Normal Stress Research Articles

Comparison of Early Postoperative Stress Distribution around Short and Tapered Wedge Stems in Femurs with Different Femoral Marrow Cavity Geometries Using Finite Element Analysis.

In total hip arthroplasty (THA), the ideal stem length remains uncertain; different stem lengths are used in different cases or institutions. We aimed to compare the stress distributions of cementless tapered wedges and short stems in femurs with different femoral marrow geometries and determine the appropriate fit. Finite element models were created and analyzed using HyperMesh and LS-DYNA R11.1, respectively. The 3-dimensional shape data of the femurs were extracted from computed tomography images using the RETOMO software. Femurs were divided into 3 groups based on the Dorr classification. The computer-aided design data of cementless tapered wedge-type and short stems were used to select the appropriate size. In the finite element analysis, the loading condition of the femur was assumed to be walking. Volumes of interest (VOIs) were placed within the femur model at the internal and external contact points of the stem based on Gruen zones. The average stresses and strain energy density (SED) of the elements included in each VOI were obtained from the preoperative and postoperative models. The von Mises stress and SED distributions of the cementless tapered wedge and short stems were similar in their respective Dorr classifications. In both stems, the von Mises stress and SED after THA were lower than before THA. The von Mises stress and SED of the cementless tapered wedge stem were higher than those of short stems. Cementless tapered wedge-type stems tended to have lower rates of change than short stems; however, Dorr C exhibited the opposite trend. In the Dorr classification comparison, the von Mises stress and SED were greater for both stems in the order of Dorr C > Dorr B > Dorr A, from Zone 2 to Zone 6. In Dorr A and B, the short stem exhibited a natural stress distribution closer to the preoperative femur than the tapered wedge stem; however, in Dorr C, the short stem may have a greater effect on stress distribution, suggesting that it may cause greater effects, such as fracture in the early postoperative period, than other Dorr types.

Pore-based prediction of crack initiation life in very-high-cycle fatigue

The porosity of the material produced by additive manufacturing technology gives rise to a notable dispersion of the crack initiation life in the very-high-cycle fatigue regime. The crack initiation life in the very high cycle fatigue regime can be divided into the initial crack initiation life and early microcrack growth life. This paper proposed a model considering the effect of pore morphology and location to predict the initial crack initiation life. The average local stress in a grain near the pore is modified by considering the relationship between pore roundness, inclination, position, and stress concentration factor. The growth life of early microcrack is determined by integrating empirical formulas based on dislocation theory. Subsequently, the probability distribution of crack initiation life is obtained, which is in good agreement with the experimental results. The competition factor is proposed to quantitatively evaluate the tendency of crack initiation from the surface or the interior, taking into account the influence of local average stress and grain size. The predicted load corresponding to the shift in crack initiation position is in accordance with the experimental results.

Acceleration effect on stress singularity and edge strength in piezoelectric/Piezomagnetic heterostructures

The acceleration effect on edge stress singularity and edge strength in piezoelectric/piezomagnetic heterostructures is investigated in this work. For the stress singularity analysis, we propose a stress function based iterative approach based on the Lekhnitskii stress functions with body forces and harmonic assumption of initial stress fields. The acceleration effect is introduced by adding body force terms to the equilibrium equations. The governing equations are obtained by applying variational principle in each process and solved by general eigenvalue problems to obtain homogeneous solutions, as well as to obtain particular solutions based on the forms of load and acceleration conditions. During the iterations, the stress oscillations can be gradually eliminated and the stress concentration can be predicted exactly located at the interfaces. Finally, an example of symmetrically layered heterostructure is presented under both in-plane acceleration and out-of-plane acceleration. It is found that both accelerations have significant effect on the edge normal and shear stresses which may further cause failure. The edge strength is also evaluated by calculating the edge average stress. This work may help to understand the acceleration effect on edge stresses and edge strength for heterostructures, as well as the trend of stress magnitude change caused by external accelerations.

