia while subjected to physiological shear stress or in static conditions. Unbiased proteomics was used to identify hypoxia-induced changes in protein expression. Using publicly available single-cell RNA sequencing datasets, differences in gene expression between the alveolar endothelial cells from COPD and healthy lungs were identified. Sixty proteins were identified whose expression changed in response to hypoxia in conditions of physiological shear stress but not in static conditions. These included proteins that are crucial for endothelial homeostasis (e.g., JAM-A [junctional adhesion molecule A], ERG [ETS transcription factor ERG]) or implicated in pulmonary hypertension (e.g., thrombospondin-1). Fifty-five of these 60 have not been previously implicated in the development of hypoxic lung diseases. mRNA for 5 of the 60 (ERG, MCRIP1 [MAPK regulated corepressor interacting protein 1], EIF4A2 [eukaryotic translation initiation factor 4A2], HSP90AA1 [heat shock protein 90 alpha family class A member 1], and DNAJA1 [DnaJ Hsp40 (heat shock protein family) member A1]) showed similar changes in the alveolar endothelial cells of COPD compared with healthy lungs in females but not in males. These data show that the proteomic responses of the pulmonary microvascular endothelium to hypoxia are significantly altered by shear stress and suggest that these shear-hypoxia interactions are important in the development of hypoxic pulmonary vascular disease.

A mathematical model for assessing shear induced bleeding risk

PurposeThe objective of this study is to develop a bleeding risk model for assessing device-induced bleeding risk in patients supported with blood contact medical devices (BCMDs). MethodsThe mathematical model for evaluating bleeding risk considers the effects of shear stress on von Willebrand factor (vWF) unfolding, high molecular weight multimers-vWF (HMWM-vWF) degradation, platelet activation and receptor shedding and platelet-vWF binding ability. Functions of the effect of shear stress on the above factors are fitted/employed and solved by the Eulerian transport equation. An axial flow-through Couette device and two clinical VADs which are HeartWare Ventricular Assist Device (HVAD) and HeartMate II (HM II) blood pump were employed to perform the simulation to evaluate platelet receptor shedding (GPIbα and GPIIb/IIIa), loss of HWMW-vWF, platelet-vWF binding ability and bleeding risk for validating the accuracy of our model. ResultsThe platelet-vWF binding ability after being subjected to high shear region in the axial flow-through Couette device predicted by our bleeding model was highly consistent with reported experimental data. As indicated by our CFD simulation results in the axial flow-through Couette device, it can find that an increase in shear stress led to a decrease in the adhesion ability of platelets on vWF, while the binding ability of vWF with platelets first increase and then decrease as shear stress elevates gradually beyond a threshold. The factor of exposure time can enhance the effect of shear stress. Additionally, the shear-induced bleeding risk predicted by our model increases with increasing shear stress and exposure time in an axial flow-through Couette device. As indicated by our numerical model, the bleeding risk in HVAD was higher than HMII, which is highly consistent with the meta-analysis based on clinical statistics. Our simulation investigations in these two clinical VADs also found that HVAD caused a higher rate of platelet receptor shedding and lower damage to HWMW-vWF than HeartMate II. The high shear stress generated in the narrow and turbulent regions of both VADs was the underlying cause of device-induced bleeding. ConclusionIn this study, the shear-induced bleeding risk predicted by our bleeding model in axial flow-through Couette device and two clinical VADs is consistent or highly correlated with experimental and clinical findings, which proves the accuracy of our bleeding model. Our bleeding model can be used to aid the development of new BCMDs with improved functional characteristics and biocompatibility, and help to reduce risk of device-induced adverse events in patients.

Different roles of P2X4- and P2Y1-receptors in the atrial pathogenesis during prolonged pressure overload.

