Cavity Expansion in Cohesive-Frictional Soils with Limited Dilation

The problem of cavity expansion from zero radius has no characteristic length and therefore possesses a similarity solution, in which the cavity pressure remains constant and the continuing deformation is geometrically self-similar. In this case, the incremental velocity approach first used by Hill (1950) to analyze cavity expansion in Tresca materials can be extended to derive a solution for limiting pressure of cavity expansion in other types of material. In this article, a rigorous semi-analytical solution is derived, following Hill's incremental velocity method, for the expansion of cavities from zero initial radius in cohesive-frictional soils with limited dilation. In particular, the radius of the elastic-plastic interface c is used in this article as the time scale and the solution for the limit pressure has been presented. Solutions are evaluated for a number of cases representative of a range of cohesive-frictional and dilatant soils. A comparison is also made between the solutions presented here and previous solutions for cohesive-frictional soils that have unlimited (on-going) plastic dilation. In particular, the influence of limited plastic dilation on the cavity limit pressure is identified and discussed.

Development and Approbation of Methodology Aimed to Define the Reasons for Turbine Unit Capacity Limitation Based on the Specified Mathematical Model of its Condenser

The purpose of this work is to develop and test the methodology of elucidation of the reasons for turbine unit capacity limitations based on a mathematical model of its condenser. This pur-pose is achieved by using a mathematical model of the condenser as part of the developed methodology, taking into account the separate effects of contamination of the heat exchange surfaces, air suction into the vacuum system and the operating mode of the main ejector. Based on operational data sampling, the value of the limiting pressure in the condenser, excess of which leads to limitation of turbine unit capacity, was determined. It was established that the cause of power limitation is the abnormal operation of the main ejector due to inadmissible high temperature in the intermediate cooler of its first stage. For regimes that were not pressure-limited, using a mathematical model, the degree of tubes contamination, its influence on the condenser pressure and the power generated by the turbine unit, and the influence of actual air suctions on the condenser pressure were determined. The most important result of the study is to determine the possibility and feasibility of using the developed and tested methodology for solv-ing similar problems for any type of turbine unit equipped with a condenser. The significance of the work lies in the fact that the proposed approach expands the possibilities of using mathemat-ical models of this class in terms of solving such problems.

Inflation-Induced Twist in Geometrically Incompatible Isotropic Tubes

The fundamental twist motion in tubes is commonly generated by torque. However, twist can also be indirectly induced by mechanical loadings (inflation/extension), growth and remodeling processes, and environmental conditions. This unusual coupling commonly originates from material anisotropy. In this study, we propose a configuration of isotropic bilayer tubes that twists upon inflation. This mechanism is based on twist incompatibility: two tubes are axially twisted in opposing directions and glued to form a bilayer tube. The residual stress that develops gives rise to deformation-induced anisotropy, which enables twist under inflation. To demonstrate the induced-twist response, we employ the neo-Hookean and the Gent models. We derive closed-form expressions for the twist angle as a function of the pressure in neo-Hookean bilayer tubes and show that a terminal angle exists in the limiting pressure. Numerical studies of bilayer Gent tubes are carried out and reveal that the lock-up effect governs the terminal twist angle. Interestingly, we find that in bilayer Gent tubes, the twist direction and handedness can be reversed upon inflation. These counter-intuitive effects, known as inversion and perversion, respectively, stem from the load-dependent variations in the ratio between the torsional stiffness of the two layers. We provide criteria that allow to program the induced twist response of bilayer tubes through the design of the properties of the two layers. This approach may be of value in the design of soft robots, artificial muscles, and soft actuators.

The Application of Polyvinylpyrrolidone as a Modifier of Tribological Properties of Lubricating Greases Based on Linseed Oil

The paper presents the research results on the relations between additive content and tribological, rheological, and oxidizing properties of lubricating greases. The greases were based on linseed oil, thickened with amorphous silica Aerosil® and modified with different concentration of polyvinylpyrrolidone. The greases were tested tribologically according to the test on T-02 testing machine and referred to the unmodified control. The evaluation of tribological properties was based on the following parameters: welding load, scuffing load, limiting load of wear, limiting load of scuffing, and limiting pressure of seizure. The results of tribological research revealed the most promising impact of the 3% addition of polyvinylpyrrolidone. All of the crucial parameters were improved in comparison to the unmodified control grease. The spectral analyses revealed that some of the components undergo oxidation during mechanical forces, leading to the formation of the oxidized organic compounds. These substances generated a layer, counteracting the wear of lubricated tribosystem. The improved resistance to oxidation of the tested lubricants with polyvinylpyrrolidone can be explained by the presence of highly hydrophilic pyrrolidone groups and hydrophobic alkyl group in polyvinylpyrrolidone (PVP) molecule. These compounds combine with hydrocarbon chains of linseed oil and act synergistically with the silicon dioxide molecules. The introduction of polyvinylpyrrolidone caused the improvement in dynamic viscosity at lower shear rates and a significant change of viscosity in low temperatures. An increased value of the yield point of the tested lubricating compositions after introduction of the additive was also observed.

Non-Darcy effects in fracture flows of a yield stress fluid

We study non-inertial flows of single-phase yield stress fluids along uneven/rough-walled channels, e.g. approximating a fracture, with two main objectives. First, we re-examine the usual approaches to providing a (nonlinear) Darcy-type flow law and show that significant errors arise due to self-selection of the flowing region/fouling of the walls. This is a new type of non-Darcy effect not previously explored in depth. Second, we study the details of flow as the limiting pressure gradient is approached, deriving approximate expressions for the limiting pressure gradient valid over a range of different geometries. Our approach is computational, solving the two-dimensional Stokes problem along the fracture, then upscaling. The computations also reveal interesting features of the flow for more complex fracture geometries, providing hints about how to extend Darcy-type approaches effectively.