2D mechanical representation of superconducting magnets: A comparative study of plane stress and plane strain

When approaching the mechanical design of a superconducting magnet, whenever possible the starting model is a 2D approximation. If rotational symmetry (solenoid-like winding) is present, the 2D representation is unique and contains no approximations. If, on the other hand, a non-axisymmetric system is opted for, the 2D representation is not unique and there are main options available, as plane stress, plane stress with thickness, plane strain and generalized plane strain. Considering z as the direction normal to the 2D plane, the plane stress option defines a stress state in which no normal or shear stresses perpendicular to the xy plane can occur (σz=σxz=σyz=0). In this option, deformation can occur in the thickness direction of the element, which will become thinner when stretched and thicker when compressed; it is generally used for objects with limited depth (thin objects).In contrast, plane strain refers to the fact that deformation can only occur in plane, which means that no out-of-plane deformation will occur (ϵz=ϵxz=ϵyz=0). The plane strain option is generally appropriate for structures of nearly infinite length, relative to their cross section, that exhibit negligible length changes under load. The “generalized plane strain” option imposes the axial strain equal to a constant value; this condition does not reproduce the real operating condition of the magnet and is therefore excluded. The “plane stress with thickness” uses the same equations as the plane stress option but, output quantities are given per unit length defined with thickness; therefore, it is again excluded from the comparison. Superconducting magnets, such as dipoles, do not fit neatly into any of the above options: they are far from thin but deform longitudinally under load. This work reports a comparative study of plane stress and plane strain in the specific case study of a dipole magnet.

The tipping point: Financial and emotional costs of care for Medicare patients with cancer.

260 Background: As cancer-related health care expenses are increasing, a greater proportion of treatment costs are shifting directly to the patient, resulting in an increased financial burden for many patients. In addition to growing healthcare costs, the inflationary environment in the US has also increased the costs of daily living expenses. Although the Inflation Reduction Act (IRA) encompasses measures for negotiating prices of specific high-cost medications within Medicare Parts B and D, given the expenses associated with cancer treatment IRA negotiation provisions will likely have limited impact on patients’ financial burden. We sought to capture the financial and emotional experiences of Medicare cancer patients about their costs of care prior to the implementation of the IRA. Methods: This cross-sectional analysis used data from a nationwide survey distributed in February 2024 by Patient Advocate Foundation (PAF). Inclusion criteria included a valid email address, age >19, self-reported cancer diagnosis and Medicare coverage. Frequencies were calculated for categorical variables. Additional information about financial challenges will be collected on a subset of cancer survey respondents in May 2024. Results: A total of 331 survey respondents with cancer completed the survey. Most respondents were female (61%), age≥56 (86%), white (73%), retired (59%), married (47%), household income <$48,000 (69%), and rural location (24%). The most common cancer types were multiple myeloma (47%) and breast (26%); 25% were diagnosed < 2 years prior, 87% were receiving cancer treatment and 52% experienced financial challenges prior to diagnosis. Almost half (45%) reported a negative change in their financial situation in the past 12 months; caused by increased living (63%), food (60%), medical care (47%) and medication (39%) costs. Overwhelming/above average financial stress (40%) was reported on the day of the survey; 30% reported spending at least 25% of their monthly income on medical costs; 69% reported financial burden due to their illness. Fifty-nine percent reported that finances impacted their emotional wellbeing. Common coping strategies to alleviate financial distress included positive attitudes, family/friend support and spiritual beliefs. Conclusions: To mitigate the impact of inflation on low-income cancer patients, it is essential for policymakers, healthcare providers, and community organizations to work together to ensure access to affordable healthcare, support services, and financial assistance programs. Additionally, raising awareness about the challenges faced by this vulnerable population and advocating for policies that address their needs can help alleviate some of the burdens imposed by inflation. While the IRA is a step in the right direction, its financial impact on patients appears limited.

Estimation of aerodynamic entrainment in developing wind-blown sand flow.