Pressure overload (PO) involve increase in interstitial fluid shear in cardiac muscle during cardiac cycles due to detachment of myocytes from the extracellular matrix and myocyte slippage. However, the effects of shear stress on cardiac muscle and their pathophysiological roles are poorly understood. We have recently discovered that shear stress induces global Ca2+ waves via activation of P2 purinergic receptors in atrial myocytes by ATP released from the cells, and that this ATP release is mediated by connexin 43 (Cx43) gap junction hemichannels. In this study, we investigated role of shear stress signaling in PO-induced atrial remodeling and failure. We used a transverse aortic constriction (TAC) rat model to increase afterload and examined shear stress responses and remodeling of their signaling molecules during the development of pathological phenotypes by progressive TAC. After 5-week TAC, atrial dimension was enlarged with ventricular hypertrophy, which was followed by severe atrial dilation as well as ventricular failure at long-term (>20-week) TAC. Atrial myocytes were enlarged following 5-week TAC, which was maintained during more prolonged TAC. In the 5-week-TAC left atrial (LA) cells, ATP release was increased with no changes in Cx43 expression and in Cx43 hemichannel-mediated dye (calcein) flux. At this stage, however, function (cation current) of P2X4 receptor (P2X4R) and their protein expressions were largely enhanced. In failed LA cells, reduction in the Cx43 expression and smaller Cx43 hemichannel-mediated dye flux were observed. In failed LA myocytes, shear-induced longitudinal Ca2+ waves that were mediated by P2Y1 receptor (P2Y1R), were enhanced with higher P2Y1R expression. The opposite changes in the shear-induced responses mediated by P2X4R and P2Y1R and in their expressions suggest that P2X4R and P2Y1R may play beneficial and harmful role, respectively, in the PO-dependent atrial pathogenesis.

A Dual DIC System for Analysis of Dynamic Mechanical Properties of Large Sandstone under Uniaxial Compression Load

In this paper, an experiment is carried out to acquire the dynamic mechanical properties of a simulated sandstone tunnel by a dual DIC system. The sandstone tunnel is simulated by large sandstone with a prefabricated hole in the center. The speckle size required by DIC system was evaluated, and the results showed that for large specimens a marker pen could be used to spot speckles and make sure that the diameters of speckle points in an image should be ranged from three to five pixels. The dual DIC system is composed of a low-speed camera and a high-speed camera. The low-speed camera is used to record the speckle patterns of the sandstone in one side during the whole process of compression load, and the high-speed camera is placed in the other side to record speckle patterns for 11.5 seconds before and after failure. It is realized that monitoring whole process of deformation and instantaneous failure in two directions is required. Measurement results are effectively analyzed. The results are shown as follows: At the initial stage of loading the sandstone is in an elastic stage without macroscopic cracks. With the increase in compression load the sandstone has several small stress releases and several obvious macroscopic cracks. In the final stage of loading, the distribution of normal stress and shear stress are almost the same, and cracks are subjected to the coupling effect of normal stress and shear stress. The two ends of the prefabricated hole perpendicular to the applied load direction are prone to cracks parallel to the applied load direction.

The proneness assessment of a mineral deposit to tectonic rockburst: A case-study of Yuzhnoe deposit

The procedure of the proneness assessment to tectonic rockburst (with fault-slip mechanism) is insufficiently described in guidelines and regulatory documents, thus, additional investigations are required in this regard. The tectonic rockburst proneness criteria at Yuzhnoe deposit, Primorye are considered to be the location of large faults in the modern stress field and the critical stress state of rock mass. It is found that the maximum (compression) principal stress, reconstructed using the methods of tectonophysics and the data on rock mass faulting, fits the orientation of the maximum compression in the stress field, determined by instrumental measurements. In this stress field, in the plane nearby the plane of the effective maximum shear stresses, a large fault exists and is traced underground and on ground surface for more than 10 km. The analysis of geodynamics at the deposit, deformation of boundaries of underground excavations, core discing in wells far from the underground excavations, as well as rock bursts both at the study deposit and at the similar Nikolaevskoe deposit nearby shows that the level of the natural stresses at Yuzhnoe deposit is rather high and the rock mass is everywhere in the critical stress state. Yuzhnoe deposit is assumed to be to tectonic rockburst prone as both criteria are fulfilled: the rock massif is in the critical stress state and there is large fault which lies comfortably for mutual movement of rock blocks.The studies were carried out using facilities of the Center for Shared Use of Scientific Equipment at the Center for Processing and Storage of Scientific Data of the Far East Branch of the Russian Academy of Sciences, supported by the Ministry of Science and Higher Education of the Russian Federation, Project No. 075-15-2021-663.