Understanding aerodynamic entrainment, a critical process in wind-blown sand dynamics, remains challenging due to the difficulty of isolating it from other mechanisms, such as impact entrainment. Aerodynamic entrainment initiates the movement of surface particles, influencing large-scale processes like sediment transport and dune formation. Previous studies focused on average aerodynamic shear stress to estimate entrainment, but the role of impulse events, which cause significant shear stress fluctuations, remains under-explored. We used 12 hot-film shear sensors to measure the spatiotemporal distribution of aerodynamic shear stress during wind-blown sand flow development. We identified impulse events exceeding the entrainment threshold and analyzed their intensity, classifying particle movement as rocking, rolling, or saltation. Results indicate that after a 2-m fetch, sediment mass flux stabilizes, with aerodynamic shear stress decreasing to 78% of the entrainment threshold. We identified key trends, including the stabilization of rocking events beyond x = 4.5 m and a significant decrease in saltation frequency, indicating fully developed wind-blown sand flow. Impulse characteristics stabilize at a greater distance (4.5 m) than sediment transport (2 m) because turbulent airflow evolves more slowly. Our findings show that impulse events significantly influence aerodynamic entrainment. These insights enhance understanding of sediment transport dynamics and improve modeling of sand dune movement.

Variation of Secant Young’s Modulus in an Unsaturated Gap-Graded Granular Fill

It is of great significance to understand the variation of stiffness in unsaturated granular materials for predicting performance of earth structures. Variation of secant Young’s modulus in an unsaturated gap-graded granular fill was investigated using unsaturated triaxial tests with local strain measurements in this work. Unlike the insignificant suction impact on shear strength in coarse-grained granular material, it seems that suction has greater effect on stiffness of the tested soil at small strain. Young’s modulus enhances as suction and net confining pressure rise since average skeleton stress increases and soil skeleton gets more stable by meniscus water. In addition, specimen at larger suction possesses greater degradation speed than that at lower ones. One equation was adopted to estimate Young’s modulus of soil. It shows that this equation may capture the variations of secant Young’s modulus of soil under different suctions and net confining pressures.

Theory and Experiment on Rock-Cutter Interfacial Friction and Rock Mohr-Coulomb Parameter Estimations

Summary The Mohr-Coulomb (M-C) failure criteria is by far the most widely used model for granular materials (including rocks and soils) in many geotechnical industries due to its simplicity. Its parameters are conventionally obtained by performing a series of pressurized triaxial compression tests (TCTs). The peak stress from each confining pressure is plotted at a single point as the maximum vs. the minimum principal stresses. The M-C parameters are obtained by the best linear fitting through the failure envelope formed by the peak stress points of interest. The TCT is time-consuming, costly, and destructive. Is there an experiment that can provide the failure envelope with one single test, even at the atmospheric pressure? This seems impossible, at least has never been rigorously reported. In this work, we present our finding of such a test. The paper first provides the experimental setup and the theoretical solution for a hemispherical scratch test of a polycrystalline diamond cutter (PDC) at low rate of cut (ROC) and low depth of cut (DOC); the theoretical characteristic response of the test is identified and validated. Next, the formula for the rock-cutter interfacial coefficient of friction (COF) is derived, which provides a theoretical guide for the friction measurement for shaped cutters. Then, the nominal average drag and thrust stresses are evaluated, which are observed experimentally and then proved theoretically to behave in a linear relation, analogous to the M-C envelope from the TCTs. We also provide a first method that can self-consistently evaluate the M-C parameters for the crushed zone, which plays a very important role in rock cutting. By comparing the M-C results for three rocks at different loading conditions, good agreements under different scratch conditions are made against the M-C parameters for several rocks from the TCTs.

Heterogeneous mineralogical composition and fault behaviour: A systematic study in ternary fault rock compositions

The heterogeneous mineralogical compositions of fault gouges, formed during fault evolution, influence frictional properties and slip behaviour. While the influence of individual mineral phases on friction has been extensively studied, the impact of varying systematically mineral phases in gouge mixtures on macroscopic frictional behaviour remains unclear. Thus, we performed 34 frictional experiments on fault gouges composed of three representative mineral phases: muscovite (platy phyllosilicate), quartz (granular silicate) and calcite (granular carbonate), known for their markedly distinct frictional properties. Using a biaxial rock deformation apparatus (BRAVA), we performed tests on fault gouges with grain sizes <125 μm under normal stresses of 50–100 MPa, at room temperature and water-saturated conditions. Our data indicate that the mineralogical composition of fault gouges significantly affects frictional strength, healing, and stability with a non-trivial pattern. Increasing the muscovite content leads to a decrease in frictional strength, from 0.62 for pure calcite and 0.56 for pure quartz to 0.33 of pure muscovite, along with reduced frictional healing and a velocity-strengthening behaviour. This weakening is promoted by a transition from localized deformation along discrete shear planes in granular-rich fault gouges to distributed deformation within the entire gouge layer with increasing muscovite content. At fixed muscovite content, frictional properties depend on the dominant granular phase. Calcite-dominated mixtures exhibit more marked frictional weakening rather than quartz-dominated ones, suggesting a non-linear mixing law between friction coefficient and muscovite content. This different trend is likely due to favourable conditions for fluid-assisted pressure-solution of calcite and foliation development, unlike quartz. When only the granular phases are mixed, we observe complex behaviour with the indentation of quartz into calcite, resulting in higher values of healing rates than those of pure end-member mixtures.Our findings provide robust insights into microphysical processes strongly dependent on the complex mineralogical compositions usually observed along natural faults.

Research on the distribution structure of 2D piston electro-hydraulic pump based on fluid-structure interaction

To address the drawbacks of traditional hydraulic power units, we embedded a 2D piston pump inside the motor rotor, proposing a 2D piston electro-hydraulic pump. The space cam mechanism serves as the primary force-bearing structure during its operation. Excessive wear occurs at the highest point of the space cam when subjected to significant axial forces, which leads to deviations between the motion law of the 2D piston and the theoretical design. Aiming this problem, we conduct research from two perspectives: theoretical analysis and fluid-structure interaction. Firstly, the operational principle of the electro-hydraulic pump is introduced. Then, the contact normal stress of the space cam mechanism is studied, and backflow and chamber pressure overshooting are discussed. Finally, the fluid-structure interaction model of the electro-hydraulic pump is established. Based on the fluid-structure interaction model, the effects of the width and depth angles of the triangular damping groove on the backflow and chamber pressure overshooting are analyzed. The simulation results demonstrate that adding triangular damping grooves can improve the flow field characteristics. With the increase in the width and depth angles, the peak flow of the backflow and chamber pressure overshooting increase, with the depth angle exerting a more pronounced effect.

Rayleigh–Taylor instability in a Casson fluid layer with heat and mass transfer

This study investigates the stability of the interface between two fluids, a Casson fluid on top and a viscous fluid below, with heat and mass transfer occurring between them. We used the potential flow theory, which simplifies the problem by ignoring tangential stresses and focusing on normal stress balance. We did not consider no-slip conditions at the boundaries, assuming zero normal velocity at these rigid boundaries instead. A second-order polynomial equation was developed to calculate the growth rate of instabilities and solved numerically using the Newton–Raphson method. The results showed that heat and mass transfer improved the stability of the interface, even though the Atwood number, a measure of instability, remained high.

Frictional Strength and Frictional Instability of Glaucophane Gouges at Blueschist Temperatures Support Diverse Modes of Fault Slip From Slow Slip Events to Moderate‐Sized Earthquakes

AbstractFluid overpressure from the water released by subducted sediments and oceanic crust is an important mechanism for generating earthquakes via brittle failure and frictional instability. If unstable, such fault materials may also host diverse fault reactivation mechanisms from slow slip events to moderate‐sized earthquakes in cold subduction zones. We examine this hypothesis for glaucophane gouge ‐ a key index minerals for blueschist facies ‐ at lower confining stresses where behavior is poorly understood. We measure friction and stability at temperatures of 100°C–500°C and effective normal stresses of 50–200 MPa, to explore the controls of temperature, stresses and excess pore fluid pressures on fault friction. The frictional coefficient of glaucophane at representative temperatures and stresses is ∼0.70, insensitive to temperature but with a slight increase at lower effective stresses. Elevating temperature promotes a transition from velocity‐strengthening to weak velocity‐weakening behavior, indicating the destabilizing effect of high temperature downdip in subduction zones. Reducing effective normal stress or concomitantly elevating pore fluid pressure further strengthens the velocity‐weakening response and would be manifest as moderate‐sized earthquakes. Our results support the potential for enhanced unstable sliding of glaucophane gouges at lower effective stresses and blueschist facies temperatures ‐ with weak to moderate velocity‐weakening responses upon fluid pressurization vital for understanding the abundance of slow slip to moderate‐sized earthquakes apparent in cold subduction zones.