Sensitivity and Calibration of Three‐Dimensional SPH Formulations in Large‐Scale Landslide Modeling

AbstractNumerical prediction of landslide runout and deposition is important for estimating landslide risk and developing mitigation plans. The choice of a suitable model and its parameters and a confident calibration strategy are crucial for numerical simulations. Here, we evaluated two constitutive models with a three‐dimensional smoothed particle hydrodynamics (SPH) method by simulating the catastrophic 11 October 2018 Baige landslide. The results indicate that both the soil mechanic and fluid models can capture the dynamic runout and deposition morphology while using different values of input parameters. A point‐wise comparison of deposit elevation can minimize the calibration error. Numerical models were constrained accurately by utilizing both the static observation data and dynamic seismic signals. The effects of friction on deep‐seated landslides motion and deposition are more significant than cohesion. The 3D model includes the effects of shear stresses and velocities inside the material body, resulting in a reduced friction coefficient compared to the 2D model (e.g., depth‐averaged model). Our study highlights the potential of the 3D SPH method for modeling large‐scale complex landslides.

Hydrological and erosion responses of steep spoil heaps to taproot and fibrous root grasses under simulated rainfalls

Spoil heaps, resulting from excavation and backfilling activities at construction sites, are one of the most important risk sources of soil erosion, threatening local ecosystems and even leading to geological disasters. However, after revegetation, spoil heaps can be transformed into available land resources such as cultivated land and forest land. Previous studies have reported the runoff and sediment reduction benefits of different vegetation measures on spoil heaps, while little information has been documented about what differences in the taproot and fibrous root grasses were transferred into the differences in hydrological and erosion processes. This study compared the effects of taproot (Artemisia gmelinii (A. gmelinii)) and fibrous root (Cynodon dactylon (C. dactylon)) grasses on soil erosion and runoff production processes and the reduction benefits of spoil heaps with silt loam soil. A series of rainfall events at three intensities (0.8, 1.2, and 1.8 mm min−1) were simulated on runoff plots (length of 3.0 m and width of 1.0 m) under treatments of A. gmelinii, C. dactylon, and bare soil (BS, as control) (each treatment was replicated), and the initial runoff time (IRT), saturated hydraulic conductivity, runoff rate (RR), flow velocity, and soil loss rate (SLR) were measured. The results showed that grasses delayed the IRTs on spoil heaps by 0.69–12.96 min compared BS, and the delay effects were more significant for fibrous root grass than for taproot grass. The soil loss reduction benefits (91.1 %) of the two kinds of grass were approximately 2.2 times greater than those of runoff volume reduction (42.1 %), and shear stress could be used to predict the soil loss rate following power functions (R2 = 0.72–0.85) for the grass-covered plots. The taproot grass exhibited a higher erosion reduction than fibrous root grass and is thus preferred to control the soil erosion of spoil heaps. Taproot grass has a greater stem diameter and can insert deeper into spoil heaps to consolidate the soil particles, which can improve roughness and hydraulic resistance, thereby producing a lower effective hydraulic shear stress that is directly exerted on soil particles. This study enhances the understanding of different grasses on the water erosion process and mechanism of spoil heaps and provides scientific guidance for selecting erosion control practices.

Damage Initiation Analysis of a Tension Stiffened Composite PRSEUS Panel Based on Modified Hashin Criteria

In this study, a damaged three-stringer PRSEUS panel simulating a midbay-to-midbay damage scenario was modelled in Abaqus and analyzed under tension. Moreover, employing the Abaqus built-in Hashin failure criteria verified the reliability of the criteria in predicting damage initiation with great accuracy. Further, these criteria were implemented via UMAT to investigate the effect of shear stress on the analysis, indicating that manipulating the coefficient of shear stress contribution led to a significant enhancement in analysis accuracy. Lastly, the same procedure was followed in the analysis of a repaired three-stringer panel, validating once again the adequacy of the adopted approach and simultaneously highlighting the efficiency of the repair technique in restoring load carrying of the PRSEUS panel. This study may provide a dependable reference presenting a simplified and significantly less computationally demanding approach for damage analysis composite structures and their repair, in addition to further applying these techniques to access the damage-arresting capabilities of these structures.

Co-culture models of endothelial cells, macrophages, and vascular smooth muscle cells for the study of the natural history of atherosclerosis.