On the influence of heat-induced evaporation over interfacial atomization driven by surface acoustic waves

In this work, the influence of evaporative flux over the atomization driven by surface acoustic waves (SAWs) of a Newtonian water drop is studied. The drop is placed on a heated substrate at constant temperature, higher than the saturation temperature at a given vapor pressure. In this manner, an interfacial temperature distribution arises along the drop free surface in terms evaporative mass flux and vapor recoil, which repercussion over aerosol size is studied by determining the asymptotic evolution equation governing the acoustically driven free surface. At such scenario, the connection between surface tension and temperature is also considered; thus, thermocapillary flow is incorporated into our drop model, described in terms of fundamental parameters, like the evaporation number, Marangoni number, and acoustic capillary number. Numerical solution of the evolution equation led us to obtain a simplified representation of the drop interfacial deformation mechanism, capable of predicting atomization and portraying the influence of evaporation over atomization. Subsequent analysis shows that the incorporation of evaporation at SAW atomization traduces in normal stresses counteracting the acoustic and thermocapillary effect, leading to the development of smaller drop aspect ratios with respect to the no-evaporative case. Being aware that the aerosol size is deeply related to the aspect ratio, we propose an analytical expression to estimate aerosol diameter under evaporative conditions. The results show that aspect ratio reduction leads to a decrement on aerosol size, up to two orders of magnitude, with respect to the no-evaporative case. Our study is a first approach providing insight about the importance of evaporation on aerosol regulation at SAW atomization.

Fault‐Valve Instability: A Mechanism for Slow Slip Events

AbstractGeophysical and geological studies provide evidence for cyclic changes in fault‐zone pore fluid pressure that synchronize with or at least modulate slip events. A hypothesized explanation is fault valving arising from temporal changes in fault zone permeability. In our study, we investigate how the coupled dynamics of rate and state friction, along‐fault fluid flow, and permeability evolution can produce slow slip events. Permeability decreases with time, and increases with slip. Linear stability analysis shows that steady slip with constant fluid flow along the fault zone is unstable to perturbations, even for velocity‐strengthening friction with no state evolution, if the background flow is sufficiently high. We refer to this instability as the “fault valve instability.” The propagation speed of the fluid pressure and slip pulse, which scales with permeability enhancement, can be much higher than expected from linear pressure diffusion. Two‐dimensional simulations with spatially uniform properties show that the fault valve instability develops into slow slip events, in the form of aseismic slip pulses that propagate in the direction of fluid flow. We also perform earthquake sequence simulations on a megathrust fault, taking into account depth‐dependent frictional and hydrological properties. The simulations produce quasi‐periodic slow slip events from the fault valve instability below the seismogenic zone, in both velocity‐weakening and velocity‐strengthening regions, for a wide range of effective normal stresses. A separation of slow slip events from the seismogenic zone, which is observed in some subduction zones, is reproduced when assuming a fluid sink around the mantle wedge corner.

Energy harvesting by car-tire using piezoelectric polymer films blended with carbon-nanotubes

Energy harvesting through harnessing mobile cars is possible by combining mechanicals systems with advanced materials. Piezoelectric polymer blends with excellent mechanical properties facilitate energy harvesting using the car-tire as a source. Furthermore, by adding simplicity of preparation to the blends with multi-walled carbon nanotubes (MWCNT), an increase of energy conversion can lead to improved existing polyvinylidene fluoride/polymethylmethacrylate (PVDF/PMMA), films. This work focuses on investigating the best concentration of MWCNT to achieve car-tire energy harvesting as a sustainable and renewable energy option. The results show that 0.05 wt% of MWCNT is the best concentration among several values. A test set-up applying normal stress, simulating car-tire deformation indicated enhanced voltage generation. Compared to the energy consumption of combustion cars, the enriched films generate up to 4.3kWh. This energy is harvested over a car trip of 100 km. A higher nanotube concentration caused saturation of the blend film and poor output. The novel enriched polymer must be tested for resisting cyclic loads to encourage sustainable energy harvesting using car tires.