This work aims to present a fast, affordable, and reproducible three-cell co-culture system that could represent the different cellular mechanisms of atherosclerosis, extending from atherogenesis to pathological intimal thickening. We built four culture models: (i) Culture model #1 (representing normal arterial intima), where human coronary artery endothelial cells were added on top of Matrigel-coated collagen type I matrix, (ii) Culture model #2 (representing atherogenesis), which demonstrated the subendothelial accumulation and oxidative modification of low-density lipoproteins (LDL), (iii) Culture model #3 (representing intimal xanthomas), which demonstrated the monocyte adhesion to the endothelial cell monolayer, transmigration into the subendothelial space, and transformation to lipid-laden macrophages, (iv) Culture model #4 (representing pathological intimal thickening), which incorporated multiple layers of human coronary artery smooth muscle cells within the matrix. Coupling this model with different shear stress conditions revealed the effect of low shear stress on the oxidative modification of LDL and the upregulation of pro-inflammatory molecules and matrix-degrading enzymes. Using electron microscopy, immunofluorescence confocal microscopy, protein and mRNA quantification assays, we showed that the behaviors exhibited by the endothelial cells, macrophages and vascular smooth muscle cells in these models were very similar to those exhibited by these cell types in nascent and intermediate atherosclerotic plaques in humans. The preparation time of the cultures was 24 hours. We present three-cell co-culture models of human atherosclerosis. These models have the potential to allow cost- and time-effective investigations of the mechanobiology of atherosclerosis and new anti-atherosclerotic drug therapies.

Modification of the swirling well cell culture model to alter shear stress metrics.

Effects of hemodynamic shear stress on endothelial cells have been extensively investigated using the "swirling well" method, in which cells are cultured in dishes or multiwell plates placed on an orbital shaker. A wave rotates around the well, producing complex patterns of shear. The method allows chronic exposure to flow with high throughput at low cost but has two disadvantages: a number of shear stress characteristics change in a broadly similar way from the center to the edge of the well, and cells at one location in the well may release mediators into the medium that affect the behavior of cells at other locations, exposed to different shears. These properties make it challenging to correlate cell properties with shear. The present study investigated simple alterations to ameliorate these issues. Flows were obtained by numerical simulation. Increasing the volume of fluid in the well-altered dimensional but not dimensionless shear metrics. Adding a central cylinder to the base of the well-forced fluid to flow in a square toroidal channel and reduced multidirectionality. Conversely, suspending a cylinder above the base of the well made the flow highly multidirectional. Increasing viscosity in the latter model increased the magnitude of dimensional but not dimensionless metrics. Finally, tilting the well changed the patterns of different wall shear stressmetrics in different ways. Collectively, these methods allow similar flows over most of the cells cultured and/or allow the separation of different shear metrics. A combination of the methods overcomes the limitations of the baseline model.

BEYOND THE ENDOTHELIUM: THE ROLE OF MURAL CELLS IN VASCULAR BIOLOGY: In vitro systems to study endothelial/pericyte cell interactions.

The vasculature is crucial for tissue development and survival, and the stability of blood vessels to perform these functions relies on the interplay between endothelial cells (ECs) and mural cells. Pericytes are a subtype of mural cells found in the microvasculature that extend their processes to wrap around the endothelial monolayer. Pericytes are recruited during vessel growth through the excretion of soluble factors from ECs where they stabilize angiogenic sprouts and induce maturation of the resident cells. Alterations in these interactions between ECs and pericytes are associated with aberrant vessel growth and disrupted vasculature function characteristic of numerous diseases. Therefore, deeper understanding of the cross-talk between these cell types has numerous implications for understanding morphogenesis and elucidating disease mechanisms. In this review, we highlight recent advances and current trends studying the interactions between ECs and pericytes in vitro. We begin by analyzing three-dimensional hydrogel platforms that mimic the tissue extracellular matrix to investigate signaling pathways and altered vascular function in disease-specific cells. We next examine how microfluidic vasculature-on-a-chip platforms have elucidated the interplay of these vascular cells during angiogenesis and vascular network formation under controlled physiochemical cues and interstitial flow. Additionally, studies have utilized microvessels to measure the effect of shear stress on barrier function through the control of luminal flow and the impact of inflammation on these vascular cell interactions. Finally, we briefly highlight self-assembling human blood vessel organoids, an emerging high-throughput platform to study ECs and pericyte interactions.