Characteristics of Effective Fractures in Deep Buried-Hill Basement Gas Reservoirs and Its Effects on Fluids: The Jianbei Slope, Qaidam Basin, China

Summary Buried hills are basement uplifts beneath sediment layers that possess significant exploration potential. Using the Jianbei Slope of the Qaidam Basin in China as a case study, we systematically investigated the types and origins of fractures in deep buried-hill gas reservoirs. In our study, we synthesized various data, including experimental results, production dynamics, and both conventional and special logging with the aim of clarifying the sequence and effectiveness of fracture formation in these gas reservoirs; analyzing the impact of effective fractures on fluid migration, accumulation, and preservation; and proposing a development plan to enhance stable production. Research reveals that since the Late Paleozoic, the region has been influenced by multiple phases of tectonic stress, deep fluid dissolution, and surface weathering leaching. This has resulted in a fracture system dominated by east-west trending deep major faults, with accompanying tectonic fractures, alongside dissolution, diagenetic, and weathering-collapse fractures. Smaller fractures oriented at an angle to the maximum principal stress and fractures with normal stress lower than the compressive strength are conducive to maintaining fracture effectiveness. Fracture widths range from 0.1 μm to 343.36 μm, with effective fractures comprising 63.49% of the total. Based on aperture and permeability, effective fractures are categorized into three levels: Level I fractures (&amp;gt;100 μm) serve as primary migration pathways; Level II fractures (10–100 μm) are well configured with dissolution pores, forming a foundation for favorable reservoir development; and Level III fractures (micron scale) enhance reservoir storage capacity by connecting fractures. The gas-water interface in the reservoir rises rapidly and unevenly. In the I + II + III fracture combination model, fluid exhibits high-conductivity channeling, leading to rapid declines in formation pressure, quick water breakthroughs in single wells, and severe water sealing. Conversely, in the II + III fracture combination model, fluid invasion is characterized by weak-to-strong finger-like intrusion, leading to prolonged stable production. Vertically, the 20-m to 60-m interval above the bedrock weathering crust has a favorable pore-fracture configuration, making it a high-quality reservoir zone in buried hills. In addition, local thick layers of Level II microfractures within the bedrock represent potential exploration targets. Considering the differential distribution of reservoir fractures, the optimal development plan is expected to achieve a recovery rate of 28.35% by 2030.

Sparse regression for discovery of constitutive models from oscillatory shear measurements

We propose sparse regression as an alternative to neural networks for the discovery of parsimonious constitutive models (CMs) from oscillatory shear experiments. Symmetry and frame invariance are strictly imposed by using tensor basis functions to isolate and describe unknown nonlinear terms in the CMs. We generate synthetic experimental data using the Giesekus and Phan-Thien Tanner CMs and consider two different scenarios. In the complete information scenario, we assume that the shear stress, along with the first and second normal stress differences, is measured. This leads to a sparse linear regression problem that can be solved efficiently using l1 regularization. In the partial information scenario, we assume that only shear stress data are available. This leads to a more challenging sparse nonlinear regression problem, for which we propose a greedy two-stage algorithm. In both scenarios, the proposed methods fit and interpolate the training data remarkably well. Predictions of the inferred CMs extrapolate satisfactorily beyond the range of training data for oscillatory shear. They also extrapolate reasonably well to flow conditions like startup of steady and uniaxial extension that are not used in the identification of CMs. We discuss ramifications for experimental design, potential algorithmic improvements, and implications of the non-uniqueness of CMs inferred from partial information.

Discretization of Thin-Walled Sections with Variable Wall Thickness

At the stage of designing thin-walled aircraft structures, to simplify calculations, their cross sections are idealized. To do this, the section with the skin and the longitudinal elements reinforcing it is replaced (when determining normal stresses) by a discrete one, consisting of concentrated areas at characteristic points. In this case, the equality of the moments of inertia of the initial and discrete sections is preserved. Such idealization is used in the calculation of thin-walled rods for normal and shear stresses (Wagner model). For sections consisting of a system of rectangular strips of constant thickness, discretization allows to set approximate values of normal and shear stresses and accurately find the locations of the singular points of the bending center (in an open contour) and the center of rigidity (in a closed one). The discrete model of a strip consists of three lumped areas: two at the edges and one in the center. The paper proposes to extend the discrete model to sections in which the skin thickness changes according to a linear law. In addition to the rectangular strip, it is possible to use elongated triangles and trapezoids, replaced by three and four concentrated areas, respectively. The possibility of using a discrete model for calculating some thin-walled sections of open and closed contours is considered. The section of an open contour is studied - the problem of transverse bending without torsion of a channel having flanges with a linearly variable thickness. Differences in the flows of tangential forces calculated from the exact and discrete models are shown. The coincidence of the results in determining the position of the bending center according to two models was established. When studying the application of a discrete model to a closed contour, its simplified option is proposed. The problem of transverse bending without torsion and finding the center of rigidity in a section with a contour line in the form of a trapezoid with front and rear walls of constant thickness and upper and lower skins and a similar section with a contour in the form of a rectangle was considered. Differences in the flows of tangential forces calculated by exact and discrete models are established. For a closed section in the form of a rectangle, the decrease in the moment of inertia for torsion due to the redistribution of material in the cross section was studied separately. It has been established that when finding the position of the center of rigidity, the discrepancy between the results of the exact and discrete models in sections with geometric parameters close to real ones was less than 1% for a rectangular contour, and 4% for a trapezoidal contour. The results indicate the possibility of extending the application of the discrete model of thin-walled cross section to the design calculations of thin-walled rods with variable skin thickness, representing practical structures.

Mechanical mechanism of dip effect on bearing capacity of the pillar strength

Abstract The dip effect on pillar strength in underground ore-body mining is well established, but the variation in stress path (magnitude and direction of stress) due to changing inclination angles requires further study. Using elasticity theory, the Euclidean mean stress tensor characterizes the stress state in pillar zones. Numerical simulations provided the second-order tensor of peak stress for each pillar unit. Through tensor statistical analysis, the Euclidean mean stress tensor matrix was calculated, and its eigenvalues and eigenvectors, representing the magnitude and direction of the principal stress, were derived. This analysis explained the intrinsic dip effect on pillar strength through principal stress characteristics. Finally, the pillar strength envelope function for varying width-height ratios at any dip angle was obtained using the random gradient descent algorithm. Results indicate that in the peak stress state, the average principal stress directions of the pillar change with orebody dip angle, affecting the stress path. The average principal stress increases with pillar size due to increased constraints. These findings offer theoretical insights for pillar design and stability analysis.

Biomechanics cerebral and carotid arteries: aneurysm development and atherosclerotic plaque detachment in the presence of combined pathologies

Today, the main cause of mortality in the world remains cardiovascular diseases. In this case, the combined pathology of the neck and head arteries, in which atherosclerosis affects the carotid arteries and there is a change in blood flow in the vertebral arteries or in the circle of Willis due to aplasia of the communicating artery, significantly increases the risk of aneurysms formation and their subsequent rupture. Assessing the risk of complications in this type of pathological condition may allow the physician to initiate timely preventive measures in specific clinical cases. The paper presents the results of modelling various variants of combined pathologies in the arteries of the neck and head. The segment under consideration includes sections of the common carotid, external and internal carotid arteries, as well as vessels of the circle of Willis and the basilar artery. The main idea of the study was to create a prognostic model to assess the risks of aneurysm formation in the circle of Willis and atherosclerotic plaque rupture in the carotid arteries. Such a system may be useful for physicians in routine practice when planning treatment tactics in patients with combined pathologies of the arterial channel. Based on the literature analysis, a number of pathologies of the cerebral and carotid arteries, most frequently occurring in various combinations, were identified: stenoses of the ICA (30 % and 70 %) and aplasia (absence) of one of the connecting arteries were considered from the point of view of geometrical features. In addition, the character of blood flow in the basilar artery, which can change its direction in steal-syndrome, was taken into account. Based on the analysis of blood flow and wall shear stress, two degrees of risk of aneurysm formation were distinguished. High risk corresponds to cases for which both of these values were statistically significantly different from the norm. Medium risk corresponds to cases for which only one of the values was statistically significantly different from the norm. For models containing atherosclerotic plaques, data on shear and normal stresses on the surfaces of atherosclerotic plaques were tabulated. The risk of plaque rupture on each side was determined for each case by analysing the result sets 11 combinations of pathological conditions with increased risk were indicated.