A Novel Yield Criterion for Nickel-Based Superalloys

Abstract With the significant evolution of modern gas turbine engines, selection of high-temperature resistant alloys in the hot section is known to be the fundamental solution to enhance the capabilities of these engines. In general, the high-temperature components are mainly comprised of polycrystalline, directionally solidified, and single crystal superalloys. Single crystal (SX) superalloys were developed in the 1980s to achieve high fatigue resistance and substantial creep rupture strength by eliminating grain boundaries. Directional solidification methods enabled the solidification arrangement of the materials to be comprised of columnar grains which are aligned parallel to the 〈001〉 direction. These casting types have been frequently used with nickel-based superalloys (NBSAs) to develop modern gas turbine blades. In this work, the yield behavior of generic SX and directionally solidified (DS) NBSAs is studied. By observing various SX and DS alloys, it was concluded with need for a novel criterion that can present anisotropic and tensile/compressive asymmetric yield surfaces. This novel criterion is comprised of the criterion proposed by Hill for anisotropic materials and the method developed by Drucker and Prager for alloys that have different tensile and compressive yield strengths. Additional terms to Hill's criterion are introduced to capture the coupling effect of normal stress and shear stress when the applied loads are not in the direction of principal axes of the material coordinate system for single crystal alloys. The parameters for the criterion are obtained from simple uniaxial tension and compression experiments. Results are compared with various well-established yield criterions. Additionally, the novel criterion is utilized to capture the effective stress and strain of multi-axial loading of turbine blades under nonisothermal conditions

Effects of shear stress on the properties of colonyforming endothelial cells in comparison with coronary artery endothelial cells

Highlights. It is assumed that pre-colonization by endothelial cells of the inner surface of tissue-engineered vessels of small diameter can serve as an effective way to prevent thrombosis. The question of choosing the optimal source of endothelial cells for use in tissue engineering remains debatable. The paper considers the features of the culture of colony-forming endothelial cells obtained from the peripheral blood of patients with coronary heart disease, in comparison with mature endothelial cells from the coronary artery.Aim. To study the effect of laminar flow on the morphological and functional characteristics of mature endothelial cells and peripheral blood-derived endothelial colony-forming cells.Methods. Coronary artery endothelial cells were purchased from the Cell Applications, Inc. Colony-forming endothelial cells were obtained from the peripheral blood of patients with coronary artery disease who underwent percutaneous coronary intervention. The cells were isolated using a Ficoll gradient and cultured in EGM-2MV culture medium containing 5% fetal bovine serum. The cells of the experimental group were cultured in µ-Luer plates in a perfusion system with a shear stress of 3 dyn/cm2 . The cultivation time was 2 days. The cells of the control group were cultured under static conditions. At the end of the cultivation we performed immunofluorescent staining for CD31, KDR/CD309, CD144, vWF, type IV collagen, F-actin.Results. Colony-forming endothelial cells and coronary artery endothelial cells retained high density and viability both under static and laminar flow conditions. Shear stress stimulated a change in the phenotype of colony-forming endothelial cells towards a mature endothelial cells, in particular, a significant increased the expression of KDR/CD309 and CD31. The action of laminar flow reduced the synthesis of von Willebrand factor, stimulated the synthesis of type IV collagen. Shear stress promoted the development of structural rearrangements in cells in response to transduction, which manifested in a change in F-actin fibrils orientation on the flow direction.Conclusion. Colony-forming endothelial cells showed a characteristic response to the action of shear stress, consisting in a change in morphology, phenotype, and secretory activity of cells, comparable to that of coronary artery endothelial cells.

Effect of Local Fluid Disturbance Induced by Weld Reinforcement Height on the Corrosion of a Low Alloy Steel Weld

Weld corrosion exists widely in the petrochemical industry and attracts great attention. Most research proves that weld corrosion originates from the material factors introduced during the welding process. However, it is noted that local fluid turbulence due to the weld reinforcement height (WRH) plays an important role in the non-uniform corrosion of welds in flowing media. Accordingly, the individual effect of the local flow on the weld corrosion of low alloy steel was analyzed by experiments and simulation in this study. Electrochemical measurements and morphology observation were conducted, combined with flow field analyses. The results showed that local fluid turbulence due to WRH affected the non-uniform corrosion of low alloy steel welds. The upstream surface and the backflow surface had the highest and lowest corrosion rates, respectively. Interestingly, the high flow velocity surface region did not have a high-corrosion rate. This is due to the combined effects of mass transfer, charge transfer, and wall shear stress. The pitting corrosion was also discussed in view of the aspects above.

Growth of Debris Flows by Soil Bed Erosion: Effects of Frictional and Hydrodynamic Shear Stresses

Debris flows are complex solid-fluid mixtures, which travel downslope under the influence of gravity. The destructive potential of a debris flow is governed by its volume and speed, both of which can be significantly enhanced by the erosion of soil bed material along the flow path. Existing friction-induced erosion theories simplify a debris flow as an equivalent fluid that induces frictional shear stress on a soil bed. Erosion occurs when the frictional stress exceeds the soil strength. Research also shows the importance of hydrodynamic stresses on the erosion of soil beds. However, the mechanism of soil bed failure under the influence of frictional and hydrodynamic shear stresses is not clear. In this extended abstract, some experimental flume test results are presented. The tests simulate the erosion of soil beds by dry sand flow and water flow to evaluate the effects of frictional and hydrodynamic shear stresses imposed on a soil bed, respectively. Findings from this research can be used to improve estimates of erosion of debris flows in mountainous regions, which will strengthen hazard assessments.

The effect of shear stress on the expression of apelin in trophoblast using microfluidic system

The apelin/APJ(apelin receptor) system is being considered to play a crucial role in cardiovascular function. It is regulated by hemodynamic shear stress and involved in many physiological and pathological processes. Apelin/APJ ,which is found to be highly expressed in placenta, are implicated in the pathophysiology of preeclampsia. In preeclampsia, the process of spiral artery invasion is attenuated, resulting in underperfusion and the elevation of shear stress in placenta. This study is to evaluate the effect of shear stress on the expression of apelin/APJ system using microfluidic system. In this study, microfluidic channels were designed to mimic the shape of the intervillous space, where the shear depend on flow rate of the microchannels. In experiment about time, HTR-8/SV neo cells were exposed to shear stress (0.5, 1.0 or 5.0 dyne/cm2) for 15min, 30min, 1h, 2h, 3h or 4h. Changes in the level of apelin were investigated using ELISA in response to applied shear stresses in a continuous cycling system through microfluidic channels. Apelin in HTR-8/SV neo cells was confirmed in all culture media. The level of apelin in culture media decreased after exposure to shear stress of 5.0 dyne/cm2 compared to exposure to shear stress of 0.5 or 1.0 dyne/cm2. The level of apelin in culture media decreased as the time for exposure to shear stress increased. Our results demonstrate that increased shear stress downregulated the expression of apelin in placenta suggesting the expression of apelin in placenta through shear stress may be involved in the pathogenesis of preeclampsia.

Application of Shear Stress to Endothelial Cells Using a Parallel Plate Flow Chamber.

Endothelial cell response to shear stress from the flowing blood plays an important role in diseases such as atherosclerosis. It is therefore essential to study how different flow regimes, including both atheroprotective laminar flow and atheropromoting disturbed flow, impact endothelial cell function. Shear stress effects can be studied in vitro using a variety of techniques, each with their own advantages and disadvantages. In this chapter, we describe how to use a parallel plate flow chamber to study the impact of both laminar and disturbed flow on endothelial cell monolayers.

Rheology of a Viscous-Plastic Liquid in a Porous Medium

The hydrodynamics of the capillary flow of a viscous-plastic liquid in cylindrical rectilinear pores is considered, as a result of which the structural velocity distribution over the pore cross section is obtained. Analytical solutions are proposed for the equations of hydraulic diffusion and nonlinear filtration for a non-Newtonian fluid in a cylindrical porous medium. It is noted that when a non-Newtonian fluid flows in a porous medium, the filtration equations take a nonlinear form due to the effective viscosity, shear, and yield stresses taken into account in its structure. The proposed solutions make it possible to evaluate the state of the porous medium and its main parameters (permeability, hydraulic diffusion, and effective viscosity coefficients). The obtained solutions are compared with existing experimental data for non-Newtonian oils.

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.

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.